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Scalable polymerization additive manufacturing: principle and optimization

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Scalable polymerization additive manufacturing: principle and optimization

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SCALABLE POLYMERIZATION ADDITIVE MANUFACTURING:
PRINCIPLE AND OPTIMIZATION

by

Huachao Mao

A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Fulfillment of the
Requirements for the Degree
DOCTOR OF PHILOSOPHY
(INDUSTRIAL AND SYSTEMS ENGINEERING)

August 2019

Copyright 2019 Huachao Mao

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Acknowledgements
I would like to extend heartfelt gratitude and appreciation to those who helped me
during my Ph.D. study. Without their help, it would be impossible for me to complete my
doctoral research.
First, I am deeply indebted to my advisor Professor Yong Chen, who introduced the
3D printing research area to me and guided me to contribute to this wonderful research
field. During the past five years, Professor Chen has spent hundreds of meetings with me.
In each meeting, we would generate a lot of ideas, schematic drawings, and plans. These
drawings witnesses Professor Chen’s mentoring on me and my research. Without Professor
Chen’s effort, guidance, and care, I cannot imagine my research, and this dissertation could
be done.
I am extremely grateful for my collaborators and committee members. Substantial
help from them paves the way for me to complete my research. Professor Wei Wu,
Professor Charlie Wang, and Professor Mitul Luhar give their generous help to my work,
from the precepting the ideas, to implementation, and the writing. Many thanks to Professor
Satyandra K. Gupta, who help me with the lab space, improvement, and promotion of my
work. I owe special thanks to Professor Stephen Lu for his willingness to be my committee
member. I am really grateful to all my committee members, for all the constructive
suggestions, comments, and encouragement they offered.
Also, I truly like to thank my colleagues and friends in lab, Jie Jin, Yuanrui Li, Yuen-
Shan Leung, Tsz-Ho Kwok, Wenxuan Jia, Xiangjia Li, Yang Xu, Yang Yang, Han Xu, Kai
iv
Xu, Dongping Deng, Xuan Song, Chi Zhou, Yayue Pan, and Pu Huang. Because of them,
I did not feel the five year’s hard work.
Lastly, I would like to say thanks to my family, who unconditionally support me even
though they are not sure what I am doing, except pursuing a Ph.D. degree in 3D printing.
Without my parents’ thirty year’s effort, I will not be here to write this dissertation. I hope
that they would be proud of me and this dissertation, even when they do not know the
English words in it. Most importantly, I would like to thank my wife Meng, who is always
willing to listen to me to explain my research and encourage me to follow an academic
career. Special thanks to my son, little Leo, who inspires me every day.

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Table of Contents
Acknowledgements ............................................................................................................ iii
Table of Contents ................................................................................................................ v
List of Tables ..................................................................................................................... xi
List of Figures .................................................................................................................. xiii
Abstract ............................................................................................................................ xix
Chapter 1 Introduction .................................................................................................... 1
1.1 Research Motivations..................................................................................... 1
1.2 Statement of Problems and Hypotheses ......................................................... 5
1.3 The Dissertation Outline .............................................................................. 10

Chapter 2 Literature Review......................................................................................... 13
2.1 Biological and Engineered Multiscale Structures ........................................ 13
2.1.1 Biological Multiscale Structures .................................................................. 13
2.1.2 Engineered Multiscale structures and Applications ..................................... 15
2.2 Additive Manufacturing and Stereolithography .......................................... 16
2.2.1 Additive Manufacturing ............................................................................... 16
2.2.2 Stereolithography: Photopolymerized Additive Manufacturing .................. 20
2.3 Scalability in Sterolithography .................................................................... 25
vi
2.3.1 Scalability Problems in Stereolithography................................................... 25
2.3.2 Methods to Address the Scalability in Sterolithography ............................. 29
2.4 Scalability Challenges and Methods in Other Manufacturing Processes .... 35

Chapter 3 Polymerization Energy Control for the In-Layer Scalability ....................... 37
3.1 Shaped Laser Beams: Down-Scale Energy.................................................. 39
3.1.1 The principle of Shaped Laser Beams ......................................................... 40
3.1.2 Hardware Prototype of Shaped Laser Beams .............................................. 44
3.1.3 Multiscale Tool Path in XY Plane ............................................................... 46
3.1.4 Benefits of Shaped Laser Beam ................................................................... 49
3.1.5 Concluding Remarks .................................................................................... 52
3.2 Hopping Light Source: Up-Scale Energy .................................................... 53
3.2.1 The Principle of Hopping Light ................................................................... 53
3.2.2 Automatic Calibration via Computer Vision (ACCV) ................................ 59
3.2.3 Tilted Focus Analysis .................................................................................. 71
3.2.4 Benefits of Hopping Light ........................................................................... 75
3.2.5 Experimental results..................................................................................... 80
3.2.6 Concluding Remarks .................................................................................... 88
3.3 Hybrid Light Source: Integrated-Scale Energy............................................ 89
vii
3.3.1 The Principle of Hybrid Light Source ......................................................... 90
3.3.2 Hardware Prototype of Hybrid Light Source ............................................... 91
3.3.3 Calibration of Hybrid Light Source ............................................................. 93
3.3.4 Related Work ............................................................................................... 98
3.3.5 Benefits of Hybrid Light Source ................................................................ 102
3.3.6 Concluding Remarks .................................................................................. 107

Chapter 4 Layer Planning for the Inter-Layer Scalability .......................................... 109
4.1 Dual Layer Thickness ................................................................................ 110
4.1.1 Dual Layer Thickness Process ................................................................... 111
4.1.2 Dual Layer Thickness Slicing Algorithm .................................................. 113
4.1.3 Process Characterization ............................................................................ 116
4.1.4 Experimental Results and Discussions ...................................................... 121
4.1.5 Concluding Remarks .................................................................................. 125
4.2 Adaptive Layer Thickness ......................................................................... 126
4.2.1 Motivation .................................................................................................. 127
4.2.2 Adaptive Slicing Based on Metric Profiles ................................................ 130
4.2.3 Adaptive Slicing of Weighted CAD Model ............................................... 145
4.2.4 Result ......................................................................................................... 148
viii
4.2.5 Extension: Different Metric and Optimal Orientations ............................. 155
4.2.6 Concluding Remarks .................................................................................. 158
4.3 Transferring Layers for High-Resolution Channel .................................... 160
4.3.1 Printing Channels with Double Platforms ................................................. 162
4.3.2 Mask Image Planning Algorithm ............................................................... 163
4.3.3 Separation Force ........................................................................................ 164
4.3.4 Bounding between two exposures ............................................................. 165
4.3.5 Fabrication Result ...................................................................................... 166
4.3.6 Concluding Remarks .................................................................................. 170

Chapter 5 Application: Mimicking the Shark Skin .................................................... 171
5.1 Reduced Drag Force in Multiscale-Structured Shark Skin ........................ 172
5.2 Fabricating Shark Skin by Combining In- and Inter-Layer Methods ........ 177
5.3 Results and Discussions ............................................................................. 181
5.4 Concluding Remarks .................................................................................. 185

Chapter 6 Conclusion and Recommendation for Future Research ............................. 187
6.1 Answering the Research Questions/Testing Hypotheses ........................... 187
6.2 Engineering Achievements and Scientific Contributions .......................... 191
6.2.1 Engineering Achievements ........................................................................ 191
ix
6.2.2 Scientific Contributions ............................................................................. 194
6.3 Limitation and Future Research Recommendations .................................. 196
Bibliography ................................................................................................................... 199

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List of Tables
Table 2-1: Comparison of laser and projector. .................................................................. 24
Table 2-2: Different methods for projection-based SAM ................................................. 31
Table 3-1: Individual calibration of each actuator ............................................................ 64
Table 3-2: Parameters of the hoppling light prototype system ......................................... 79
Table 3-3: Comparison between different SL processes ................................................... 80
Table 3-4: Printing small features ..................................................................................... 81
Table 3-5: Fabrication results of the ring model ............................................................. 103
Table 4-1: Fabrication time of different models ............................................................. 120
Table 4-2: Comparison between different SL processes ................................................. 124
Table 4-3: Slicing Efficiency Comparison ...................................................................... 149
Table 4-4: Slicing performance comparison with other slicing algorithms .................... 150
Table 6-1: Six tested hypotheses ..................................................................................... 188
Table 6-2: Scalability Improvement by SAMs ............................................................... 191

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List of Figures
Figure 1-1: Multiscale structures exist in nature and human-made objects. ....................... 1
Figure 1-2: Functionality of structures at different scales .................................................. 2
Figure 1-3: Research Problem: Enlarging the Scalability Δ. .............................................. 6
Figure 1-4: Hypotheses to expand the scalability within a layer. ....................................... 8
Figure 1-5: Research scope: expanding the scalability Δ. ................................................ 12
Figure 2-1: Biological and engineered multiscale structures. ........................................... 15
Figure 2-2: Typical AM processes. ................................................................................... 17
Figure 2-3: Schematic drawing of the SLA process from Hull’s groundbreaking patent 21
Figure 2-4: Photopolymerization mechanism ................................................................... 22
Figure 2-5: Two types of light sources are used to trigger polymerization ...................... 24
Figure 2-6: Trade-off between fabrication efficiency v.s. Feature resolution. .................. 26
Figure 2-7: The trade-off of part size v.s. Feature resolution. .......................................... 28
Figure 2-8: Trade-off among fabrication size, resolution, and efficiency ........................ 29
Figure 3-1: Three representative scalable light sources .................................................... 38
Figure 3-2: The principle of scale down SAM ................................................................. 39
Figure 3-3: Shaped beam optics. ....................................................................................... 40
Figure 3-4: Multiple apertures for different micropatterns ............................................... 41
Figure 3-5: Laser beam after a pinhole aperture ............................................................... 43
Figure 3-6: CAD model of the scale down SAM system. ................................................ 45
Figure 3-7: Another implementation of shaped laser beams. ........................................... 46
xiv
Figure 3-8: Exemplar Multi-scale tool paths for scale down SAM. ................................. 49
Figure 3-9: Comparison between single scale fabrication and multi-scale fabrication. ... 50
Figure 3-10: A complex test case with multi-scale features ............................................. 52
Figure 3-11: The idea of scale-up SAM. ........................................................................... 53
Figure 3-12: Scale up SAM process schematic ................................................................ 54
Figure 3-13: Schematic of the optical design of the proposed scale-up SAM process..... 55
Figure 3-14: Process flowchart of the scale-up SAM ....................................................... 56
Figure 3-15: Motion synchronization framework in hopping light .................................. 57
Figure 3-16: An illustration of the motion blur issue in hopping light ............................. 58
Figure 3-17: Calibrating optics in hopping light............................................................... 59
Figure 3-18: Calibrating pipeline ...................................................................................... 60
Figure 3-19: Calibration of the projection pixel size in microscope image space. ........... 62
Figure 3-20: Calibration of the X motion in the image space. .......................................... 63
Figure 3-21: Calibration of the rotation angle in the image space. ................................... 64
Figure 3-22: Schematic drawing of computing the motion blur correction...................... 66
Figure 3-23: Synchronized motion in hopping light ......................................................... 67
Figure 3-24: Misalignment: the non-parallel moving direction and image orientation .... 69
Figure 3-25: The image stitch adjustment ........................................................................ 70
Figure 3-26: An illustration of the focus error by tilting the image. ................................. 71
Figure 3-27: Focus error distribution on one image ......................................................... 72
Figure 3-28: Reducing the tilting angle to reduce focus error .......................................... 73
Figure 3-29: Focus error related to the number of cycles ................................................. 74
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Figure 3-30: Composite motion of hopping light. ............................................................ 76
Figure 3-31: Efficiency comparison between discrete motion and continuous motion .... 77
Figure 3-32: The fabrication speedup using the hopping light source. ............................. 78
Figure 3-33: Fabrication of a complex large area pattern ................................................. 82
Figure 3-34: A complex pattern with 10K resolution ....................................................... 83
Figure 3-35: Printing fractal shapes .................................................................................. 84
Figure 3-36: A test case of periodic walls ......................................................................... 85
Figure 3-37: Printing grating patterns ............................................................................... 86
Figure 3-38: Printing thousands of micropillars ............................................................... 87
Figure 3-39: Printing free form object using hopping light .............................................. 87
Figure 3-40: The idea of scale integration by combining two different scale processes. . 89
Figure 3-41: Schematic diagram and information flow of the hybrid-source system. ..... 91
Figure 3-42: Prototype of the hybrid light source ............................................................. 92
Figure 3-43: Calibration mapping from angle space to pixel space ................................. 95
Figure 3-44: Mapping of reference data points................................................................. 97
Figure 3-45: Complete coordinate transformation diagram .............................................. 98
Figure 3-46: Functional microfeatures found on bodies of creatures ............................... 99
Figure 3-47: benefit of the hybrid light source ............................................................... 102
Figure 3-48: The benefit of hybrid light source .............................................................. 103
Figure 3-49: Time comparison among processes across various micro-textures ........... 105
Figure 3-50: Stem model with different microfeatures distributed on its four leaves .... 107
Figure 4-1: Three methods to optimize the process ........................................................ 109
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Figure 4-2 Multiscale decomposition of a 3D model ......................................................110
Figure 4-3: A schematic diagram of the dual layer fabrication process ...........................113
Figure 4-4: Buffer region for multiscale toolpaths ..........................................................115
Figure 4-5: Multiscale tool path generation algorithm ....................................................116
Figure 4-6: The schematic diagram of resin recoating for small layers’ boundaries .......117
Figure 4-7: Efficiency of dual layer thickness .................................................................119
Figure 4-8: Fabrication of the porous structure .............................................................. 122
Figure 4-9: The fabricated complex parts with a quarter coin ........................................ 123
Figure 4-10: Tradeoff between resolution and efficiency. .............................................. 128
Figure 4-11. The pipeline of scalable layer thickness ..................................................... 129
Figure 4-12: Illustration of the metric profile: error density function. ........................... 131
Figure 4-13. The framework of the proposed scalable layer .......................................... 133
Figure 4-14: Illustration of the error metric .................................................................... 134
Figure 4-15: Sampling for profile construction. ............................................................. 138
Figure 4-16: Illustration of Dynamic Programming ....................................................... 140
Figure 4-17: An example to show the scalable layer algorithm...................................... 141
Figure 4-18: Adaptive slicing algorithm based on dynamic programming .................... 143
Figure 4-19: Example of the scalable layers ................................................................... 144
Figure 4-20:CAD model with weighted surface ............................................................. 146
Figure 4-21: Slicing comparison between weighted and non-weighted CAD model .... 147
Figure 4-22: Slicing Efficiency Comparison Visualization. ........................................... 150
Figure 4-23: Visualize the slicing performance of different slicing algorithms ............. 151
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Figure 4-24: Adaptive slicing results of various models ................................................ 153
Figure 4-25: Fabrication results of hearing aid model by different slicing methods. ..... 154
Figure 4-26: Fabrication results of hand model by different slicing methods. ............... 154
Figure 4-27: Metric Profiles with different geometric error ........................................... 155
Figure 4-28: Optimizing the printing orientation............................................................ 157
Figure 4-29: Comparing scalable layers and scalable channels. ..................................... 160
Figure 4-30: Challenges of printing transparent micro-fluid channels ........................... 162
Figure 4-31: Fabrication method of scalable channels ................................................... 163
Figure 4-32: Detaching mechanism in scalable channels ............................................... 165
Figure 4-33: Bounding force test. ................................................................................... 166
Figure 4-34: Simple channel fabrication and testing ...................................................... 167
Figure 4-35: Printing channel with different height........................................................ 168
Figure 4-36: An integrated 3D printed device ................................................................ 169
Figure 4-37: 3D structures with micro fluid channels. ................................................... 170
Figure 5-1: Mimicking shark skin................................................................................... 172
Figure 5-2: Multiscale toolpath planning for shark skins ............................................... 176
Figure 5-3: Fabricating shark skin. ................................................................................. 178
Figure 5-4: Small-scale features can change the large-scale object’s surface property .. 184
Figure 5-5: A drop of water on the surface ..................................................................... 185
Figure 6-1: Illustration of contributions: expanding the scalability Δ ............................ 194

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Abstract
After nature’s millions of years’ evolutions, multiscale structures in plants and animals,
such as lotus leaves, shark skin, butterfly wings, and human bone, exhibit splendid
advantageous functionalities, including superhydrophobicity, drag reduction, structural
color, and light-weight strength and many more. Various fabrication methods have been
developed to duplicate these multiscale structures. As a major additive manufacturing
process, stereolithography (SLA) has become a prevalent fabrication method for complex
structures with high resolution. In SLA, three-dimensional structures are fabricated layer
by layer, and each layer is patterned through the dynamic mask for polymerization. The
dynamic mask enables SLA with flexible manufacturing capability compared with
lithography and micro-machining.
However, it is still challengable for current SLA processes to effectively and
efficiently fabricate multiscale structures. Through thirty years’ research, two types of
dynamic mask generation methods are developed: laser scanning and mask image
projection. The laser scanning deposits energy for resin polymerization sequentially,
referred as “temporal” energy control. The mask image projection utilizes a digital
micromirror device (DMD) to project a mask image for resin polymerization
simultaneously, referred as “spatial” energy control. The fixed laser spot size results in a
trade-off between the fabrication efficiency and the laser spot resolution, while the fixed
number of pixels in DMD chips leads to a trade-off between the printing size and the pixel
resolution. Both “temporal” energy from scanning laser and “spatial” energy from DMD
chips cannot effectively and efficiently pattern layers for multiscale structures.
xx
To fill this research gap between the multiscale structures and ineffective fabrication
methods, we developed advanced “spatial and temporal” polymerization energy control to
effectively and efficiently fabricate multiscale structures. By coupling the “spatial” and
“temporal” energy control methods, we fundamentally improve the scalability in three
ways. Firstly, adding the “spatial” modulation to the laser beam can dynamically change
the laser spot size when needed. Secondly, adding the “temporal” modulation to the
projection-based system enables the projection energy control to cover a large area by
scanning. Thirdly, directly combining the two energy control systems mitigates the
drawbacks of each method individually.
Besides the critical challenges in patterning one layer, AMs fabricate 3D structures
layer by layer and use very thin layer thickness to ensure the high-resolution features are
printed, which leads to a largely increased number of layers and hence impractical long
fabrication time. Based on the philosophy of treating features at different scales differently,
three layer-planning methods are proposed to effectively and efficiently fabricate
multiscale structures.
The first layer planning method is dual layer thickness where the interior is printed
using a large layer thickness, and the boundary is printed using small layer thickness. The
second approach is adaptive slicing, where the layer thickness is not uniform but adaptive
to the geometry error. The third method is transferring layers, which adds an auxiliary
platform to fabricate the “roof” of the ultra-thin channels and transfer the roof to normal
SLA process. All these three layer-planning methods could improve the efficiency, size,
and resolution without any tradeoff among each other.
xxi
By utilizing the advanced polymerization energy control and optimized layer planning,
the scalability of AM processes could be largely improved. Currently, as a proof of concept,
we have already developed hardware prototypes and software algorithms. Several test
cases are fabricated to verify the effectiveness and efficiency of the proposed scalable
additive manufacturing. Also, two applications are identified to show the benefit of the
multiscale structures. A lotus leaf’s multiscale structure is mimicked, and the printed parts
exhibit superhydrophobic property. Moreover, the multiscale of shark skin is designed and
fabricated. The drag reduction of the printed parts is observed compared with smooth
surfaces.

1
Chapter 1 Introduction
1.1 Research Motivations
There exist considerable demands for objects with multiscale features, due to their
enhanced mechanical properties (e.g., stability, strength, and flexibility) with other unique
functionalities, such as super wettability, shown in Figure 1-1. Such splendid multi-
functional material property comes from the hierarchical structures, whereby the
meso/micro scale structures improve the light-weight mechanical strength, while the
micro/nanoscale features provide the specialized functionality. Nature has given us
countless examples, after the millions of years’ evolution.

Figure 1-1: Multiscale structures exist in nature and human-made objects. Human-tissue (a) and
bones (b) are in fact structured with multiscale features. Nacre (d) has very high strength due to its
hierarchical structures. The Nepenthes leaf (e) exhibits slippery surface by multiscale structures.
The microchannel device(f) and textured surface (c) are human-made macroscale objects with
micro-scale features.
For instance, multiscale structures, like lotus leaves, gecko feet, and butterfly wing
exhibit super hydrophobicity/-philicity, dry adhesin and structural color. These
2
functionalities would inspire us to design, fabricate, and apply the similar multiscale
structures for engineering purposes. Bae [1] gave a holistic review on the advantageous
functionalities of multiscale structures, as in Figure 1-2.

Figure 1-2: Functionality of structures at different scales. The structural hierarchies in nature
exhibit various splendid properties and have tremendous applications. [1]

To reproduce these functional multiscale structures, researchers have developed
various fabrication methods [1]. Micro-machining, for example, is an important method
for fabricating molds, which could be transferred to other materials. Hawkes [2] modified
the micro-machining processes, which yields the multiscale gecko-inspired structure [3].
However, micro-machining suffers from the tool interference so that complex structures,
like hollowed one, are difficult to be machined out. Lithography is another commonly used
fabrication methods to generate micro- and nano-scale features, such as nanoimprint
lithography [4] and soft lithography [5]. Though lithography could generate high-
resolution features by transferring the mask pattern to the substrates, it requires
sophisticated multiple steps to fabricate complex multilayer structures [6].
3
In comparison, additive manufacturing is becoming prevalent for fabricating
multiscale structures, due to its capability of fabricating complex geometries. Especially,
stereolithography, one type of AM, has the capability of fabricating free-form and complex
3D structures with high resolution. By the name, stereolithography is the “stereo” version
of “lithography”, i.e., multiple layers of lithography. But, significantly different from the
conventional lithography, which requires the predefined masks, stereolithography
dynamically changes the mask pattern for each layer without the limited total number of
masks. In stereolithography, two widely-used methods are developed to generate the mask
pattern for each layer. The first method is using an optical laser scanner, which scans a
laser spot to fill the whole layer. This method generates the mask sequentially by scanning
the whole layer dot by dot. Because the laser energy is sequentially deposited to the
material, this method is so-called “temporal” energy control.
The other mask generation method utilizes a Digital Mirror Device (DMD), from
Texas Instruments, to project a mask image pattern for the whole layer. The DMD chip has
an array (e.g., 1920X1080) of tiny mirrors (e.g., ~7.5umX7.5um), and each mirror could
be individually turned on and off to determine whether that pixel has the energy for
polymerization or not. By controlling the millions of mirrors, the polymerization energy is
spatially modulated to generate the designed mask patterns, so that this method is also
named as “spatial” energy control. In sum, the material in scanning laser-based
stereolithography is polymerized sequentially due to the temporal energy control from the
scanning laser, while the material in mask image projection-based stereolithography is
polymerized simultaneously, due to spatial energy control from the DMD chip.
4
Both these “spatial” and “temporal” energy control methods have fundamental
challenges when patterning the masks for multiscale structures, which have features
spanning different length scales, from micrometer to centimeter. In the laser-based
“temporal” energy control, the laser spot size is squeezed to tens of micrometers to ensure
microscale features are printed, but it takes impractically long time to scan such tiny laser
spot to fill a macroscale layer. Also, in the projection-based “spatial” energy control, the
limited total number of pixels in the DMD chip introduces an inevitable trade-off between
the feature resolution and part size. If each pixel is scaled down to microscale level for
printing high-resolution features, then the total image size is too small for large scale parts.
If each pixel is scaled up for large parts, then the microscale features cannot be printed.
Therefore, both the “spatial” and “temporal” energy control has critical issues in
patterning layers for multiscale structures. Besides the critical challenges in patterning one
layer, AMs fabricate 3D structures layer by layer and use very thin layer thickness to ensure
the high-resolution details are printed, which leads to a largely increased number of layers
and hence impractical long fabrication time.
A significant research gap exists between the huge demand of multiscale structures
and the enabling fabrication processes. It is desirable and urgent to develop fabrication
processes that can effectively and efficiently fabricate multiscale structures, i.e., macro
objects with micro-scale features. In this dissertation, we proposed both advanced
polymerization energy control and optimized layer planning approaches to effectively and
efficiently fabricate these multiscale objects, which is promoted as Scalable Additive
Manufacturing (SAM).
5
1.2 Statement of Problems and Hypotheses
In this dissertation, we are seeking answers to the following question:

How can we effectively and efficiently fabricate macroscale objects with microscale
features using polymerization additive manufacturing?

For the sake of clarity, I would like to introduce a concept:
Scalability: the capability to effectively and efficiently fabricate macro-scale objects
with micro-scale features.
By this definition, Scalability contains three key aspects, fabrication efficiency, object
size, and feature resolution, which can be respectively quantified as “printing volume per
second”, “total volume”, “number of features per millimeter”. Figure 1-3 shows a radar
chart with these three attributes. In each axis, the closer to the origin, the worse that aspect
is. Each process can be characterized in this chart as a triangle area. A larger triangle area
represents better scalability.
6

Figure 1-3: Research Problem: Enlarging the Scalability Δ.
With the definition of scalability, our research problem of effectively and efficiently
fabricating multiscale structures becomes:
Primary research question

how can we address the scalability of polymerization additive
manufacturing?

As additive manufacturing processes are mostly layered manufacturing, the above
research problem can be further divided into two subproblems:

Q1: How can we improve the in-layer scalability of polymerization
additive manufacturing?

and
7

Q2: How can we improve the inter-layer scalability of polymerization
additive manufacturing?

To answer these two questions, we proposed the following hypotheses respectively:

H1: Advanced spatial and temporal polymerization energy control could
improve the in-layer scalability.
H2: Optimized layer planning methods could improve the inter-layer
scalability.

Hypothesis H1 is proposed because conventional polymerization energy control is
either “temporal” energy from scanning laser or “spatial” energy from DMD chips, either
one of which cannot effectively and efficiently pattern layers for multiscale structures, i.e.,
having poor scalability. However, by coupling the “spatial” and “temporal” energy control
methods, we may have the possibility to improve the scalability fundamentally.
Depending on how the “spatial” and “temporal” energy control methods are coupled,
we can further divide the hypothesis H1 into three sub-hypotheses:

H1.1: Adding spatial modulation to the laser-based temporal energy
control system would improve the in-layer scalability.
8
H1.2: Adding temporal modulation to the projection-based spatial energy
control system would improve the in-layer scalability.
H1.3: Combining the spatial energy control system and temporal energy
control system would improve the in-layer scalability.

Specifically, H1.1 adds the “spatial” modulation to the laser spot shape and size, which
can dynamically change the size when needed. Compared with the original temporal energy
control, H1.1 propose an energy control method with better resolution. H1.2 adds the
“temporal” modulation to the projection-based system, which enables the projection
energy control to cover a large area by scanning. H1.3 directly combines the two energy
control systems, which mitigate the drawbacks of each method. All these hypotheses are
tested in Chapter 3. The above three sub-hypotheses are essentially trying to expand the
scalability chart along with different directions, as shown below:

Figure 1-4: Hypotheses to expand the scalability within a layer.
9
Hypothesis H2 is proposed because an object’s features across different layers are not
equally difficult and efficient to be fabricated. If treating the features across different layers
differently, we might be able to improve the scalability. For example, the boundary portion
of an object requires higher resolution, while the inner portion of an object requires higher
throughput. If different layer thicknesses are used for the inner and boundary portion, then
we could largely improve the scalability. Similar, for a complex model, some layers are
not sensitive to layer thickness, which could be printed using thicker layer thickness, hence
to improve the efficiency and the scalability. Lastly, some objects may have very thin
channels, (for example, 5 um channels in microfluidics), which is quite challenging for the
current SLA processes. If processing these channels differently with other layers, then we
might be able to achieve the scalability required for fabricating the objects with these
channels. All these ideas are potential sub-hypotheses for the hypothesis H2,

H2.1: Dual layer thickness could improve the fabrication efficiency and
resolution, and hence improve the inter-layer scalability.
H2.2: Adaptive layer thickness could improve the fabrication efficiency
and inter-layer scalability.
H2.3: Transferring layers method could fabricate ultra-thin layers and
improve the inter-layer scalability.

10
1.3 The Dissertation Outline
The dissertation documents the study related to the question of “how we can
effectively and efficiently fabricate multiscale structures.”
Chapter 1 introduces the research motivation and research problems. Motivated by the
benefits of multiscale structures and the lack of effective fabrication methods, this
dissertation is driven by the research question of “how we can effectively and efficiently
fabricate multiscale structures.” To answer this question, I proposed two hypotheses that
the advanced polymerization energy control and optimized layer planning would be the
answers to the question. The new concept of “Scalability” is proposed to define the
capability of a process to effectively and efficiently fabricate the multiscale structures.
Moreover, the research questions are essentially how we can improve the scalability.
Chapter 2 reviews all the fundamental fields related to the research questions,
including the benefit of multiscale structures, comparing different additive manufacturing
processes, the fundamentals of the stereolithography, scalability problems and methods in
stereolithography, scalability in other manufacturing processes.
Chapter 3 and Chapter 4 provides the major answers to the research questions and
verify the hypotheses. Chapter 3 mainly tests the hypotheses that “advanced spatial and
temporal polymerization energy control improves the in-layer scalability.” By coupling the
spatial and temporal energy control methods, three advanced energy control approaches
are tested to fundamentally improves the in-layer scalability.
11
Chapter 4 mainly tests the hypotheses that “optimized layer planning methods improve
the inter-layer scalability.” Three layer-planning methods are developed, including dual
layer thickness, adaptive layer thickness, and transferring layers.
Chapter 5 applies the methods in Chapter 4 and Chapter 5 to fabricate the shark skin
inspired multiscale structures. Artificial multiscale shark skin structures are designed and
fabricated, and the drag reduction tests are conducted.
Chapter 6 concludes the paper with highlighted contributions and recommended future
research.
Some of the texts have been published in [7] [8] [9] [10].
As a visualization, the research scope is shown in Figure 1-5, which mainly tries to
answer the proposed two hypotheses, H1 and H2. Also, the additive manufacturing process
considered in this dissertation is stereolithography.
12

Figure 1-5: Research scope: expanding the scalability Δ.

13
Chapter 2 Literature Review
This section briefly summarizes state of the art in SLA processes with emphasis on
the fabrication of multiscale structures. Firstly, I review the multiscale structures that
motivate the work in this dissertation. Then, I review additive manufacturing and
stereolithography, and the basics of the SLA process and the inherent trade-offs among
fabrication efficiency, feature resolution, and part size, which commonly exist but are
poorly addressed in SLA processes. Then, I review the related work that has been done to
address these tradeoffs. Besides, the scalable methods in subtractive manufacturing are also
reviewed for comparison and inspiration.
2.1 Biological and Engineered Multiscale Structures
Nature evolves out millions of successful species and most of these successes related
to the multiscale biological structures from millions of years’ iterations. This section briefly
reviews the functionalities and importance of the multiscale biological structures, and how
human are inspired and engineer new multiscale materials.
2.1.1 Biological Multiscale Structures
Multiscale structures, such as lotus leaves, gecko feet, and butterfly wings are
ubiquitous [1], resulting from millions of year’s evolutions. Different scales serve as
different purpose, where microstructures enhance the mechanical strength while
nanostructures provide other multiple functionalities, i.e., wettability [11] [12], structural
color [13] [14], or dry adhesion [2]”.
14
Besides the above-mentioned multiscale surfaces, multiscale bulk material has also
attracted much research. Natural bulk materials, such as wood, nacre, diatom, and bone,
exhibit exceptional strength with minimal weight. This is achieved by the hierarchical 3D
architectures from the nano- to macro scale, usually spanning at least five orders of
magnitude in size [15].
Often, the multiscale bulk structures not only are light-weight and strong but also serve
as the channels for transporting other materials. Such multi-functionality is extremely
important for biological material, for instance, bone [16] [17] and bamboo [18].
Also, multiscale surfaces usually are multifunctional, at one hand they provide
improved mechanical strength, and at another hand, they also have a couple of other unique
functionalities. For example, the microstructures of butterfly wings are not only structural
light [13] [14], but also, they enable unidirectional water transportation [19]. Ritchie [20]
also pointed out that the multiscale structures may release the conflict between strength
and toughness.
15

Figure 2-1: Biological and engineered multiscale structures. a) is the engineered hierarchical
lattices structure [21], and b) is the multiscale biological structures of bone [17].
2.1.2 Engineered Multiscale structures and Applications
Inspired by the multiscale material in nature, multiscale biomimicry materials and
metamaterials are also enabled by the advanced manufacturing methods in recent years,
and supreme material properties and applications are achieved. Engineered multiscale
surface materials show the exceptional unique property. General speaking, nature species
have evolved to have lots of micro and nanostructures along with their body surfaces, to
interact with and adapt to the environment. Abundant of research has been done to mimic
the multiscale structures for various applications, including super hydrophiid [22], super
wettability [23], resilient material [24], dry adhesion [25], tissue scaffolds [26], drag
reductions [27], tough material [28], sensors [29] and more. Yang [30] presented a
comprehensive review of 3D printed bioinspired structures. Bae [1] also gave a deep
review of the fabrication and application of multiscale surface structures.
16
Besides directly mimicking the multiscale biological structures from nature,
researchers also developed plenty of multiscale metamaterials, that do not exist in nature.
Engineered multiscale bulk materials have super properties. Typical engineered multiscale
structures, including porous structures [31] [26], micro-lattice structures [32] [33], fractally
patterned structures [34] [35] have increased the mechanical strength. Wegst summarized
some multiscale structural material [36].
2.2 Additive Manufacturing and Stereolithography
Benefiting from the capability of fabricating complex and free-form structures, AM is
becoming a promising manufacturing process for multiscale structures. Among the AM
processes, stereolithography has the highest resolution, which is the basic AM principle
studied in this dissertation. Therefore, this section compares the commonly used AMs and
reviews the fundamental research in SLA.
2.2.1 Additive Manufacturing

Additive Manufacturing is such a manufacturing process that could fabricate three-
dimensional (3D) objects by additively assembling the elementary material in a predefined
digital model. Additive Manufacturing is often called 3D printing, the analogy to the 2D
printing technologies. Most AMs are layered manufacturing and repeat “2D printings” on
top of previous layers. This manner of fabrication enables AM with various advantages
over subtractive manufacturing, such as tool-less, complexity-free, near-net, and mass-
customization.
17
Over the past few decades, more than hundreds of AM processes have been invented.
For the last two decades, several excellent review papers and books dedicated to AM have
been written [37] [38] [39] [40] [41] [42] [43] [44] [45] [46]. In this literature review, I
would like to review the most commonly used AM processes briefly. Based on the way of
manipulating raw materials, the widely used AMs could be grouped into five classes:
material extrusion, material jetting, powder bed fusion, vat polymerization, and other AMs,
as shown in Figure 2-2.

Figure 2-2: Typical AM processes. The highlighted “Vat Polymerization” is the fundamental AM
principle studied in this dissertation.
Material extrusion is the most widely-used AM principle, due to its simplicity. Fused
Deposition Modeling (FDM) [47] [48] [49] is a common material extrusion based AM.
FDM 3D printer uses a heated nozzle to extrude the melted polymer and deposit to the
previously built layer, and the extruded material is immediately cooled down and solidified
18
due to the property of thermoplastic. Direct Ink Writing (DIW) is another successful
material extrusion-based AM, for the capability of printing functional objects with multiple
materials [50]. Truby and Lewis summarized the pioneering work in using DIW for
printing 3D soft maters [51] [52] [53]. Both DIW and FDM suffer from low efficiency due
to the point by point manufacturing.
Material jetting is similar to material extrusion in a way that nozzles are utilized.
However, the nozzles for material jetting utilize piezo actuators to jet out a large number
of liquid droplets within a short time, and also multiple jetting nozzles simultaneously jet
out droplets. Such high-frequency jetting method could print parts with high-resolution and
high-efficiency. Sitthi [54] presented the ink jetting based AM could printing components
with multiple materials. However, the material should have very low viscosity (mostly less
than 100 cp) for the jetting nozzles, which excludes out many materials for this process,
especially viscous engineering resin with additives. The company XJet developed low-
viscosity solutions with the metallic and ceramic nanoparticle, which pave the way to print
parts with metal and ceramic using material jetting AM [55].
Besides using nozzles to deliver material, another important method is the powder bed,
where a doctor blade sweeps the powder and distribute the powder evenly to cover the
previously printed layers, then a power source, like a laser or electron beam, melts
(sometimes just sinters) the powder to attach to the previous layer. Selective Laser
Sintering (SLS) [56] is a commonly used principle, in which a high-power laser is focused
and scanned by two rotating mirrors, and selectively sinters the metal powder to form one
19
layer. Depending on the powder binding mechanism, SLS is derived as Selective Laser
Melting [57] [58].
In addition to nozzle and powder bed, resin vat is the third popular way to deliver the
material for AM systems, specifically for the liquid resin. The liquid resin is photo-curable
resin, which forms a cross-link under the light curing. After one layer is patterned, the
liquid resin could automatically refill and recoat the previous layer. This is very different
from the nozzle- or powder bed-based AMs, which needs piezo actuators or blades to
deliver the material actively. The AM processes utilizing this photo-curable resin are often
called stereolithography (SLA) or Vat Polymerization. SLA has many advantages
compared with other AM processes, and the work in this dissertation is based on SLA. The
detailed literature review will be done in the next sub-section.
Besides the above commonly used AMs, there are many other successfully AMs that
process material differently. For example, the Direct Energy Deposition DED is metal AM
method that coaxially delivers the metallic powder and deposits a thin layer on the substrate
and previous layers [59]. Comparing with the SLS and DED, some other novel AMs that
do not require high powder during the printing attract a lot of research effort, such as binder
jetting [60] and selective separation shaping [61]. Binder jetting is a typical method [60],
which utilize jets out adhesive liquid to bind the metallic powder. After printed, the green
parts are heated in an oven to remove the adhesive liquid and sinter the powder. SLS and
DED require high temperature during printing which increases the cost. The binder jetting
could avoid the high temperature during the printing and largely reduce the cost, but the
sintering of the whole green parts in the oven causes severe shrinkage.
20
Materials for AMs
The materials for AMs could be divided into four types: metal, plastic, ceramic, and
organic. Though each AM process targets for one specific type of material, researchers
have modified them to cover more materials. For example, most metal AM processes, e.g.,
SLS, and binder jetting are applicable to the polymer [62] [63]. Moreover, because the
polymer has many different types and mechanism to be bounded, there exist various other
AMs principle for polymers. Besides polymer, ceramic is the third major type of material
[64] used in AMs for the unique properties, such as piezoelectricity, high-temperature
melting, and so on. Travitzky [65] gives a comprehensive review of the AMs to 3D printing
ceramic-based material. Leung and the author also did work on the digital material design
[66] [67].
To date, most common AMs are improved to cover as many types of materials as
possible. Material extrusion could support metal, ceramic, plastic, and organic materials.
Material jetting could support plastic, ceramic, and metal. Powder bed fusion could also
support plastic and metal. Vat polymerization could support all four types of materials.
Because different AMs require different forms of the raw material and different mechanism
to connect the materials, the major task of developing materials for AMs is processing the
material into the forms that the AMs need.
2.2.2 Stereolithography: Photopolymerized Additive Manufacturing
Invented in 1983, SLA was the first commercialized AM process [68]. Thanks to the
high resolution, SLA has become the dominating AM process for the applications with
high-resolution requirement. Since invention, it has become a famous Additive
21
Manufacturing (AM) process. Many areas, such as medical molding [69] and product
prototyping, have achieved exceptional success with SLA. Dentists have used
stereolithography for dental implants [70] [71] , orthodontics, and oral surgery [72]. Small-
scale models fabricated by SLA have been used in architecture as a modeling tool. Due to
the high resolution, SLA has been applied in many fields, such as biomedical engineering
[73].
In the breakthrough patent [1], Hull formulated the fundamental idea of SLA processes:
exposing light to the liquid resin and trigger the polymerization reaction to solidify the
liquid resin into a solid part, shown in Figure 2-3.

Figure 2-3: Schematic drawing of the SLA process from Hull’s groundbreaking patent [68].
The fundamental photo polymerization law was proposed by Lambert in [74], as
shown in Figure 2-4. Induced by the light, the photo-initiator is excited to generate the free
radical, which can enable the formation of crosslink between monomer and oligomer. This
process is called polymerization. With this photo-induced polymerization, the liquid resin
22
is cured to be solidified. The whole research in this dissertation is based on this principle
to additively manufacturing objects.

Figure 2-4: Photopolymerization mechanism
Lambert [74] gave a governing equation to characterize the polymerization process.
Given the light intensity I, and light exposure time t, the curing depth is determined as
C
d
=𝐷 𝑝 ln⁡(
𝐼 ⋅𝑡 𝐸 𝑐 ) (1)
where D
p
is the penetration depth. Also, this term is related to material property and
derived as
D
p
=
1
ℎ

(2)
Hence, the polymerization law can be rewritten as:
C
d
=
1
ℎ
ln⁡(
𝐼 ⋅𝑡 𝐸 𝑐 ) (3)
Centered on the above governing polymerization equations, Jacobs [75] summarized
the fundamental research progress in the SLA field.
23
When invented, SLA used a laser spot to trigger the polymerization, and an X-Y-Z
linear stage is utilized to translate the relative position of the laser spot so that the
polymerization could take place in a 3D space. Hull [68] also realized the mechanical linear
stage was slower than an optical scanner. Then two scanning mirrors are then incorporated
in the SLA process, which becomes the standard implementation of SLA. However, even
when the optical scanner boosted the mechanical speed, the sequential scanning leads to
sequential polymerization, and it takes a very long time to cure one layer.
To overcome the limitation of low efficiency from sequential scanning, in 1993,
Takagi [65] proposed a parallel process that the mask pattern is simultaneously projected
onto the liquid resin surface to fabricate one layer. However, these masks are prefabricated,
and to print a new 3D model, a great number of different masks are required. Bertsch [76]
firstly utilized a liquid crystal display (LCD) to generate the dynamic mask to cure a whole
layer simultaneously, which results in efficient parallel polymerization compared with the
sequential laser-based polymerization. However, at that time, LCD has two major
drawbacks, 1) each pixel size is large, and 2) the energy from each pixel is low, which
elongate the resin curing time. Comparing with LCD, the Digital Micromirror Device
(DMD), invented by Texas Instruments, becomes popular in stereolithography to its
excellent displaying performance. Sun [77] used the DMD chip as a dynamic mask
generator and developed a projection-based SLA, which large increase the fabrication
efficiency.
Figure 2-5 compares the representative two primary power sources in SLA: laser and
DMD projectors.
24

Figure 2-5: Two types of light sources are used to trigger polymerization: laser (left) and projector
(right).
Both light sources have advantages and disadvantages, as summarized in Table 2-1.
The laser light source could generate very smooth contour, while the projector has
pixelized features. However, the projector has a million individual pixels, which can define
the 2D shapes in a parallel way, which is very efficient. In comparison, the laser light
source requires the sequential scanning, which is slow for large parts.
Table 2-1: Comparison of laser and projector.
Light source
Pattern
generation
Energy
Modulation
Advantages Disadvantages
Laser Scanning
varying
speed
smooth
contour, multi-
direction,
Slow, defocus,
Projector Mask Image grayscale Fast,
pixelized,
unidirectional
To sum up, the laser-based SLA is temporally controlling the polymerization, while
the projection-based SLA is spatially controlling the polymerizations. Beyond these two
primary light sources, in this dissertation, I would propose a combined spatial and temporal
energy control for polymerization, which could fundamentally address the drawback
associated with spatial or temporal energy control.
25
2.3 Scalability in Stereolithography
Though two primary power sources, laser, and projector, are widely used in SLA, they
both have difficulties in fabricating multiscale structures, which are so-called scalability
problems. This section reviews these scalability problems in SLA, and they are addressed.
2.3.1 Scalability Problems in Stereolithography
Since SLA was invented in the 1980s [68], various research has been done to improve
its fabrication performance including fabrication speed [78] [74] [79], part size [21],
geometry resolution [80] [77] [81] [82], and scalability [21] [83], etc. However, three main
tradeoffs need to be made among the fabrication performances in the SLA process,
including (1) fabrication efficiency versus feature resolution, (2) part size versus feature
resolution, and (3) the ratio of part size to feature size versus fabrication efficiency. How
to address such tradeoffs is the primary motivation of researchers, which is reviewed as
follows.
Fabrication speed versus feature resolution.
Two types of feature resolutions need to be considered in the SLA process, the XY
planar resolution, and the Z-axis resolution. For the layer-based SLA processes such as
LSL [84], P SL [77], and LaP SL [21], the trade-off between the Z resolution and the
fabrication efficiency exists as well. In order for the SL processes to achieve a high Z-axis
resolution, the thin layer thickness is required, which will lead to an increased number of
layers. Because extra time is required in the layer-based fabrication processes to separate
the built layers from the platform and to refill liquid resin, the increased number of layers
leads to a longer fabrication time. Consequently, the fabrication speed will be reduced. Due
26
to the trade-off, the commercial SL machines typically use a practical layer thickness such
as 50 m or 100 m.

Figure 2-6: Trade-off between fabrication efficiency v.s. Feature resolution. Feature resolution is
computed as the number of voxels per mm. Each star point represents one SLA process.
Many approaches have been proposed to reduce the additional time of separating the
built layers from the platform and refilling liquid resin. For example, separating built layers
by a sliding mechanism may require less time than the separating approach of moving the
building platform up-and-down [78]. Vibration is another method to reduce the separation
time by using an acoustic vibration source to assist the layer separation [85]. The CNC
accumulation [10,11] is another method to achieve simultaneous resin curing and recoating
by immersing the curing tool inside the photocurable resin; hence, the separation and
refilling time can be reduced. However, these approaches can only reduce the part
separation and resin refilling time to a certain extent. Consequently, using less layer
27
number in the SL process is still preferred to increase the fabrication speed, while it will
reduce the Z resolution of the printing process at the same time. Recently, the continuous
liquid production method (CLIP) [86] creates a liquid interface between the curing part and
the bottom film to facilitate the fast recoating and to eliminate the waiting time for part
separation. However, the CLIP process has significant difficulty in fabricating objects with
large cross-section areas since resin cannot quickly flow into the center of a large area [87].
As to the XY resolution, only the laser-based SL process [84] needs to compromise
between the XY resolution and the fabrication speed. That is, using a larger laser spot size,
one layer can be filled more quickly; however, the feature resolution will be worse at the
same time. In comparison, if a smaller laser spot size is used, the quality can be improved;
however, the required fabrication time will also increase.
Part size versus feature resolution
The projection-based SL processes utilize a digital micromirror device (DMD) to
generate a mask image that can be used to cure the whole layer simultaneously. Such
capability enables the projection-based SL process to have a faster fabrication speed.
However, a DMD has a limited number of pixels, e.g., a typical DMD can only have a
maximum of 1920 1080 pixels. Hence, the part-size-to-feature-size ratio in the projection-
based SL processes (e.g., P SL [77] and CLIP [86]) is limited, which leads to the difficulty
in fabricating a large-sized part with highly detailed features.
28

Figure 2-7: The trade-off of part size v.s. Feature resolution. The feature resolution is computed as
the number of voxels per mm. Each star point indicates on SLA process. All current SLA processes
lie in a narrow region. The top-right region is the ideal region to fabricate objects with large part
size and high resolution.
part-size-to-feature-size ratio versus fabrication speed
As discussed before, in the conventional SL processes compromise needs to be made
between the part-size-to-feature-size ratio and the fabrication speed. It is difficult to
directly scale up the micro-SL process to build objects with large sizes. For example, an
intuitive method to scale up the micro-SL process is by translating the part in the XY plane
so that the overall printing area can be increased [88]. Another scale-up approach is to
utilize the scanning mirror to shift the projected image into a larger building area [21].
29
However, these direct scale-up approaches will take much longer time when fabricating
large-size parts.
Figure 2-8 a) sums up the typical trade-off among fabrication efficiency, size, and
resolution, which exist in most AM processes. Figure 2-8 b) is the research goal:
simultaneously improving the efficiency, size, and resolution without tradeoffs. In this
research, we proposed both hardware and software approaches to address the trade-offs
above effectively and fabricate a macro-scale part with micro-scale features using a fast
fabrication efficiency.

Figure 2-8: Trade-off among fabrication size, resolution, and efficiency. Tradeoffs exist in most
typical AM processes.
2.3.2 Methods to Address the Scalability in Stereolithography
The tradeoff among efficiency, size, and resolution has become a significant issue that
prevents most additive manufacturing processes from being widely adopted for industrial
applications. Researchers have proposed various methods to mitigate the tradeoff. In this
subsection, we reviewed the research efforts to solve the tradeoff and to achieve scalable
30
additive manufacturing. Because stereolithography processes are classified into projection-
based and laser-based depending on which light source the processes use, we reviewed
them separately. In addition to these methods to achieve scalable light source for a single
layer, the methods to be scalable along the z-direction will also be reviewed.
Methods to address scalability in projection-based Stereolithography
The limited number of the total pixels in a mask image sets a bottleneck for the
projection-based SL process to fabricate a part in a large area with a higher resolution. That
is, the total number of pixels in a layer is fixed. A typical DMD can only have a maximum
of 1920 1080 pixels. Hence, the part-size-to-feature-size ratio in the projection-based SL
process (e.g., P SL [77] and CLIP) is limited, which leads to the difficulty in fabricating a
large-sized part with highly detailed geometric features.
An intuitive method to enlarge the total number of pixels of each layer is to project
multiple images for one layer, and thus the total number of pixels could be largely increased
by the number of images in one layer. For example, [89] and [88] segment one layer into
many sections, and project an image to the first section; then move the projector to the
adjacent section, stop it to project a corresponding image for this section; and continue this
procedure to fill all the sections. Although such stop-and-project method could achieve
large area fabrication with a high resolution, the fabrication speed is much slowed down
due to the extra projection transition time.
To eliminate this transition time, Suman Das [90] developed a continuous moving
light method, called Large Area Maskless Photopolymerization (LAMP), in which the
projector is continuously moving, and also the images continuously refresh according to
31
the projector’s current position. A similar idea was commercialized by Prodways. This
method is promising for its speed; however, two fundamental issues arise. First, because
of the continuous motion, the projector needs to refresh the image at each pixel’s distance.
It requires a high-speed refresh rate, which is a possible but expensive task and makes the
projector controller much more expensive. Further, if the exposure time for each pixel is
reduced, for example, in the situation of a high Z-axis resolution (i.e., with a small layer
thickness), the required refresh rate becomes incredibly high, e.g., 10,000 Hz, which is very
hard for current DMD chips. Without such super high refreshing rate, the projection images
are blurred due to the moving pixels.
To avoid the refresh rate issue, Zheng [10] used two scanning mirrors to change the
position of each image rapidly. A customized f-theta lens is used to solve the focus issue
of the tilted image. However, even if a customized focusing lens is used, the building area
is still limited to a relatively small area due to the limited field of view.
Table 2-2 compares all those above scalable projection-based SLA.
Table 2-2: Different methods for projection-based SAM
Methods Key Idea Pros Cons
Stop & Project
[89] [88]
Translation and projection
are separated
High feature quality Slow printing speed
LAMP
[90]
Refresh the images for
each pixel’s distance
Very large building area
Super high refresh rate,
Motion blur
LAPμPL
[21]
Use galvo mirrors to
move image quickly
No motion blur
Large area f-theta lens,
Limited building area

32
Methods to Address the Scalability in Laser-based Stereolithography
Besides projection-based SLA, researchers also proposed scalable laser-based SLA to
address the tradeoff among fabrication efficiency, resolution, and size. The production
efficiency of laser-based SLA is determined by many factors, such as light spot diameter,
scanning speed, hatch space, and curing depth [91]. Among them, the light spot diameter
is the most direct way to determine production efficiency.
The diameter of the light spot is determined by the entire optical system and could be
difficult to control precisely. Therefore, most SLA systems set the spot diameter as a
constant. The specific value is a tradeoff between the size of the part that is being built and
the desired resolution, which is typically about 0.1% to 0.5% of the overall dimension. For
this reason, a variable beam spot that can improve production efficiency while keeping
high resolution became a promising direction for stereolithography. With a variable beam
spot, the large spot can fill an open area quickly and small spot can build details that require
high resolution. Many studies have been carried out on methods to change spot size. Miller
et al. developed an SLS workstation that has two laser spot sizes by adding and removing
an aperture in the light path [91]. Yi et al. reported a stereolithography process that uses
dynamics focusing mirror to change spot size. Several specimens demonstrated more than
25% building time saving [92]. Tian proposed a dynamic focus system to generate the
different sizes of the laser beams, but how the different sizes are combined was not covered
[93]. Lehtinen achieved different curing depth by using different wavelength lasers [94].
Choi utilized dual lasers in a single setup to double the building volume [95]. By
dynamically changing the focus of laser spot [96], variable laser spot size with different
33
resolutions can cure features at different sizes. In our work [10], we also presented a multi-
scale fabrication approach using an optical filter with high-contrast gratings. However,
only the resolution in the XY plane was considered while the multi-scale in the Z-axis was
not considered [10].
Layer Planning Methods for General Additive Manufacturing
Previous methods are solving the tradeoff in a layer. Across different layers, there are
also lots of research effort trying to solve the tradeoff by optimizing the layer planning.
Layer-based additive manufacturing fabricates a part by successively accumulating
material layer by layer, in which an essential computational step is slicing. In the step of
slicing, the input CAD model is intersected with a set of horizontal planes, and this results
in a set of closed curves or polygons at different height levels. Assuming each layer is
fabricated by extruding the intersected contour with small layer thickness, such an
extrusion introduces the staircase error [97], which is directly related to the surface angle
and the layer thickness [98]. Slicing methods can be classified into uniform (having an
equal thickness in all layers) or adaptive ones (with unequal layer thicknesses in different
layers). While uniform slicing is fast and straightforward, adaptive slicing is proven to be
able to fabricate parts with higher accuracy and shorter building time.
⚫ Layer Planning Objective: Surface quality
Various slicing procedures have been discussed in previous surveys of AM technology
[99], where different geometric errors measure the resultant quality -- e.g., cusp height,
surface roughness (Ra), and area or volumetric deviation. The most widely used error
measurement is the cusp height [100]. Kulkarni and Dutta [101] reduced the staircase effect
34
by controlling the maximum allowable cusp height using 12 different expressions. The
relationship between the maximal allowed cusp height and the normal vector at any point
on the tessellated model is used to find the thickness of each layer. Yan et al. [102] [103]
followed this idea and developed an adaptive slicing method that works directly on point
cloud by using moving least square surfaces. This error measurement has also been used
widely in different applications [104] [105] [106] [107] [108]. Recently, Wang et al. [109]
presented an adaptive slicing method considering both the cusp height and saliency
criterion. The Ra value [110], which is commonly used in design or manufacturing practice
to specify surface roughness, is a similar measurement that can be used as well. Differently,
Zhao [111] introduced area deviation by comparing the measured deviation of the interior
area of the layer contours to check whether the layer becomes thicker or thinner. However,
a staircase effect appears on the layer while two contours have a similar area but totally
different shapes. All of these errors can be classified as 2D measurements. They become
less suitable when the geometry of an input model between two neighboring slices becomes
more complex. To address the problem, Kumar and Choudhury [112] presented a volume
deviation for adaptive slicing. This technique is a promising solution for slicing CAD
models with remarkable higher precision. However, since it works directly with surfaces
of the part to mathematically compute the related volumes, the geometric complexity of
the surfaces would need some complicated mathematical computation that may jeopardize
the validity of such a system.
⚫ Global Slicing
35
Most of the previous work (e.g., [113]) first cuts the entire part from the bottom-most
to the top-most position at the maximal thickness that is allowed by the AM process, and
then applied the specific error to decide if some thicker layers need to be further sliced into
thinner ones. However, the presence of any concave or convex area may yield a significant
geometry deviation error when no staircase effect is identified at either slicing layers. In
contrast, Hayasi and Asiabanpour [114] started slicing at the minimal allowed thickness,
then allows the current layer becomes thicker or thinner while comparing the obtained error
with the given tolerance.
Singhal et al. [110] presented a comprehensive and more accurate direct slicing
procedure by detecting the sharp concave/convex vertices and then subdividing a large
layer into a number of thinner layers if sharp concave/convex vertices are detected.
Wang et al. [109] proposed an iterative method to refine the slicing plan obtained by
previous greedy methods. All these slicing procedures are trying to obtain the geometry's
sharp changes as accurately as possible, either by cutting at minimum thickness or by
checking the sharp vertices. However, the expensive computation prevents applying this
methodology at very high resolution. To solve this dilemma, we will introduce a slicing
algorithm that optimizes the slicing plan on a profile, which can be efficiently constructed
from the CAD model.
2.4 Scalability Challenges and Methods in Other Manufacturing
Processes
For comparison and inspiration, it is also essential to review the approaches for other
manufacturing processes to address the scalability problems. In machining, rough
36
machining and fine finishing are combined to speed up the machining and guarantee the
surface quality. For example, in milling, different sizes of cutters are utilized sequentially
so that the coarse cutter quickly removes most of the material, and the finishing cutter is
then used to polish the surface. A lot of tool path planning algorithms are proposed to
optimize the machining time and quality [115] [116] [117]. Gupta also did a lot of work in
fabricating multiscale structures using FDM processes [118] [119] [120].
To enable subtractively manufacture parts with features across different length scales,
researchers have proposed various methods. Firstly, different sizes of tools are sequentially
used; for instance, the milling [115]. Secondly, different processes are hybrid together, and
each process handles features at specific scales. For example, machining and polishing are
usually combined to generate smooth features over large parts. Thirdly, large linear stages
are used to translate the micromachining tools to cover very large parts. Combining
additive and subtractive manufacturing is another way to achieve scalable manufacturing.
The hybrid process between 3D printing and robotic polishing is a typical scalable
approach to generate smooth part [121].
Several ideas of this dissertation are inspired by these methods to achieve scalable
subtractive manufacturing. For example, the method of coarse and fine cutters inspires that
various sizes and shapes of laser spots could be combined in a single additive
manufacturing process in chapter 3.1. Also, the idea of the variable cutting depth in milling
enlighten us to propose two layer-planning methods: dual layer thickness in chapter 4.1
and adaptive layer thickness in chapter 4.2.
37
Chapter 3 Polymerization Energy Control for the In-Layer
Scalability
As mentioned above, the scalability of the primitive “temporal” and “spatial” energy
control is limited. The primary issue is that the polymerization of primitive energy control
can only fabricate parts within a limited scale range. To improve the scalability of
photopolymerization, we propose three advanced polymerization energy control methods,
by coupling the spatial and temporal energy control mechanisms.
Firstly, adding the “spatial” modulation to the laser beam can dynamically change the
laser spot size when needed. This method is called “down-scale energy” as the shape laser
beam provides better resolution. Secondly, adding the “temporal” modulation to the
projection-based system enables the projection energy control to cover a large area by
scanning. This method is called “up-scale energy” because the resolution maintains the
same while the building size increases by scanning. Thirdly, directly combining the two
energy control systems mitigates the drawbacks of each method. This method is called
“integrated-scale energy,” as a laser and a projector are integrated so that the projector
solidifies the interior while the laser spot cures the boundary.
These three advanced polymerization energy control methods lay the effective
hardware foundations for patterning the multiscale structures. Moreover, we further
improve the efficiency based on the methodology of treating features at different scales
differently. A three-dimensional (3D) object can be decomposed into two portions: interior
(macro-scale features) and boundary (micro-scale features). The geometry accuracy is
determined by the boundary (micro-scale features), which can be verified by the fact that
38
3D objects are modeled by Boundary-Representation. Meanwhile, the fabrication speed is
dominated by the interior (macro-scale features) as most fabrication time is spent on
recoating and solidifying the interior portion. If we can use a large-scale and powerful light
source to quickly print the interior and use a small-scale light source to print the boundary
accurately, then we can both save fabrication time and preserve the fine features.
These three methods target to improve the scalability within one layer, shown in Table
3-1. The rest of this Chapter discusses them in detail.

Figure 3-1: Three representative scalable light sources

39
3.1 Shaped Laser Beams: Down-Scale Energy
1

As shown in Figure 3-2 a), the first way to achieve Scalable Additive Manufacturing
(SAM) is increasing the resolution while keeping the building volume, which is called scale
down SAM. In the proposed scale down SAM, we add an additional laser in the system,
which has only one-tenth of the original laser spot, in Figure 3-2 b). This small laser spot
is added to generate high-resolution features.

Figure 3-2: The principle of scale down SAM, using two different sizes of the laser
spot in one additive manufacturing process.

1
The full text of this section has been published on Journal of Micro and Nano-Manufacturing, as Mao, H.,
Leung, Y.S., Li, Y., Hu, P., Wu, W. and Chen, Y., 2017. Multiscale Stereolithography Using Shaped Beams.
Journal of Micro and Nano-Manufacturing, 5(4), p.040905.
40
3.1.1 The principle of Shaped Laser Beams
The idea of the proposed method is to use laser beams with optimal shape and scale to
fabricate features at different size scales, as shown in Figure 3-2 c). That is, a large laser
beam can be used to cure the central portion of a layer, while a small laser beam can be
used to solidify boundary contours and sharp features. Also, laser beams with different
shapes can be used to fabricate complex patterns that are appropriate for the laser beam
shapes. Such a curing strategy enables fast fabrication speed and high feature resolution
since the large laser beam can save time in curing a larger area while the small laser beam
can fabricate sharp features.
Shape Laser Beams
To realize the proposed multi-scale fabrication process, we first discuss how to create
laser beams with different sizes and shapes. Figure 3-3 shows the optical path to generate
shaped beams. Unlike the optics of the conventional laser-based SL process, a unique
device with designed apertures is added in the optical path, as shown in Figure 3-3. The
collimated laser beam passes through the controlled aperture before passing through the
focusing lenses.

Figure 3-3: Shaped beam optics.
41
The purpose of adding a designed aperture is to modify the shape of the laser beam so
that the correspondingly cured features will have desired shapes and sizes. Figure 3-4
demonstrates four different apertures and their correspondingly cured geometric features.
In Figure 3-4, the aperture at the leftmost column is a circle (diameter of 0.5mm), which
enables the whole laser beam to pass through. Accordingly, the output cured feature is an
elliptical shape, which reflects the profile of the input laser. The second aperture to the left
is a small hole (diameter of 0.05mm), which blocks the outer portion of the input laser
beam and let only the beam’s center portion pass through. The corresponding cured feature
is a 50 m cylinder, which validates that the proposed aperture can modify the input laser
beam regarding its shape and size. The right two apertures show modified laser beams with
different shapes; accordingly, the cured features are related micropatterns. Such shaped
beams are useful in quickly fabricating a functional surface with different features such as
micropatterns of pillars.

Figure 3-4: Multiple apertures for different micropatterns. Top row: different apertures patterns;
bottom row: the fabricated patterns and the size of each fabricated dot.
42
The shape of the laser beam’s cross-section can be modified into any geometry in a
fashion similar to the shaped-beam electron-beam lithography, which has been used in the
semiconductor industry. Due to the small aperture sizes, an added aperture plate can have
a library of beam shapes with hundreds of different sizes and shapes. By integrating
variable apertures in the optics, our SL process can simultaneously improve the fabrication
speed and surface quality. The aperture plate with desired sizes and shapes can be
fabricated by common lithography technologies such as photolithography and nanoimprint
lithography [122].
Beam Shape Control
To control the focused spot shape, we analyze how the laser beam changes after
passing through apertures that are a set of pinholes. Essentially small pinholes are a low-
pass filter, which can filter out the high-frequency laser mode, resulting in a clean Gaussian
beam. Therefore, a pinhole aperture can be used to regulate the laser beam and to reduce
the size of the laser spot significantly.
Specifically, due to the Fraunhofer diffraction when the light beam passes through a
pinhole, the output beam follows a complex Airy Pattern, which is derived from Fraunhofer
diffraction theory [123]. As shown in Figure 3-5, the Airy Pattern has a series of sharp dark
rings alternating with broader bright rings. The core of the Airy Pattern contains 86% of
the total light in the image, and this core ring can be approximated by a Gaussian beam
with the same peak and FWHM diameter [124]. This Gaussian beam approximation works
nicely in our fabrication process since only the core peak region can reach the critical resin
curing energy 𝐸 𝑐 .
43

Figure 3-5: Laser beam after a pinhole aperture
The intensity distribution of the output beam passing a pinhole can be approximated
as:
𝐼 (𝑟 )=𝐼 0
exp⁡(−
2𝑟 2
𝜔 0
2
)
and 𝜔 0
=𝐾𝑑 , where d is the diameter of the pinhole, and K is the magnification factor of
the optic system. According to the photo-induced polymerization mechanism [125] [126],
the resin is polymerized only if the input energy is greater than a critical energy level, i.e.
𝐼 (𝑟 )×𝑡 ≥𝐸 𝑐 (4)
Solving the equation gives us the width of the cured feature
𝑤 =2𝑟 =𝐾𝑑 √2ln𝑡 +2ln
𝐼 0
𝐸 𝑐 (5)
Equation (5) governs the size of a beam shape, which shows that simultaneously
increasing the exposure time and decreasing the aperture diameter can improve the feature
resolution. However, increasing the scanning speed will sacrifice the XY scanning position
resolution, which provokes a large scanning distortion. Also, the shape feature cannot be
changed only by tuning the exposure time. In comparison, decreasing the aperture diameter
can improve feature resolution without affecting the scanning position accuracy. This is
44
the major benefit of using the dynamic apertures to change the beam shape and size, as
discussed in our method. Also, we conducted dosage tests (i.e., finding the appropriate
scanning speed) for each aperture to compensate for the laser power change due to different
aperture diameters.
3.1.2 Hardware Prototype of Shaped Laser Beams
Figure 3-6 shows the schematic diagram of our prototype system. The scalable light
source is realized by switching the apertures with different scales and shapes. Small-scale
laser beams are used to define the geometry details while large-scale laser beams are
applied to cure the interior body of the object. The dynamic aperture in Figure 3-6 is
dynamically switched by a linear stage to the required size.
The fabrication process significantly improves the printing speed in two aspects. First,
only the boundary is built for each small layer. This can save a significant amount of
scanning time since the inner portion is not filled by the small laser beam. Second, the
separation time and recoating time for each small layer are significantly less. In each small
layer, only the boundary portion is cured, which is bounded with the constrained window;
such boundary portion can be easily separated and recoated due to the small area.
45

Figure 3-6: CAD model of the scale down SAM system.
We also have another implementation of the proposed shape laser beam, as shown in
Figure 3-7. Instead of using a linear stage to switch the apertures for the different laser
beam, this implementation utilizes a special grating filter to modulate the beam shapes. The
center of the grating filter is a 25 um hole, which is transmissive to both 405 nm and 445
nm. Beyond this hole, the center portion with 300um is full of nanograting pattern, which
can reflect 405 nm laser. Therefore, when the 405nm laser beam passes through this grating
filter, only the center with 25um is transmissive, and this results in a 25um laser beam. The
whole 445nm laser beam, instead, can entirely pass without any shape modulation. By
using this grating filter, the following setup combines two different laser beam into a single
setup, which realizes the idea of scaling down the resolution while keeping the building
volume.
46

Figure 3-7: Another implementation of shaped laser beams.
3.1.3 Multiscale Tool Path in XY Plane
Within each layer in the XY plane, a specific 2D pattern needs to be solidified by the
light sources. A large-scale light source, e.g., a large laser spot or a projector, will be used
to fill up the 2D pattern as much as possible, and the rest uncovered region will be filled
up by a small-scale light source, e.g., a small laser spot.
An algorithm to divide a sliced 2D layer into boundary and interior and to plan the
scanning paths for different size-scale laser beams is presented in this section. The
algorithm is inspired by the infeasible features identification method [127], in which a
computation method is presented to recognize the minimum feature size enabled by a 3D
printing machine to ensure the small features of an input CAD model can be fabricated.
47
Similarly, in the multi-scale SL process, we need to identify which regions can be cured
by a large size laser beam and which features require a small size laser beam instead.
Accordingly, different tool paths for both small and large size laser beams will be generated.
Our method is mainly based on two geometric operations: the grow- and shrink-based
offsetting operations with a distance r on a given solid S [128]. Suppose a ball is defined
as
r
b with radius r, the two offsetting operations can be defined as:
(1) S grown by r as
r r
b S S  =  , and
(2) S shrunk by r as
r r
b S S  =  .
We now introduce our multi-scale toolpath generation approach for the multi-scale SL
process. The algorithm structure is first presented followed by the algorithm
implementation.
Multi-scale toolpath generation
A toolpath p(r, h) is defined as a function of radius r and thickness h, which is
evaluated on every slicing at the desired resolution. Within each slice, the generation
process can be broken into two steps: (1) computing pA(rsmall, hthin) and pB(rlarge, hthin) on
the XY plane with thickness hthin, and (2) computing pC(rlarge, hthick) along the Z axis with
thickness hthick – this is the case when the interior of a large region is filled. Note that in
this study we only use three types of beam (pA , pB , pC) to illustrate the multi-scale
fabrication idea. Our method is general and can be used for more beam size and shape
variations.
Toolpaths on the XY plane.
48
In the algorithm, the key step is to determine the offset region of the large beam 𝑝 𝐵 .
Given a 2-dimensional loop defined in E
2
as shown in Figure 3-8 (bottom row), the interior
region D will be fabricated by toolpaths 𝑝 𝐴 and 𝑝 𝐵 . The region is first offsetted by the large
laser beam’s radius ↓
𝑟 , and we can obtain the start point at the top-left corner of 𝐷 ↓
𝑟 ⁡for
the toolpath. The tool tip (at center of beam) then sweeps from left to right and top to
bottom until it reaches the bottom-right corner in 𝐷 ↓
𝑟 , producing scanline pattern for pB.
Via subtracting the offset region of pB, D – 𝑝 𝐵 ↑
𝑟 is the rest of the region that is separated
for the small beam pA (Green outline in Figure 3-8). Toolpath pA is built upon the same
process. The overall procedure is illustrated in Figure 3-8. For toolpath planning with N
scales of beam, N-1 times of subtraction are performed to produce N number of toolpath
regions. The process will be terminated whenever the region is empty, since there will be
no starting point for current tool tip.
49

Figure 3-8: Exemplar Multi-scale tool paths for scale down SAM.
3.1.4 Benefits of Shaped Laser Beam
Figure 3-9 demonstrates the benefits of the presented multi-scale SL process. The
pyramids (a) and (d) were fabricated using a similar fabrication time. However, pyramid
(a), which was fabricated by the multi-scale process, has a much smoother slope surface
with a sharp corner. In comparison, a pyramid (d) was fabricated using the traditional layer-
based SL process, which shows typical stair-stepping defects.
50

Figure 3-9: Comparison between single scale fabrication and multi-scale fabrication. a) The
fabrication results based on multi-scale layer thicknesses - 20µm was used for the boundary, and
100µm was used for the inner portion; b) a close-up to show a high Z resolution; c) a close-up to
show a high XY resolution; d)-f) The fabrication results using a single layer thickness of 100µm.
The fabrication time based on the two methods is approximately the same. The scale bars in a) and
d) are 1mm, and the rest scale bars are 0.2mm.
The first multi-scale fabrication mechanism is to use shaped laser beams with different
sizes and shapes. A simple approach to achieve such shaped laser beams is discussed based
on switching the apertures on a plate. A small laser beam can be used to build shape details
while a large laser beam can be used to cure the interior region of the object. The second
multi-scale fabrication mechanism is to use multi-scale layer thicknesses in the Z axis,
which will be discussed in detail in Chapter 4.1. This novel multi-scale curing strategy
enables our fabrication process to be not only fast but also capable of achieving a high XYZ
resolution. The fabrication results based on the developed process have verified the benefits
of the multi-scale curing strategy.
51
Complex Parts with Multiscale Features
Shown in Figure 3-10, three more complex parts have been fabricated to verify the
proposed multi-scale tool path planning framework. The fabrication results based on the
accordingly planned tool path are shown in Figure 3-10. The successful fabrication of these
parts validates the proposed multi-scale fabrication process. Especially, the part “Lion” has
features ranging from the centimeter’s main body to tens of micrometers’ hairs.
Figure 3-10 shows the features at different scales that are fabricated by our multi-scale
SL process. The “Lion” part has been sliced into 500 layers using 20µm layer thickness. If
the slices are fabricated using the conventional SL process, the small laser beam needs to
scan the whole 500 layers, and after curing each layer a Z stage linear translation will then
be followed. On average, it will take ~90 seconds to cure the whole layer using a small
laser beam, and ~30 seconds for the Z stage to move up and down for a large distance so
that liquid resin can be recoated to build next layers. In comparison, our multi-scale
fabrication process saves time both in the XY plane and along the Z direction. In the XY
plane, only the boundary area will be cured by the small laser beam, while the interior area
is quickly cured by the large laser beam. Along the Z direction, for each small layer with
0.02mm thickness, only the boundary will be cured, and the Z stage only moves up by a
small distance of 0.02mm (refer Chapter 4.1 for details). The interior area will be cured in
every five layers using the large laser beam, and the Z stage will move up-and-down once.
Thus 4 out of 5 times of curing the interior area and moving the Z stage up-and-down would
be saved. Combining all these benefits, it only takes <20 seconds for each layer on average,
which is at least 6 times faster than the conventional SL process.
52

Figure 3-10: A complex test case with multi-scale features. Image color changes using different
microscopes.
3.1.5 Concluding Remarks
The section presents a novel scale down SAM process and the related tool path
planning framework for fabricating macroscale objects with microscale features. A major
contribution of our work is to present a multiscale fabrication mechanism within one layer
to optimize the fabrication speed, feature resolution, and scalability simultaneously. The
multiscale fabrication mechanism is to use shaped laser beams with different sizes and
shapes. A simple approach to achieve such shaped laser beams is discussed based on
switching the apertures on a plate. A small laser beam can be used to build shape details
while a large laser beam can be used to cure the interior region of the object. The fabrication
results based on the developed process have verified the benefits of the multiscale curing
strategy. This work was published on Journal of Micro and Nano Manufacturing [8] and
other related work are also published [9] [10].
53
3.2 Hopping Light Source: Up-Scale Energy
The second method to achieve SAM is increasing the building size while maintaining
the fabrication resolution, called scale up SAM. An XY linear stage is added into a micro
projection-based SLA process, which can enlarge the printing area by translating the whole
projection modular.

Figure 3-11: The idea of scale-up SAM.
3.2.1 The Principle of Hopping Light
The idea of this process is dividing one layer in a large area into a set of small sections,
which will be cured one by one. The transition between the sections will be realized by
moving the projector system using the XY linear stage. However, unlike the traditional
discrete movement of a projector system, the DMD system in our setup moves
continuously, while the image for a particular section will be fixed at that area by using a
galvo-mirror (a rotating mirror) to create a complementary reverse motion to cancel out the
projector’s movement. Hence, by incorporating both XY linear stage and the galvo-mirror,
the mask video projection process can generate mask images at a set of fixed positions to
54
solidify 3D object while maintaining a fast-moving speed to quickly cover a large building
area.

Figure 3-12: Scale up SAM process schematic. (a) The schematic principle of proposed moving
light SLA. An XY linear stage moves the light beam, which is also rotated by a galvo mirror during
the moving. (b) Each exposure covers a small portion of the large building area. (c) The rotating
mirror can tilt the light beam so that the projected image stays at a fixed position.
Built on a conventional SL process, we used a relay lens to image the DMD pattern
onto the focal plane with 1:1 magnification. The whole optical module is mounted on an
XY linear stage. The projected image’s motion is a combination of an XY stage and a galvo-
mirror rotation. After passing a reflective mirror, the light beam projects up to a tank
containing liquid resin. The Z-axis lifts the platform, which carries the 3D printed objects.
55

Figure 3-13: Schematic of the optical design of the proposed scale-up SAM process. The rotating
mirror is used to correct the motion blur introduced by the moving of the linear stage.
The overall fabrication flowchart is shown in Figure 3-14. An input 3D model is first
sliced into many 2D layers. Each layer is further divided into many adjacent sections. For
sections in the same row, the DMD projects mask images one section after another while
keeping moving continuously. After one row is solidified, the DMD system shifts to the
next one, and the process is repeated by the continuously moving projection light. When
all the rows are finished, the Z stage lifts to separate the fabricated layer with the tank and
to refill fresh resin with given layer thickness. The process is repeated until all the layers
are finished. The fabricated 3D object can be taken out and sent to post-processing.
56

Figure 3-14: Process flowchart of the scale-up SAM. The input 3D model is sliced into layers, and
each layer is divided into sections. The projector continuously covers the sections in the same row
and then shifts to the adjacent row.
Motion Synchronization
Our proposed system consists of three critical actuation systems: an XY linear stage,
a galvo mirror, and a DMD-based light engine. These three actuation systems are required
to move jointly so that the projected image can cure a small section of the large building
area without any motion blur, and then rapidly switch to the next section using the fast
motion provided by the galvo mirror. Figure 3-15 a) shows the motion synchronization
framework. We first synchronize the galvo-mirror rotation and projector transition via a
micro-controller. This synchronization means two aspects, 1) the same starting time, and
2) a proper rotation to transition speed ratio, such that the projected image can stay at a
fixed position. The same starting time is guaranteed through the microcontroller to generate
a synchronization signal. The speed ratio is calibrated so that the projected image is not
moving. A microscope is installed in our prototype system to assist in observing whether
the image moves or not.
57

Figure 3-15: Motion synchronization framework in hopping light. a) The hardware framework of
motion synchronization, b) the motion relationships among the actuators.
The master controller is an 8-axis joint motion controller, KFLOP from dynomotion
(Calabasas, CA) KFLOP generates synchronized signals for all three actuation systems.
The XY linear stages are lead-screw based stages with stepper motors. The stepper motor
driver is KSTEP from dynomotion. The galvo mirror is purchased from Sunny Technology
(Beijing, China). This large galvo mirror can reflect a light beam with a diameter of 12mm,
which is sufficient for our purpose. The galvo mirror is essentially driven by a DAC motor,
and the corresponding driver and controller are also from Sunny Technology. This DAC
motor controller can be programmed before running, and the commands are stored in the
buffer. Then the DAC motion can be triggered by a TTL signal, which is generated by the
KFLOP so that we can synchronize the galvo mirror and the stages. As for the DMD-based
light engine, we used a PC’s timer API to synchronize and control the exposure time.
Figure 3-15 b) shows the joint motion relationship among the galvo mirror, the XY
stages, and the light engine. We can see that, due to the correction of galvo mirror, the
58
image position maintains steady while the stage position is moving, and then rapidly jump
to the next section’s position (in sec).
Motion Blur Correction
Due to the motion of the DMD device, the projected image will be blurred if the image
is not constantly refreshed after moving each pixel’s distance. Figure 3-16 shows the issue
of motion blur when the DMD is continuously moving during the light exposure. Figure
3-16 b) shows the blurred image captured at the focal plane by a microscope. In Figure
3-16 b), we can observe that the bright dots are moved so that they form darker lines, just
as the motion blur issue in photography. Such blurred image leads to blurred printed
features and even under-cured features. The key idea of our research is to use a rotating
mirror (a galvo mirror) to compensate the X stage linear motion and to guarantee the
projected image is just static when the X stage is moving, and no motion blur exists, as
shown in Figure 3-16 c).

Figure 3-16: An illustration of the motion blur issue in hopping light. a) If the light beam is not
moving and static, the projected image is static with no blur, b) the projected image is blurred when
the light beam (projector) is moving during the light exposure; and c) if a rotating mirror
59
continuously compensates the stage's motion, the projected image can also be static with no motion
blur.
3.2.2 Automatic Calibration via Computer Vision (ACCV)
In order to improve the performance of our mask video project SL system, several
calibrations are required. First, we should first calibrate the individual motion of each
actuation systems (the mirror, the XY stages, and the DMD-based light engine). Second,
the speed ratio between the X linear stage and the galvo mirror should be calculated based
on the individually calibrated motion of the linear stage and the mirror. Only the right ratio
can correct the motion blur. Also, the image size should be computed based on the
individual motion of the X linear stage and the DMD projection patterns, so that the system
can update the image precisely after the linear stage moves one image size’s distance.
Thirdly, the whole layer is cured with successive multiple exposures. The edges between
different exposures should be well stitched.
The calibrating optics is designed as below:

Figure 3-17: Calibrating optics in hopping light. We mount a microscope to capture the projected
image on the plane of resin polymerization.
The whole calibration pipeline is summarized in Figure 3-18.
60

Figure 3-18: Calibrating pipeline. Step 1: estimate the motion of each actuator in the microscope
image space; step 2: correct the motion blur by calculating the ratio between actuators; step 3: fine
tune the image pattern to ensure seamless stitch.
We utilized a computer vision toolbox in MATLAB to do the calibration above. The
computer vision toolbox provides feature-based image matching.
Computer vision assisted image motion estimation
The goal of the motion synchronization is to ensure that there is no motion blur during
the moving. We mounted a microscope (Pluggable USB microscope with 2M pixels, 250x
magnification, from Plugable ) to capture the projected image on the focal plane. If the
projected image from this microscope is not moving when the linear stages move, then
there will be no motion blur for our photo-polymerization.
To detect whether the captured image is moving or not, we performed image
processing algorithms to analyze these captured images. Correctly, the computer vision
toolbox from MATLAB is picked to do such image processing and to estimate the motions
between two images. The motion estimation algorithm has three steps: 1) detecting the
SURF (Speeded-Up Robust Features) features of two images; 2) matching the SURF
61
features between two images, and 3) estimating the transformations of these two images
based on the matched SURF features.
In our calibration pipeline, we intensively utilized this motion estimation tools to
estimate the image motion when the system’s actuators move. All the three actuation
systems (the XY linear stage, the galvo mirror, and the DMD patterns) can lead to changes
in image positions captured by the microscope. We first characterized all these three
actuators’ motion in microscope image space. Moreover, by calculating their motion
relationships, we can correct the motion blur with synchronized motion.
Motion Estimation of Individual Actuation System
In this subsection, we calibrate the individual motion of each actuator in the
microscope image space. By “image space” here and after, we mean the images captured
by the microscope.
⚫ Calibration of projected pixel size in the microscope image space
The first calibration we performed is to measure the size of the projected image. Our
optical system is designed to have 1:1 relay imaging, i.e., the projected image size is the
DMD chips size. However, in practice, the magnification ratio will slightly deviate from
1:1 due to the fine-tuning adjustment. To measure the image size, we projected two image
patterns (the second image is 38 pixels offset from the first one as shown in Figure 3-19a))
and capture two images by the microscope (Figure 3-19 b)). Then we run the image
processing algorithm with these two microscope images. Figure 3-19 e) shows the
estimated motion, and Figure 3-19 f) shows the calibrated offset.
62
The algorithm estimates the image motion vector as (34.9753,0.6419) (unit: a pixel
in image space), which means comparing the first captured image and the second captured
image is 0.6419 pixels offset along the height direction and 34.9763 pixels offset along the
width direction. Because the input two image patterns have 38 pixels offset, hence, we can
know that each pixel in the image pattern has the width of
|(34.9753,0.6419)|
38
=0.9206 pixels
This value indicates the physical one pixel at the focal plane has the size of 0.⁡9206
pixels in the microscope image.
Also, the motion vector in microscope image space is computed as
𝐶⃑
𝑃 𝑥 =(𝑐 1
𝑃 𝑥 ,𝑐 2
𝑃 𝑥 )=
(34.9753,0.6419)
38
=(0.9204,0.0169).
(6)

Figure 3-19: Calibration of the projection pixel size in microscope image space.
⚫ Calibration of the X stage motion in the microscope image space
63
Figure 3-20 shows the calibration of the X stage’s motion. We captured one image
first and then moved the x stage with 1 millimeter, and then captured the second image.
The image processing algorithm estimates the image motion as 𝐶⃑
𝑋 =(𝑐 1
𝑋 ,𝑐 2
𝑋 )=
(122.3538,5.0379)⁡pixels .
This vector indicates that if the X stage moves 1mm forward, the captured image will
move 122.3538 pixels along the width direction and 5.0379 pixels along with the height
direction.

Figure 3-20: Calibration of the X motion in the image space.
⚫ Rotation Angle in the microscope image space
To measure the galvo mirror rotation angle in the image space, we again captured one
image first and then rotated the galvo mirror with 0.36 degree, and then captured the second
image using the microscope.
The two captured images at two galvo mirror positions (the angle between these two
positions is 0.36 degree) are shown in Figure 3-21. By running the image processing
64
algorithm, we estimated the image motion as (−94.3139,−2.2479) (unit: pixel in image
space). This result shows that if the mirror rotates 1 degree, then the image will move
𝐶⃑
𝑅 =(𝑐 1
𝑅 ,𝑐 2
𝑅 )=
(−94.3139,−2.2479⁡)
0.36
=(−261.9831,−6.2442)⁡pixels
(7)
which means, if the galvo mirror rotates 1 degree forward, the captured image will
move -261.9831 pixels along with the width and -6.2442 pixels along with the height.

Figure 3-21: Calibration of the rotation angle in the image space.
The above three calibrations give detailed procedures on how to calibrate the
individual motions of the X linear stage, the galvo mirror, and the DMD-based image
pattern from the captured images. We summarize the individual calibration results in Table
3-1.
Table 3-1: Individual calibration of each actuator
Actuator Actuator’s Motion Estimated Image Motion (Pixels in Microscope)
X Linear Stage 1 millimeter
𝐶⃑
𝑋 =(𝑐 1
𝑋 ,𝑐 2
𝑋 )=(122.3538,5.0379)
65
Galvo Mirror 1 degree
𝐶⃑
𝑅 =(𝑐 1
𝑅 ,𝑐 2
𝑅 )=(−261.9831,−6.2442)
DMD pattern 1 pixel
𝐶⃑
𝑃 𝑥 =(𝑐 1
𝑃 𝑥 ,𝑐 2
𝑃 𝑥 )=(0.9204,0.0169)

Motion Blur Correction
Based on the individual calibrated results, we can compute the exact speed ratio and
the moving distance for each mask image exposure. The galvo mirror is added to cancel
image blur introduced by the motion of linear stage. The motion of the projected image on
the focal plane is the composite motion of the linear stage and the rotation of galvo mirror
α𝐶⃑
𝑅 +𝛽 𝐶⃑
𝑋 , where 𝐶⃑
𝑅 𝑎𝑛𝑑 ⁡𝐶⃑
𝑋 represent the motion vector caused by the motion of galvo
mirror, X stage, and 𝛼 ,𝛽 are the galvo mirror rotation speed and X stage moving speed
respectively. Because the projected image needs to be static during the motion of the linear
stage, the required composite motion of the projection image is zero, i.e.
α𝐶⃑
𝑅 +𝛽 𝐶⃑
𝑋 =0
⃑⃑
.
(8)
However, this condition cannot be satisfied, 𝐶⃑
𝑅 𝑎𝑛𝑑 ⁡𝐶⃑
𝑋 are not parallel (𝐶⃑
𝑅 ×𝐶⃑
𝑋 ≠
0). Ideally, if the optical module and the linear stage are well aligned, these two image
motions should be parallel. But, in our implementation, there is a slight angle between these
two motions. Based on the calibration this angle is:
𝜃 𝑋𝑅
=cos
−1
(𝑐 1
𝑋 ,𝑐 2
𝑋 )⋅(𝑐 1
𝑅 ,𝑐 2
𝑅 )
|(𝑐 1
𝑋 ,𝑐 2
𝑋 )|⋅|(𝑐 1
𝑅 ,𝑐 2
𝑅 )|
=0.99 degree (9)
Considering this angle, we need to translate the Y linear stage to ensure the composite
motion of the projected image is static. That is, the composite motion of the galvo mirror,
X stage and Y stage are zero:
66
α𝐶⃑
𝑅 +𝛽 𝐶⃑
𝑋 +γ𝐶⃑
𝑌 =0
⃑⃑
,
(10)
where, 𝐶⃑
𝑌 represents the motion vector introduced by the Y stage, and 𝛾 is Y stage
moving speed. Here we assume XY stages are perpendicular, then we can immediately
obtain 𝐶⃑
𝑌 =(𝑐 2
𝑋 ,−𝑐 1
𝑋 ).

Figure 3-22: Schematic drawing of computing the motion blur correction
By solving the above linear equation, we can obtain the speed ratios:
𝛼 𝛽 =−
𝐶⃑
𝑋 ⋅𝐶⃑
𝑋 𝐶⃑
𝑅 ⋅𝐶⃑
𝑋
𝛼 𝛾 =−
𝐶⃑
𝑌 ⋅𝐶⃑
𝑌 𝐶⃑
𝑌 ⋅𝐶⃑
𝑌
𝛾 𝛽 =
𝛼 𝛽 /
𝛼 𝛾 =
𝐶⃑
𝑋 ⋅𝐶⃑
𝑋 𝐶⃑
𝑅 ⋅𝐶⃑
𝑋 /
𝐶⃑
𝑌 ⋅𝐶⃑
𝑌 𝐶⃑
𝑌 ⋅𝐶⃑
𝑌 =
𝐶⃑
𝑅 ⋅𝐶⃑
𝑌 𝐶⃑
𝑅 ⋅𝐶⃑
𝑋
(11)
By plugging the values calibrated in our system, the speed ratio between the galvo
mirror and the X linear stage is calculated as:
𝛼 𝛽 =0.4674
𝑑𝑒𝑔𝑟𝑒𝑒 𝑚𝑚
, (12)
That is, if the X linear stage moves 1mm, the galvo mirror needs to rotate 0.4670
degrees, so that the projected image can stay at the same position. With the calibrated ratio
between these two motions, the combined motion of the projection image is static. Hence
no blur motion of the mask image exists when curing a section of a layer.
The speed ratio between the Y linear stage and the X linear stage is calculated as:
67
𝛾 𝛽 ==0.0173
(13)
This value shows that, if the X linear stage moves 1mm, the Y linear stage needs to
move 0.0173 mm so that the moving direction can be parallel to the image motion of the
galvo mirror, and hence the motion blur can be corrected. Although this value is small, it
will cause 0.0173∗6mm=0.1040 mm deviation for every exposure, which is not
acceptable, if not considered.
By applying this speed ratio, we recapture the images at two positions, as shown in
Figure 3-23. The images have less than a half pixel’s motion. The overlapped images
indicate that by the synchronized motion, the motion blur is removed within a pixel. The
images shown in Figure 3-16 c) also verify that the synchronized motion can correct the
motion blur between the Galvo mirror and the X linear stage.

Figure 3-23: Synchronized motion in hopping light
Physical size of the projected image
68
From the individual calibration, we can compare the X linear stage motion and the
projection image size in the image space, and obtains that the physical size of each pixel at
the focal plane is
𝑤 𝑝 =
|𝑐 1
𝑃 𝑥 ,𝑐 2
𝑃 𝑥 |
|𝑐 1
𝑋 ,𝑐 2
𝑋 |
=7.517⁡𝜇𝑚 .
(14)
This value is very close to the theoretical pixel size. The amplification factor is 1.0 in
our optical system, and the physical size of the pixel in the DMD chip is 7.5 𝜇𝑚 .
Therefore, the projected image size is
𝑆 𝑋 =7.517μm⋅800=6.013⁡mm
𝑆 𝑌 =7.517μm∗1280=⁡9.622⁡mm
(15)
Image Stitch
After the motion blur has been corrected, we tried to fabricate one layer and observed
that the edges at different exposures are not well stitched, as shown in Figure 3-24 a). This
problem comes from the fact that the orientation of the projected image is not parallel to
the Galvo mirror’s rotation direction, which introduces the misalignment among exposures,
as shown in Figure 3-24 b).
69

Figure 3-24: Misalignment: the non-parallel moving direction and image orientation
The angle between the orientation of the projected image and the Galvo mirror’s
rotation direction can be computed as
𝜃 𝑃 𝑥 𝑅 =cos
−1
𝐶⃑
𝑃 𝑥 ⋅𝐶⃑
𝑅 |𝐶⃑
𝑃 𝑥 |⋅|𝐶⃑
𝑅 |
(16)
To solve the problem, we offset the image pattern for each section to follow the
moving direction accordingly. For two adjacent exposures, the image should offset
𝑊𝑖𝑑𝑡 ℎ⋅tan(𝜃 𝑃 𝑥 𝑅 )=800⋅tan(𝜃 𝑃 𝑥 𝑅 )=14⁡𝑝𝑖𝑥𝑒𝑙𝑠 . (17)
where 800 is the number of pixels along the X stage direction, which is the width of
the DMD pattern, 𝜃 𝑃𝑅
is the angle of the mirror rotation direction and the image orientation.
Figure 3-24 c) shows the corrected image stitch based on the strategy.
By considering the orientation, we can fine-tune the image stitch to achieve seamless
overlapping between adjacent image sections, as shown in Figure 3-25.
70

Figure 3-25: The image stitch adjustment ensures a seamless stitch between adjacent exposures.

In this section, we mainly discuss how to use computer vision algorithms to calibrate
the process’s motion parameter automatically. The proposed calibration pipeline has three
steps. Firstly, all the actuators’ motion are calibrated in the microscope image space, and
three motion vectors are obtained: microscope image motion vector 𝐶 𝑋 when X stage
moves 1mm, microscope image motion vector 𝐶 𝑅 when Mirror rotates 1 degree,
microscope image motion vector 𝐶 𝑃 𝑥 when the planned image pattern shifts 1 pixel along
the X axis. Then, based on these three vectors, we compute the speed ratio of the mirror
rotation to the X stage translation, and the speed ratio of Y stage to the X stage translation
in order to compensate the angle between X stage and the mirror rotation. Lastly, reusing
the three vectors, we calibrate the angle between the image orientation and mirror rotation,
and compute the offset of the image along Y axis to compensate this angle.
71
3.2.3 Tilted Focus Analysis
To eliminate the motion blur, we introduced the galvo mirror to compensate for the
image motion. However, the rotation of the light beam potentially tilts the image and
defocuses the projection image on the building plane. This section tries to analyze the
focusing issue of a tilted image.
Focus error by tilting the image
The following figure shows the focus errors when the projector shifts from the well-
focused position to a neighboring position by a small distance.
dx
x
y

Figure 3-26: An illustration of the focus error by tilting the image.
For a pixel (x, y) in an image, the well-focused length should be ( )
0
, f x y , while after
the projector shift dx, the focal length changes to ( ) ,
dx
f x y . The focus error should be
𝑑𝑓 =𝑓 𝑑𝑥
(𝑥 ,𝑦 )−𝑓 0
(𝑥 ,𝑦 )=√(𝑥 +𝑑𝑥 )
2
+ℎ
2
−
√
𝑥 2
+ℎ
2
,
(18)
where h is the distance between the gyro mirror and the image plane.
Figure 3-27 shows the focus error of all the pixels when the parameters are set as ℎ=
110⁡𝑚𝑚 .
72

Figure 3-27: Focus error distribution on one image
From Figure 13, we can see that the max error locates on the corner of the image.
Notice that the maximum focus error is
𝑑 𝑓 𝑚𝑎𝑥
=√(𝑥 +𝑑𝑥 )
2
+ℎ
2
−
√
𝑥 2
+ℎ
2
≤
𝑑𝑥 (𝑑𝑥 +2𝑥 )
2ℎ

(19)
Plugging the parameters in the prototype, we have
𝑑 𝑓 𝑚 𝑎𝑥
=
𝑑𝑥 (𝑑𝑥 +2𝑥 )
2ℎ
=
6∗(6+2∗6)
2∗110
𝑚𝑚 =0.49⁡mm
(20)
The allowable depth of focus Δ can be estimated as⁡[129]
Δ=2CN
v
𝑓 =2𝐶 𝑣 𝐷 =2∗0.01∗
120
25.4
=0.09 (21)
Hence, the max focus error exceeds the allowable focus depth. To resolve the
defocusing issue, we propose a strategy of fractional movement, in which the moving 𝑑𝑥
is only be fra action of a projection image size. Consequently, the focus error can be
reduced to be smaller than the allowable focus depth.
Method to reduce focus error: reducing the tilting angle
73
Therefore, if the moving distance of the projector stays in the controlled value during
the whole process, the max focus error will be acceptable (smaller than the allowable focus
depth). This indicates that once the projector moves to the critical position, the gyro mirror
should start a new rotation cycle, and the DMD device should prepare a new mask image
to project on the building plane (refer to Figure 3-28).
Target Image
Projector Motion
Gyro Mirror Navigation
Image Motion
Cycle 1 Cycle 2 Cycle 3 Cycle 4

Figure 3-28: Reducing the tilting angle to reduce focus error
If the moving distance for one mirror rotation is a fraction of the image size, say
1
𝑛 𝑥 ,
then the focus error would be
𝑑 𝑓 𝑚𝑎𝑥
=
⁡
1
𝑛 𝑥 (⁡
1
𝑛 𝑥 +2𝑥 )
2ℎ
=(
1
𝑛 +
1
2𝑛 2
)
𝑥 2
ℎ

(22)
By introducing cycle, one section can be exposed by several images, which will reduce
the moving distance for each image, and accordingly reduce the tilt angle. Eventually, the
max focus error can be reduced down to the acceptable error of the projection system.
Figure 3-29 shows that the max focus error will decrease with more cycles used for one
image.
74

Figure 3-29: Focus error related to the number of cycles
In Figure 3-29, the max error reduces to 0.043mm⁡if the moving distance is 1/8 of the
image size, which is smaller than half of the depth of focus
Δ
2
=0.045mm . Eight cycles
for one image means the projector should project eight images within the exposure time
(800 milliseconds) for one image. It is feasible for any projector with a refresh rate of 60
Hertz.
For a given depth of focus Δ, we have
𝑑 𝑓 𝑚𝑎𝑥
≤
Δ
2
,
(23)
which gives us
𝑛 ≥
1
√
1+
ℎΔ
𝑥 2
−1

(24)
0 2 4 6 8 10 12 14 16 18 20
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
X: 8
Y: 0.04339
n: cycles for one image
df
max
: max focus error
max focus error at different number of cycles
75
where ℎ is the distance between the mirror and the focal plane, Δ is the depth of focus,
and 𝑥 is the image size. This value is the number of cycles which we should decompose
one image size into. In our prototype, the required number of image cycles is
n≥
1
√
1+
110∗0.09
6
2
−1
=7.4
(25)
Hence, it is safe to set the number of image cycles as 8.
In this section, we analyze the focus of a tilted image system. To solve the defocus
issue introduced by image tilting, we propose a fractional motion method, in which the
moving distance for each mirror rotation cycle is only a fraction of the image size. This
can largely reduce the defocus effect, and we also derive the required number of cycles for
one image such that the defocus is acceptable.
3.2.4 Benefits of Hopping Light
This section analyzes the performance of the proposed process, including the
fabrication efficiency, fabrication area, and feature resolution. In this section, theoretical
analysis of the characteristic of the developed multi-scale fabrication process is presented.
We first present how to control the beam shape for different sizes. We then explain the
process of recoating resin. Finally, we discuss the appropriate fabrication speed based on
the analytic results.
As mentioned above, a continuous moving light is generated by synchronizing the XY
stage and the galvo mirror, so that the projected image could stay at a fixed position as a
result of the combined motion. Figure 3-30 b) shows how the image position is combined.
Notice that the rotating angle of the galvo mirror in Figure 3-30 b) has rapid jumps
76
periodically, which lay the foundation of the continuous moving light. The “image position”
curve is the desired image motion such that the image could steadily be exposed to each
section.
Target Image
Projector Motion
Gyro Mirror Navigation
Image Motion
Image 1
Projector Position
Image Position
Mirror Rotating Angle
Image
1
Image
2
Image
3
Image
4
Image
5
Image
n
Time
Positio
n
Time
Image 2 Image 3 Image 4
a)
b)

Figure 3-30: Composite motion of hopping light.
By comparing to the traditional discrete projector movement, the building speed is
significantly improved. The required time for fabricating one section in the traditional stop-
and-go process is determined as:
𝑡 𝑑𝑖𝑠 =𝑡 𝑐𝑢𝑟𝑒 +𝑡 𝑡𝑟𝑎𝑛𝑠 =
{

𝑡 𝑐𝑢𝑟𝑒 +
𝐿 𝑣 +
𝑣 𝑎 , 𝑖𝑓 ⁡𝐿 >
𝑣 2
𝑎 𝑡 𝑐𝑢𝑟𝑒 +2
√
𝐿 𝑎 , 𝑜𝑡 ℎ𝑒𝑟𝑤𝑖𝑠𝑒 (26)
Where 𝐿 is the image size, v is the maximal speed of the linear stage, and a is the
maximal accelerations.
In comparison, by using the continuous moving light, our building time for one section
is only
𝑡 𝑐𝑜𝑛
={
𝑡 𝑐𝑢𝑟𝑒 , 𝑖𝑓 ⁡𝑡 𝑐𝑢𝑟𝑒 >𝐿 /𝑣 𝐿 /𝑣 , 𝑜𝑡 ℎ𝑒𝑟𝑤 𝑖𝑠𝑒
(27)
Hence, the time ratio between the conventional process and our process is
77
𝑡 𝑑𝑖𝑠 𝑡 𝑐𝑜𝑛
=
𝑡 𝑐𝑢𝑟𝑒 +𝑡 𝑡𝑟𝑎𝑛𝑠 𝑡 𝑐𝑢𝑟𝑒 =1+
𝑡 𝑡𝑟𝑎𝑛𝑠 𝑡 𝑐𝑢𝑟𝑒 (28)
Depending on the curing time for each section, the fabrication speed ratio could reach
max{
𝑡 𝑑𝑖𝑠 𝑡 𝑐𝑜𝑛
}=1+2
√
𝑣 2
𝑎𝑠

(29)
which could be a very huge speedup if the linear stage has a large speed-to-
acceleration ratio, where the stage needs a long time to accelerate and deaccelerate.
Figure 3-31 compares the effect of continuous moving light and discrete moving light.
V
t
Time for discrete motion
Time for continuous motion

Figure 3-31: Efficiency comparison between discrete motion and continuous motion
In our implementation, the image size is 𝐿 =6mm , the maximal speed of the linear
stage is 𝑣 𝑚𝑎𝑥
=10mm/s, and the maximal acceleration is a
𝑚𝑎𝑥
=20⁡mm/s
2
. When we
set the curing time for each exposure as 𝑡 𝑐𝑢𝑟𝑒 =0.8𝑠 , the speedup is 2.375X. If we reduce
the layer thickness, then the curing time will be reduced. Our process becomes significantly
faster in the high Z resolution printing scenario.
78

Figure 3-32: The fabrication speedup using the hopping light source.
It is also interesting to compare our proposed process with continuous moving using
a very high refresh rate projector. Besides the high cost of the projector, such process is
also not feasible in a high Z resolution scenario. It is because, in the high-resolution
scenario, the curing time is very short (which could reach 100 ms), and the projector needs
to refresh 800 images (for the image size 1280×800), which means the refresh rate
reaches as high as
800
0.1
=8000. It is not feasible for current projectors available in low cost.
A special controller is required for such a high refresh rate. This refresh rate will become
even higher if the layer thickness continues to drop down. Another issue of this high
refreshing process is that the projected image is blurred to some extent due to the sweeping
of pixels in the continuous movement of the projector.
Hence, by these comparisons, our proposed process has better performance, especially
when the layer thickness is small. Our current setup could fabricate parts with 200mm size.
As mentioned before, our process has advantages in a high Z resolution scenario, which
79
could achieve 10 m in our current setup. Moreover, the lateral resolution is determined
by the projected image size. Current the image size is around 9.6𝑚𝑚 ∗6𝑚𝑚 (for
1280×800 pixels), and hence the resolution for each pixel is around 7.5𝜇𝑚 .
The parameters for the prototype are:
Table 3-2: Parameters of the hoppling light prototype system
Time for a Single Exposure 800ms
Image Size 6mm  9.6mm
Tested Image # 132 = 26
Tested Large Image Size 78mm  19.2mm
Cycles Per Image 8
Stage Travel Capability 200mm  100mm  100mm
Maximum Travel Speed 10mm/s
Distance between Mirror and the Focal Plane 110mm
Light Wave Length 405 nm
Layer Thickness 0.02mm
Resin Refilling Time 20s
Fab Time for 1 Cube Centimeter 0.37hr

Comparing with other SL processes
As discussed in the “Introduction” section, many novel SL processes have been
developed to address issues in the SL process. We compare our multi-scale SL process
with some representative SL processes in literatures, including the laser-based SLA (LSL)
[84], the projection-based micro SLA (PuSL) [77], the two-photon polymerization (TPP)
[130], the continuous interface liquid production (CLIP), and the large area projection-
based micro SLA (LaPuSL) [21].
Table 3-3 lists the details of the comparison. We compared these processes in five
primary fabrication metrics, including part size, feature resolution, part-size-to-feature-size
ratio, fabrication speed, and cost. The data in Table 3-3 is estimated from the referenced
80
official website or the published paper. The ratio is calculated as the ratio part size to
feature size. As shown in Table 3-3, the conventional SL processes face trade-offs among
fabrication speed, resolution, scalability and cost. The components of our setup are all off-
the-shelf. The total cost of the setup is less than six thousand dollars. To the best of our
knowledge, no other fabrication processes can provide such a combination of large
fabrication part, micro-scale features, fast fabrication speed, and low cost.
Table 3-3: Comparison between different SL processes
Metric LSL PuSL TPP CLIP LaPuSL Two Beams
Ours
Part Size
(mm)
125 3 0.2 141 80 40 75
Feature Size(um) 155 3 0.1 75 5 30 7.5
Ratio 800 1000 2000 1900 16000 1333 10000
Layer thickness (um)
25 5 - 1 5 20 20
Speed
/1cm
3
(hr)
6 300 3000 0.1 6 3 0.4
Cost $$ $$$ $$$$ $$$$ $$$$ $ $$

3.2.5 Experimental results
The proposed SL process offers a cost-effective and robust moving light method to
fabricate high-resolution features over a large area with good throughput. We used CAD
models with various geometrical complexity and sizes to verify the capability of the
presented multi-scale SL process.
Test 1: Small features
To test the printing of small features, we designed image patterns with only a few
pixels. Table 3-4 shows that we can successfully fabricate smaller features with 2, 3 and 5
81
pixels. Moreover, the feature size is around 19 m, 27 m and 50 m, respectively. These
small dots are uniformly printed over a large area of 75mm  19.2mm.
Table 3-4: Printing small features

Test 2: Human Lung Slice
The single image resolution is 1280  800 pixels. To verify the moving light capability,
we picked a test image pattern with resolution 4000 2560, as shown in Figure 3-33 a). This
image pattern is divided into 5 2 = 10 sections. Figure 3-33 b)-f) shows the fabricated
results. We did not observe the stitch edges, which indicates that different exposures are
seamless connected. The tiny “finger” in Figure 3-33 f) is around 37 m.
82

Figure 3-33: Fabrication of a complex large area pattern. a) The design image pattern with
4000*2560 pixels; b) the printed part; c)-f) the details of the printed part. Scale bars shown in the
figures are b) 10mm, c) 500 m, d) 200m, e) 500 m, and f) 200 m.
Test 3: Branches and Roots
We tried to fabricate an image pattern with 10K resolution. Moreover, this image
pattern is divided into 13 2 = 26 sections. The fine details in Figure 3-34 c)-e) validate our
methods, and more importantly, these fine features are uniformly fabricated over the very
large building area 78mm  19.0mm.
We should mention that the building area is only limited by the travel range of our
prototype system. We can fabricate parts with size 200mm  100mm  100mm based on
our current implementation. Moreover, an even larger size can be easily achieved by using
XY linear stages that have a larger moving distance.
83

Figure 3-34: A complex pattern with 10K resolution. a) image pattern of one layer. b) the printed
part. c)-e) are details of the printed result. Scale bar: b) 10mm, c) 500um, d) and e) 200um.
Test 4: Triangles at different scales
An image pattern with triangles at different scales was designed to illustrate the
multiscale capability of the proposed SL process. We used the proposed moving light
process to fabricate one layer of the designed pattern. The printed results are shown in
Figure 3-35 b)-f). The results show that we can uniformly obtain 50um holes among a large
area with 80mm length.
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Figure 3-35: Printing fractal shapes. a) Designed triangle pattern at different scales;
b) shows a single layer (as printed), and c)-f) reveal the detailed shapes at different scales.
Scale bars: c)-d) 500 m, e) 200 m, and f)100 m.
Test 5: Periodic walls
We designed an image pattern with repeated walls, and the width of the wall is about
100 m and the repeating pitch is 600 m. Notice that the whole printing area is 80mm, and
the printed results are shown in Figure 3-36 with the wall features uniformly distributing
on the large printing area.
85

Figure 3-36: A test case of periodic walls. a) shows the “wall” pattern design, and b)-d) are as
printed results with 4 layers, each layer thickness is 40 m. Scale bar are: b) 500 m, c) 200 m, and
d) 100 m.
Test 6: Grating
To validate the bonding between successive exposures, we designed the grating
patterns as shown in Figure 3-37 a). Figure 3-37 b) and c) show that no visible bonding
defects. Moreover, Figure 3-37 d) shows the details of the bonding between two exposures.
The smooth transition of two exposures at the bonding validates the proposed moving light
process.
86

Figure 3-37: Printing grating patterns. a) Grating design. b)-d) show the printed part. Scale bar: b)
and c) 500 m, and d) 100 m.
Test 7: Pillar Array
Figure 3-38 demonstrates the fabrication of 3D objects. Figure 3-38 a)-c) show the
CAD design of the pillar array. The design is an array of conical pillars. The repeating pitch
is 600 m and each pillar has a 120 m bottom and 30 m. The height of each pillar is 2mm.
The layer thickness is 40 m and there are 50 layers in total. Figure 3-38 g)-k) illustrate
the as-printed results. The printed pillar has a 30 m tip, as shown in Figure 3-38 k). In total,
there are 4000 pillars to print with a similar quality.
87

Figure 3-38: Printing thousands of micropillars. a)-c) show the design of the pillar array. d)-f) are
the sliced image pattern. g)-k) are the microscope captured image for the printed result. Scale bar:
g) 10mm, h)-i) 500 m, j) 100 m, and k) 20 m.
Test 8: Freeform object
To demonstrate our process’s capability of fabricating freeform parts, we printed a 3D
fish as shown in Figure 3-39. Each layer is divided into 5×2 sections. The fabrication of
this 3D object verified the capability of our mask video projection based SL process.

Figure 3-39: Printing free form object using hopping light
88
3.2.6 Concluding Remarks
The section introduced a novel scale up SAM for fabricating three-dimensional macro-
scale objects with micro-scale features. A significant contribution of our work is to develop
the concept of continuous hopping light to optimize the fabrication speed, resolution, and
scalability at the same time. By utilizing a galvo mirror to compensate the image motion
caused by the motion of the linear stage, our method can successfully correct the motion
blur and enable continuous moving light SL process with a low projector refresh rate and
larger building volume. We provided a detailed methodology of how to construct the
motion synchronization and how to calibrate the parameters using computer vision
algorithms. Also, we proposed fractional moving distance to reduce the defocus of the tilted
image. Theoretical and experimental results have verified that the proposed method can
successfully fabricate 3D objects with macro-scale size with micro-scale features.
The proposed scale-up SAM could largely improve the fabrication efficiency and size,
and hence improve the scalability of SLA.

89
3.3 Hybrid Light Source: Integrated-Scale Energy
The third method to achieve SAM is combining a high-resolution laser and a large
area projector into a single process. The hybrid-source SLA manufacturing process
essentially integrates two distinctive light sources of laser and DLP projection. The mask-
image projection is a popular SLA process for its easy configuration and excellent
reliability. The DLP projector samples bitmap image and displays light patterns according
to pixels in the foreground of the image. The on/off states of each pixel can be controlled
at any time by pipelining a series of images to the projector, selectively curing the portion
of resin at our wish. The focus of each pixel from DLP shares the same focal length from
the projector and constitutes a focal plane, which would be aligned to the fabrication plane
where photo-polymerization of the liquid resin occurs.

Figure 3-40: The idea of scale integration by combining two different scale processes.
While mask-image projection internally processes uniqueness of each layer by DLP,
the laser scanning method controls exposure by directing the laser beam through a pair of
90
orthogonal mirror galvanometers (abbreviated as galvo). The rotation of each galvo mirror
is controlled by a servo motor, which can process and execute a stream of angular position
data at a fixed rate. The scanning speed of the laser beam can be controlled by the difference
of the adjacent pair of data in a data stream. Thus, for the same line segment to be scanned,
the linearly interpolated data with finer mesh will have a slower scanning speed, which will
affect the dosage of the laser to the photosensitive resin.
3.3.1 The Principle of Hybrid Light Source
For our hybrid-source manufacturing process, the optical path and focal plane of each
respective light source are mutually independent of the other. Since the size of the
minimum unit of an optical source such as the individual mirror in DLP chip and laser
beam directly determines the resolution of fabrication parts, the exact alignment of
fabrication plane and focal points of light sources must be ensured. A beam splitter is used
to separate locations of light sources and merge their focal planes, as presented in Figure
3-41. Since the DLP projection cures the entire layer at a time regardless of image
complexity, its high throughput suits the fabrication of the inner portion. For the outer
surface of the part, the high-resolution laser can be used to draw the contours of each layer,
achieving a smoother surface finishing. More importantly, the micro textures on the surface
of the part cannot be fabricated by DLP projection due to its poor resolution.
91

Figure 3-41: Schematic diagram and information flow of the hybrid-source system.
Since the DLP projection cures the entire layer at a time regardless of image
complexity, its high throughput suits the fabrication of the inner portion. For the outer
surface of the part, the high-resolution laser can be used to draw the contours of each layer,
achieving a smoother surface finishing.
3.3.2 Hardware Prototype of Hybrid Light Source
The design of the entire machine is presented in Figure 3-42. The laser diode has the
power of 220 mW and an adjustable lens at the output. A bi-convex lens (N-BK7 from
Thorlabs) with a focal length of 250 mm is selected to focus the laser beam with sufficient
depth of field. Each galvo mirror has a scanning speed of 30 kilo-points per second (Kpps)
with travel angle of 12◦ and resolution of 0.003◦ (4000 steps), covering the circular
envelope with the radius of 53 mm (step size of 25 µm). The DLP projector has the
projection envelope of 128 mm × 80 mm with a pixel resolution of 1280×800 (100 µm per
pixel). Therefore, the effective build area of the combined hybrid-source system is the
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center rectangle of the DLP envelope circumscribed by the laser envelope with a size of
76.8 mm × 80.0 mm. The thickness of the beam splitter would cause the reflection of the
beam at the second surface, which forms a so-called “ghost image” at the fabrication plane.
The energy of the ghost image is weaker than that of the main beam spot. Thus it does not
affect fabrication so long as the scanning speed is larger than 0.001 m/s.

Figure 3-42: Prototype of the hybrid light source. Illustrations of (a) machine design and (b) the
actual machine of the hybrid-source 3-D printer with key components annotated. Note that the
mirrors are made transparent to see the laser path, and the Z-direction linear stage is omitted in the
diagram to show light paths of two sources.
There are four components finely adjustable in the hardware system: projector, lens,
mirror mount A and B. The light projection of DLP projector is focused at the fabrication
plane by a precision manual stage beneath the top plate. Mirror mount A and B are tuned
to direct the laser beam to the center of the galvo mirror and finely adjust the object distance
to the twice of focal length. During the focusing of the laser, the lens can be tuned in Y -
direction to find the correct image distance (also twice of focal length). Eventually, the
beam size can be determined by measuring the width of line features printed by laser
scanning method. In total, a mesoscale DLP projection and micro-scale of 50-µm shaped
93
beams are configured in the hybrid system to enable multi-scale stereolithography
fabrication.
3.3.3 Calibration of Hybrid Light Source
The focal planes of two independent light-sources can be mechanically aligned with
fabrication plane to achieve the smallest curable feature, but the exact dimensional
positioning mapping between these light sources are difficult to align mechanically due to
image distortions in many degrees of freedom. Busetti et al. proposed a calibration method
to map the positions of two sources [131]. However, the non-linearity of galvanometer was
not concerned as its angular control might not be exactly accurate as predicted, leading to
the imperfection at the corners of the building area. The environmental disturbance that
occurs before the actual manufacturing process, for example, the mirror galvanometers
being reset to a slightly different angular position once powered-on (zero drift), should be
accounted as well. In this paper, a systematic and robust software calibration method is
introduced to tackle non-linearity and drifting characterized above.
The proposed calibration method essentially unites three mutually independent space:
physical space on the fabrication plane, the pixel space of the DLP projector and angle
space of galvo mirrors. Denote (x,y) as the pixel coordinate at x
th
column, y
th
row of the
image, and denote (α,β) as the rotational angle coordinate of two galvo mirrors. The pixel
space can be calibrated to physical space using the method proposed by Zhou et al. [132].
Then the layer information with toolpath can be fully represented in pixel space by two
operations: (1) construct a fixed bijective function mapping discrete pixel values (x,y) in
94
pixel space to angular positions (α,β) in angle space, and (2) set a projective transformation
to correct changes in angle space due to zero drift. These operations are detailed as follow.
Mapping of pixel space (x,y) to angle space (𝛂 ,𝛃 )
As the focal plane of pixel space has aligned with the actual fabrication plane, the size
of each discrete pixel remains constant (100 µm). Denote x-axis as the width of the image
and y-axis as height with origin set on the top-left corner of the image. Since the galvo
mirror demonstrates high non-linearity, interpolation is used to linearize the mapping
bijection. Choose M × N points that equally divide pixel space into (M − 1) × (N − 1) grids
and set corners of each grid as reference points. The pixel values of four corners of (i,j)
th

grid are denoted as [
(𝑥 𝑖 ,𝑦 𝑗 ) (𝑥 𝑖 +1
,𝑦 𝑗 )
(𝑥 𝑖 ,𝑦 𝑗 +1
) (𝑥 𝑖 +1
,𝑦 𝑗 +1
)
]. Measure angle space coordinates (α
i
,β
j
)
that directs laser to pass through exactly the corresponding pixel point (x
i
,y
j
) as shown in
Figure 3-43 (a-c). Repeat such step for all corners of grids in pixel space to obtain the set
of all reference coordinates.
95

Figure 3-43: Calibration mapping from angle space to pixel space, (a) shows a 5 × 6 square-grid
points separated by 160 pixels mapped by angle space, which fully covers our build area. (b) is an
image of projection only under the microscope, which is pinpointed by laser in (c). These data set
would be used to interpolate any point from pixel space to laser’s angle space (d) by bilinear
interpolation (e). α can be replaced by β in (e) since they are obtained in the same way.
Given the reference points, the mapping of all discrete points can be linearized using
bilinear interpolation bijection:

(30)
where (x,y) is pixel coordinate enclosed in (i,j)th grid. The bijection returns the
mapped coordinate in angle space. The more grids we use, the more accurate the result
would be.
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Zero drift correction of angle space with projective transformation
The mappings of reference data set (x
i
,y
j
) → (α
i
,β
j
) provides sufficient information
for mapping between spaces of two optical sources. However, occasional zero drift can
happen to the hardware configuration, resulting in changes of angle space and invalidating
the original bijection. Re-measuring all M × N reference points would construct the new
bijection, but it is a laborious method to accommodate changes. Here, a projective
transformation method is introduced to correct the linear distortion of angle space. Denote
coordinates of newly changed angle space as (α′,β′), and the transformation is presented
as follows.

(31)
The eight parameters 𝑝 1
to 𝑝 8
of transformation matrix P account for translation,
rotation and projection of original angle space, and they can be solved by plugging four
pairs of angle coordinates at four corners of both angle space. Only four measurements are
required to solve for P, and all original angle coordinates (α,β) can be transformed to the
new angle space with such a method. Figure 3-44 shows the correction of angle space to
match the pixel space.
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Figure 3-44: Mapping of reference data points between pixel space (square) and angle space (cross).
(a) shows original angle space data measurements, which differ from actual drifted new angle
space. (b) shows correction effect by the projective transformation with the error no larger than 1
pixel. Note that pixel space is always fixed, and each photo is taken with 30-second-long exposure
to capture laser scanning through all reference points.
The information flow of coordinates through the calibration process is summarized in
Figure 3-45.
98

Figure 3-45: Complete coordinate transformation diagram: from pixel space to the new angle space
with all data points used to transform an arbitrary (x,y). The distortion is exaggerated in the
diagram.
Besides the dimensional calibration of the system, the energy calibration is also
necessary to ensure a uniform laser power distribution. The raw power distribution on the
fabrication area is measured to normalize the laser speed. For regions where the laser power
is less than the maximum, the speed of beam spot would be lowered by multiplying the
interpolated normalized power percent to have uniform power output across the fabrication
plane. So far, the hardware design and configuration of our hybrid-source additive
manufacturing system are presented.
3.3.4 Related Work
Nature has inspired generations of scientists with complex yet practical surface
structures found on a living creature, which enable special mechanical or dynamical
functions to adapt to the natural environment [133]. Sharkskin is a well-known example of
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illustrating the utility of microstructures to improve hydrodynamic performance. Patterns
of micro-scale denticles on the shark’s streamlined body (Figure 3-46 (a-b)) are capable of
creating greater leading-edge vortices than the perfectly smooth surface, reducing the drag
force of the fluid [134] [135]. Plants also take advantage of micro-scale features to thrive.
Lotus leaves exhibit superhydrophobic property through the multicellular trichomes
structure [136]. Hook structures formed with hairs (Figure 3-46 (cd)) are found on the shoot
of common bean, which enhances its adhesion for climbing [136]. Both creatures benefit
from integrating micro-scale structures of features to their macro-scale body. Efficient
fabrication of such type of geometry is addressed in this paper.

Figure 3-46: Functional microfeatures found on bodies of creatures. (a) shows a leaf of lotus
(Salvinia minima) with (b) multicellular hair of four trichomes from a common base [CSB09].
(credit: Z. Cerman, et al.) (c) represents the shoot of a common bean (Phaseolus vulgaris) with
terminal hook structures (d) [BMBK17]. (credit: W. Barthlott, et al.). The scale bar is 200 µm.
100
To reproduce such mesoscale objects with microstructure in biomimetic products, it
is usually challenging to fabricate directly with traditional manufacturing processes such
as milling or injection molding. Additive manufacturing (AM), in contrast, is a novel
manufacturing technology that fabricates through layer-based directional accumulation
with digital information of each layer, regardless of the geometrical complexity of the part.
Thus, AM technology is increasingly used in exploring biomimetic applications for its fast
prototyping and freedom of geometric design [30] [12].
Among various types of accumulation method, stereolithography accumulation (SLA)
has been one of the most extensively used manufacturing process found in industrial and
commercial additive manufacturing machines since its invention with the world’s first AM
process [68] [137]. It fabricates each layer by photopolymerizing a thin film of
photosensitive resins at designated XY positions and accumulates 2-D layers in Z-direction
to form a 3-D object. However, the inherent trade-offs among the fabrication area, speed
and resolution exist in all SLA-based manufacturing processes. For limited resources as
the number of pixels of a projector, enlarging the fabrication area would inevitably reduce
resolution, and vice versa. In this paper, a hybrid-source manufacturing process using a
multi-scale method is proposed and demonstrated to enhance the resolution of fabrication
without sacrificing efficiency, especially for a mesoscale part with micro-scale features.
Conventional SLA processes such as mask-image projection and laser scanning rely
on the single light source to cure liquid resin into a solid part. Mask image projection uses
the projector as an energy source, which has a Digital Light Processing (DLP) device to
control the light on/off state of each pixel. When the pixel is turned on, the photosensitive
101
resin at the position of the pixel is cured, and dynamic patterns of pixels can be displayed
to fabricate specific shape. While the resolution of the mask-image projection method
heavily depends on the build area, the laser scanning method achieves the high-resolution
equivalent to the spot size by focusing the laser beam. In contrast to the high throughput
projection method that simultaneously solidifies every pixel in the same layer, laser
scanning only cures resin at beam spot at a time. Many approaches have been developed
on top of either method to address the trade-offs. Scanning projection SLA process expands
fabrication area multi-fold by moving the projector source in XY -directions [89] [88].
Although the resolution can be shrunk to micro-scale and conserved during each grid of
projection, it would take multiple times of exposure to fabricate single large layer. Thus,
the building time would be multiplied by the number of projections per each layer.
Projection micro-stereolithography (PµSL) process is capable of fabricating microscopic
features, but its fabrication size is usually limited to several millimeters [138]. Similarly,
direct laser writing (DLW) only achieves the nano-scale resolution within an area of
hundreds of µm
2
[139] [140]. Directional SL accumulation has the capability of fabricating
microfeatures with relatively larger size constraints [141]. However, it requires an effort to
align the immersed guide tool with the pre-fabricated part to build individual feature. Thus,
it is not efficient to build densely distributed features with a large number. All these
methods manage to enhance the building area or resolution by manipulating light source,
but the inherent trade-off does not resolve. Nor can these methods fabricate micro-textures
together with macro-objects at the same time. Designing a novel hybrid-source method that
synergistically integrates each method to facilitate fabrication of micro-textured objects is
102
the key challenge in this paper. The fabrication results prove that hybrid-source process
achieves high-resolution without sacrificing efficiency.
Zhou et al. established the concept of the hybrid-source manufacturing method and
developed an image-based systematic slicing and toolpath planning algorithm from a
software perspective [83] [142]. However, only the laser toolpath of the contour is planned
in his work, and a CAD system for designing general textures is desired. Multi-scale
methods have been developed to fabricate with different beam sizes, but the efficiency of
laser scanning is still limited by its sequential nature [8] [92].
3.3.5 Benefits of Hybrid Light Source
By combing a laser and a projector, we can, in fact, make full advantages of both light
sources. We utilized the projector to quickly cure the interior of one layer, and then use the
laser to scan the boundary and the micro-scale features. Figure 3-47 shows one test case.
Along with the large solid part, we can also fabricate the fine features shown in the right
of Figure 3-47.

Figure 3-47: benefit of the hybrid light source. The major interior portion is cured by the projector
and the boundary micro-scale features are cured by the laser.
103
Besides fabricating small scale features, the laser can also eliminate the XY aliasing
resulted from the pixeled image. Figure 3-48 clearly shows the defects introduced by the
projector’s pixels. Moreover, our fabrication time mainly is same with projector’s, and our
surface quality is much better than the projection-based SLA’s result.

Figure 3-48: The benefit of hybrid light source: can both save fabrication time and preserve the fine
features. The boundary is scanned by the laser, which can eliminate the pixeled aliasing in the XY
plane.
Table 3-5: Fabrication results of the ring model. The black scale bar is 10 mm, and the white scale
bar is 500 µm
104

Fabrication Efficiency
Microtexture
Process Image & Toolpath Results Microscopic View
None
Projection

Laser

Hybrid

Bar Hybrid

Triangle Hybrid

Tri-
Hybrid
Cross

105
The hybrid-source SLA process fabricates the mesoscale objects with high throughput
mask-image projection and cures the micro-scale surface textures with high-resolution
laser scanning. Two test case models are selected and fabricated to demonstrate the
proposed process. The first part is a ring mesh created by slicing the middle one-third part
of a sphere with a diameter of 30 mm. Then a cylindrical through hole is cut at the center
of the flat surface. The ring model is fabricated with projection-only, laser-only, and
hybrid-source process, respectively. Then various types of micro-features are added on the
curved outer surface. The photosensitive resin used is MakerJuice
TM
G+. The image &
toolpath planning, fabrication results, and time required are presented in Table 1 and Figure
3-49.

Figure 3-49: Time comparison among processes across various micro-textures. The layer thickness
is 50 µm for all trials. Micro-textures are only fabricated on laser and hybrid tests. The laser
scanning speed on the fabrication plane is 0.1 m/s for contours and 0.01 m/s for microfeatures for
all trials.
106
For the solid ring without any micro-textures, the surface fabricated by pure projection
has undesired circular patterns due to the poor resolution of the projector (the microscopic
view in projection process). In contrast, the laser and hybrid methods produce better surface
quality and eliminate the aliasing patterns, and the hybrid method maintains the same
throughput as projection, which takes less than half of the time of pure laser method as
shown in Figure 3-49. The micro-features added to the ring model require high-resolution
laser, so the textured body cannot be fabricated by pure projection. The hybrid-source
process is still twice faster than pure laser method for the ring model with various micro-
textures. The efficiency advantage of the hybrid method would be more significant for the
large-area, large-volume complex mesh.
With the proposed CAD system that enables arbitrary selections of any surface portion
on which a type of micro-texture from the library is attached, a solid model can have many
types of micro-textures on certain areas. A stem model, for example, is designed to have
each of the four microfeatures in the library on each face of its four leaves, as shown in
Figure 3-50.
107

Figure 3-50: Stem model with different microfeatures distributed on its four leaves. (a) is the mesh
of the stem model, whose surfaces are selected and assigned with unique micro-textures. (b) is the
actual result fabricated by the hybrid-source process. (c-j) are zoomed-in and microscopic pictures
of each microfeature on the leaf surface. The white scale bar is 200 µm.
3.3.6 Concluding Remarks
The hybrid-source stereolithography additive manufacturing system presented in this
paper integrates the DLP projection method and the laser scanning method to fabricate
108
meso-scale parts with micro-scale textures efficiently and accurately. The hybrid-source
process possesses the high resolution of the laser system (50 µm spot size, 25 µm step size)
and high throughput of projection method (8 seconds per layer of 50 µm). Hierarchy of
meso- and micro-scale complexity is achieved with the proposed system, whose efficiency
advantage over single-source method is demonstrated by test cases. For large-area, large
volume solid parts commonly found in nature-inspired structures, the hybrid source process
will be more efficient than traditional laser-based method.

109
Chapter 4 Layer Planning for the Inter-Layer Scalability
The previous chapter proposed three polymerization energy control mechanisms,
which cope with the scalability within one layer. This Chapter presents optimized layer-
planning methods to improve scalability among multiple layers.
The fundamental philosophy of optimizing layer planning is again treating different
features differently. As shown in Figure 4-1, we have observed three types of different
features: boundary and interior (Figure 4-1a), large and small slopes (Figure 4-1b), ultra-
thin and large channels (Figure 4-1c).

Figure 4-1: Three methods to optimize the process. a) Dual Layer thickness via Geometry
Decomposition, b) Scalable layer thickness via Adaptive Slicing, c) scalable channels.
Correspondingly, we proposed three layer-planning methods. The first method is dual
layer thickness via geometry decomposition, where the interior is printed using a large
layer thickness, and the boundary is printed using small layer thickness. The second
approach is adaptive layer thickness via adaptive slicing, where the layer thickness is not
uniform but scalable to the geometry error. The third method is transferring layers, which
adds an auxiliary platform to fabricate the “roof” of the ultra-thin channels, and transfers
that “roof” to a normal SLA process.
The rest of this chapter will discuss these three methods in detail.
110
4.1 Dual Layer Thickness
2

Generally, we can decompose a 3D object into two scales: interior and (exterior)
boundary. Noted that the geometry information is solely determined by the boundary. This
idea can also be reflected from the boundary representation (B-Rep). Only the boundary
defines the geometry shape. Based on this observation, we proposed dual layer thickness
curing strategies.
Boundary features can be fabricated using the finest light source, while the interior
portion can be quickly cured using the most powerful light source. Optimized combinations
of multiscale light sources are investigated in this study.

Figure 4-2 Multiscale decomposition of a 3D model. Decomposing 3D objects into macro-scale
features (interior) and micro-scale features (boundary).
In layered SLA, a recoating process is required to distribute a thin layer of liquid resin
on the previously built layers before the next layer can be solidified. The recoating process

2
The full text of this section has been published on Journal of Micro and Nano-Manufacturing, as Mao, H.,
Leung, Y.S., Li, Y., Hu, P., Wu, W. and Chen, Y., 2017. Multiscale Stereolithography Using Shaped Beams.
Journal of Micro and Nano-Manufacturing, 5(4), p.040905
111
is time-consuming. For example, for the projection-based SL process with a short curing
time, the recoating process can take 50-90% of the total building time. Hence the
fabrication speed can be 2~10 times faster if the recoating time could be reduced or
eliminated. This is the core idea of our ultra-fast MIP-SL process [80] and Carbon3D’s
Continuous Liquid Interface Product (CLIP) approach [86]. In addition to the recoating
time of each layer, another critical issue in the SL process is the large separation force if
the layer size is large. In the bottom-up projection-based approach, the traditional “pulling
up” separation leads to a significant suction force between the cured layer and the resin
tank. To address the problem of the large separation force, Zhou et al. [143] used the sliding
motion along the X-axis for layer separation. Similarly, Pan et al. [78] used the sliding
along the shearing force direction to significantly speed up the building process of the
projection-based SL process. The approach has also been adopted in the laser-based SL
process [84]. However, even with the sliding mechanism, the separation between the cured
layers and the resin tank is still challenging if their contact area is large.
4.1.1 Dual Layer Thickness Process
The meaning of “multi-scale” in this study is two folds. One is multi-scale beams,
which is related to the XY resolution; another is multi-scale layer thickness, which is related
to the Z resolution. Different scales have their unique advantages. For example, a small
laser beam and a small layer thickness can cure features with high resolution, while a large
laser beam can quickly solidify a large portion of resin, and a large layer thickness will
require less resin recoating time.
112
In this section, we present a multi-scale fabrication process based on a multi-scale
laser beam and multi-scale layer thickness. The method of selecting appropriate laser beam
sizes and layer thicknesses based on the given CAD model’s geometry is presented.
Figure 4-3 shows the framework of such a multi-scale fabrication process. First, a
given 3D model is sliced into a set of two-dimensional (2D) layers using a large-scale layer
thickness. Then each large layer is further sliced into many small 2D layers using a small-
scale layer thickness. We then use the following curing strategy to fabricate the sliced
layers.
• Use the small-scale laser beam to fabricate the boundary of each small layer,
which contains the shapes of all the detail geometric features.
• After the boundary portions of a small layer have been cured, move the Z
linear stage up by the small-layer thickness.
• After all the small-layers’ boundaries in this large layer have been fabricated,
move the Z stage up and down so that the part can be completely recoated.
• After the fabricated layers were fully recoated with resin, the common
interior area of the large layer is cured using the large-scale laser beam.
The above curing strategy is repeated for every large layer until all the 2D layers have
been fabricated. The algorithm to divide a sliced layer into the boundary and interior
portions, and accordingly, to plan the scanning paths for different size-scale laser beams is
discussed in Chapter 3.1.
113

Figure 4-3: A schematic diagram of the dual layer fabrication process. The multi-scales in the XY
plane are achieved by the large and small beams, and the multi-scales along the Z axis are realized
by the large and small layer thickness.
4.1.2 Dual Layer Thickness Slicing Algorithm
Dual Layer Thickness Tool Path Planning. Same as the notations in Chapter 3.1, a
toolpath p(r, h) is defined as a function of radius r and thickness h, which is evaluated on
every slicing at the desired resolution. Within each slice, the generation process can be
broken into two steps: (1) computing pA(rsmall, hthin) and pB(rlarge, hthin) on the XY plane with
thickness hthin, and (2) computing pC(rlarge, hthick) along the Z axis with thickness hthick – this
is the case when the interior of a large region is filled.
Integrating toolpath pC with large radius rlarge and thickness hthick in the process can
effectively reduce the fabrication time. Given m number of slices W, which represent the
cross-section of an object with thickness hthin, and the thickness hthick of pC should equal to
m × hthin. We first search for any common interior regions that can be fabricated in all of
114
the m slices. By doing so, intersection operations between these m slices are performed,
and region E for pC is produced Figure 3-8. After that, we shrink the region E with rlarge to
generate pC and grow the path pC with rlarge to acquire the offset region of pC. Once the
offset region Oc is determined, we can produce toolpaths pA and pB from the subtracted
region (D-Oc) for every slice ∈𝑊 . This process will be repeated in every m number of
slices of the object. Figure 4-4 (left) illustrates the main idea. Those m layers are fabricated
without the common region, and this region will be filled right after the m
th
layer is
produced.
The presented algorithm is simple, easy to implement, and able to generate scanning
paths for laser beams with different sizes and thicknesses. One implementation of the
algorithm is discussed as follows.
Implementation
We implement our slicing using the LDNI model [144] since a computed LDNI model
can be easily converted into high-resolution images by classifying the in/out state of a given
point. We slice at a resolution between 20µm to 80µm per pixel.
Contour. To ensure small features can be made in the process, we reserve a boundary
region for contour generation. Contour toolpath is defined by a chain of small segments
that describe the features along the tangent of the surface. We use the small beam (rsmall,
hthin) to fabricate the boundary, and the toolpath construction is based on the work [145].
We reserve the boundary region by shrinking the cross-section O with a radius equal to
𝑑 =2×𝑟 𝑠𝑚𝑎𝑙𝑙 (diameter of small beam 𝐵 0
), and the computed offset 𝑂 ↓
𝑑 will then
become the input for toolpath planning of 𝑝 𝐶 .
115
Distance between scanline pattern. For toolpaths 𝑝 𝐴 , 𝑝 𝐵 and 𝑝 𝐶 , one of the
parameters that can be adjusted by users is the distance between each scanline. The tool
paths need certain overlapping since the laser beam may not be exactly the same radius as
expected. This could be caused by the noise and vibration from the machine. In order to
ensure the tool paths are blended together, we set the overlapping rate 𝛼 as 0.7 such that
the distance between two scanlines is equal to 2×𝑟 ×𝛼 .
Buffer region for toolpath 𝒑 𝑪 . Another concern considered is that the extracted
common region E could lead to empty region (or nearly empty) in some slices from W. An
example is illustrated in Figure 4-4. Even though we have boundary region to prevent E
from completely empty, it is difficult for the (i+1)
th
layer to support the rest of the layer
from W. Therefore, a buffer region, with radius 𝛽 , is also added to prevent potential failure.
The pseudo-code of our whole toolpath generation is shown in Algorithm 1.

Figure 4-4: Buffer region for multiscale toolpaths. (Left) Failure may occur since only the boundary
region is supporting the other m-1 small layers. (Right) A buffer radius 𝜷 is added to reduce the
common region E.

Algorithm 1: Toolpath Generation
116
Input: LDNI model ρ, pixel width 𝝈 ,⁡small beam radius τ, large beam radius
ɛ, high thickness £, low thickness 𝜸 , blend ratio 𝜶 and buffer radius 𝜷
Output: toolpath 𝒑 𝑨 ,𝒑 𝑩 ,𝒑 𝒄 and contouring toolpath c
1. for⁡⁡𝑖 to 𝑙 do // l layers of model ρ with thickness 𝛾
2. 𝑂 = Gen e r a t e S li c es(ρ, 𝜎 ,𝑖 );
3. 𝐿 =𝑂 . off se t(-τ×2);
4. 𝑐 ← Contour(𝑂 −𝐿 ); //obtain contour c
5. m = £/ 𝛾 ;
6. if 𝑖 %m == 0 then
7. for⁡⁡1 to 𝑚 do
8. R← In t er s ectio n(𝐿 ,⁡ Gen er a t eS li c es(ρ, 𝜎 ,𝑖 +1));
9. end for
10. R ←⁡R. off set(-𝛽 );
11. 𝑝 𝑐 ← S c a n li n e(R, ɛ) // obtain contour 𝑝 𝑐
12. end if
13. 𝐷 ← 𝐿 −𝑝 𝑐 . off set(ɛ);
14. 𝐷 ′
←⁡𝐷 . off s et(-ɛ);
15. 𝑝 𝐵 ← S c a n li n e(𝐷 ′
, ɛ); // obtain contour 𝑝 𝐵
16. ⁡𝐵 ←𝐷 −𝑝 𝐵 . off se t(ɛ);
17. 𝐵 ′
←⁡𝐵 . off s et(-τ);
18. 𝑝 𝐴 ← S c a n li n e(𝐵 , τ); // obtain contour 𝑝 𝐴
19. // repeat 16-18 for more beam size
20. end for
Figure 4-5: Multiscale tool path generation algorithm
4.1.3 Process Characterization
The theoretical a4nalysis of the main characteristics of the developed multi-scale
fabrication process is presented in the section. We first present how to control the beam
shape for different sizes. The process of recoating resin is then explained. Finally, the
fabrication speed based on the analytic results is discussed.
Boundary Resin Recoating
The main reason for the fast recoating of small layers is shown in Figure 4-6. The resin
flow can be modeled as a Hele-Shaw flow. Denote the small layer thickness as ℎ
1
(20µm),
117
the boundary width as 𝑏 (0.5mm) and the boundary perimeter as 𝐿 . According to Hele-
Shaw flow modeling, the refilling liquid resin flow is
𝑄 =
ℎ
3
12𝜇 ∇𝑃𝐿 =
ℎ
3
12𝜇 𝑃 𝑏 𝐿 . (32)

Figure 4-6: The schematic diagram of resin recoating for small layers’ boundaries
Suppose that the liquid resin is incompressible fluid. To fully recoat the boundary, the
amount of resin should reach 𝑄𝑡 =𝐿𝑏 ℎ. Hence the recoating time is
𝑡 =12𝜇 𝑏 2
𝑃 ℎ
2
.
(33)
This equation indicates that the recoating time has a second order relationship with the
boundary width. In our implementation, the viscosity of the resin is around⁡μ=0.1Pa∙s,
the air pressure is⁡P=101325pa ,⁡h=0.02mm, and b=0.5m. Hence, the recoating time
ist=12∗0.1∗
0.5
2
101325∗0.02
2
=7.4ms , which is sufficiently fast for the 3D printing process.
In contrast, the conventional SL process recoats the whole layer instead of the boundary,
and the recoating width of each layer can be as large as the whole platform, e.g. 50mm.
Hence the recoating time for the whole layer can reach to⁡𝑡 =12∗0.1∗
50
2
101325∗0.02
2
=74𝑠 ,
which is significantly longer. This explains why the up-and-down motion is required for
the conventional SLA process in order to speed up the resin recoating process.
Fabrication Speed
118
As shown in the above discussion, the recoating time of the small layers’ boundary is
ignorable compared with the large layers’ recoating time. Hence, in our multi-scale
fabrication process, only the boundary portion is cured for each small layer. Hence only
the boundary portions require recoating. Due to the ignorable recoating time for these
boundaries, our process can achieve nearly continuous polymerization for the small layers.
By making full advantage of it, the proposed method not only maintains the same
fabrication speed for the large layer thickness but also preserves the detailed features that
can be fabricated using the small layer thickness.
Figure 4-7 illustrates the fabrication time of the conventional SL process and the
proposed multi-scale SL process. The meaning of the notations can be found in the
nomenclature. In Figure 4-7, the bottom row shows the time distribution of the proposed
process, i.e., curing five small layer boundary, and then curing one large layer with one up-
and-down motion. We omit the boundary recoating time and the aperture changing time
since they are much less than others. In the layer fabrication process, the aperture changes
twice, from the large beam to the small beam and vice versa. The total changing time in
our prototype system is less than 1 second. This changing time can be further shortened if
a faster switch mechanism is applied. In comparison, as shown in the top row of Figure
4-7, the conventional process to achieve similar feature resolution requires the recoating
time 𝑡 𝑢𝑑
in order to recoat the whole layer, and 𝑡 𝑖 0
by using the small laser beam to cure
the whole layer.
119

Figure 4-7: Efficiency of dual layer thickness. Time consumption for five small layers between
multi-scale fabrication and single scale fabrication.
Notice that the curing time of the large beam 𝑡 𝑖 1
and that of small beam 𝑡 𝑖 0
follows
𝑡 𝑖 0
=𝑆 𝑋𝑌
𝑡 𝑖 1
, in which 𝑆 𝑋𝑌
is the ratio of the large beam size to the small beam size. The
speed improvement of our multi-scale method over the conventional single-scale SL
process can be modeled as:
𝑉 𝑚𝑢𝑙𝑡𝑖 /𝑉 𝑠𝑖𝑛𝑔𝑙𝑒 =
(𝑡 𝑖 0
+𝑡 𝑏 0
+𝑡 𝑢𝑑
)𝑠 𝑍 𝑡 𝑖 1
+𝑡 𝑏 0
𝑆 𝑇 +𝑡 𝑢𝑑
=𝑠 𝑍 𝑆 𝑋𝑌
𝑡 𝑖 1
+𝑡 𝑏 0
+𝑡 𝑢𝑑
𝑡 𝑖 1
+𝑡 𝑏 0
𝑆 𝑇 +𝑡 𝑢𝑑
(34)
Note that the speed acceleration ratio is dependent on the built model size as well as
geometry complexity. For a solid layer, we can assume the scanning time for its inner
portion is much longer than that for its boundary portion, i.e. 𝑡 𝑏 ≪𝑡 𝑖 . Therefore, we can
omit the 𝑡 𝑏 term, and approximate the speed acceleration ratio as:
𝑉 𝑚𝑢𝑙𝑡𝑖 /𝑉 𝑠𝑖𝑛𝑔𝑙𝑒 ≈𝑠 𝑍 𝑆 𝑋𝑌
𝑡 𝑖 1
+𝑡 𝑢𝑑
𝑡 𝑖 1
+𝑡 𝑢𝑑
≈{
𝑠 𝑍 𝑠 𝑋𝑌
, 𝑖𝑓 ⁡𝑡 𝑖 0
≫𝑡 𝑢𝑑
𝑆 𝑍 , 𝑖𝑓 ⁡𝑡 𝑖 0
≪𝑡 𝑢𝑑
(35)
Note 𝑡 𝑖 0
≫𝑡 𝑢𝑑
happens when the target part has a large solid area. For such cases, our
multi-scale fabrication approach makes full advantages of the multi-scale beam diameters
and multi-scale layer thicknesses, which is 𝑆 𝑍 𝑆 𝑋𝑌
times faster than conventional layer-
based SL process. For example, in our prototype system, SZ = 5 and SXY = 4. Hence our
current implementation is 5∗4=20 times faster than the traditional SL process in order
to achieve the similar XYZ resolutions.
120
When 𝑡 𝑖 0
is comparable with 𝑡 𝑢𝑑
, the time for the layer separation and resin recoating
is longer than the resin curing time. This happens when the part is small. In such cases, our
process needs only one up-and-down transition for every 𝑆 𝑍 layers. Compared with the up-
and-down transition for every layer in the conventional SL process, our fabrication speed
is⁡𝑆 𝑍 =5 times faster.
Table 4-1 shows the fabrication time of the tested models. All parts are fabricated
using 20 m layer thickness. A is the bounding box area (unit 𝑚 𝑚 2
), H is the height of the
model (unit 𝑚𝑚 ), 𝑡 𝑚𝑢𝑙𝑡𝑖 and 𝑡 𝑠𝑖𝑛𝑔𝑙𝑒 are the fabrication time of our method and the
conventional SL process, respectively (unit minute), and Vm/Vs means the fabrication
speed ratio.
Table 4-1: Fabrication time of different models
Model A (mm
2
) H (mm) 𝒕 𝒎𝒖𝒍𝒕𝒊 (min) 𝒕 𝒔𝒊𝒏𝒈𝒍𝒆 (min) V m /V s
Pyramid 36 3 27 117 4.3
Wood Pile 18 3 18 81 4.5
Porous 25 1 15 65 4.0
Lion 315 10 187 1102 6.7
Turbine 100 5 65 275 4.2

Nomenclature

ℎ
1
The layer thickness of large layers
ℎ
0
The layer thickness of small layers
𝐵 1
The size of large beam
𝐵 0
The size of small beam
𝑡 𝑏 0
Time for curing small layers’ boundary
𝑡 𝑖 0
Time for curing small layers’ inner portion
121
𝑡 𝑏 1
Time for curing large layers’ boundary
𝑡 𝑖 1
Time for curing large layers’ inner portion
𝑡 𝑢𝑑
Time for up-and-down, (resin recoating)
𝑠 𝑍 Scale ratio of layer thickness along the Z direction. 𝑠 𝑍 =ℎ
1
/ℎ
0

𝑠 𝑋𝑌
Scale ratio of beam area in the XY plane.
𝑆 𝑋𝑌
=𝐵 1
/𝐵 0

𝐼 Light intensity
𝜇 Viscosity of resins
4.1.4 Experimental Results and Discussions
The proposed SL process offers two main benefits: 1) providing a cost-effective and
robust shaped-beam method to fabricate 3D objects with high-resolution features, and 2)
presenting a multi-scale tool path planning framework to efficiently fabricate 2D layers
using shaped beams. We used CAD models with various geometries to verify the presented
multi-scale SL process.
Lattice Structures Using Shaped Beams
In general, we can use a single aperture based on a small pinhole to generate a small
laser spot, and use it to cure any shape of a given part. However, it requires significantly
long scanning time in order to build lattice structures with a large number of beams. In
order to speed up the fabrication speed, an aperture with 3×3 pinholes can be used to shape
the laser beam. The correspondingly fabricated pattern is a 3 by 3 dots array as shown in
122
Figure 4-8 (a). By using such a shaped beam with multi-pinholes, the resin curing speed is
9 times faster than that of using a single pinhole.

Figure 4-8: Fabrication of the porous structure. a) Beam shape used in this test case; b) the
fabricated pattern; c) the input cad model; d) and e) shows the printed part, and f) shows the large
compression ratio.
A porous lattice structure has a large elasticity, which does not exist in a solid object
using the same material. Figure 4-8f shows the compression test. A 40% elasticity strain is
observed. The purposes of using shaped beams, like the one with multiple holes, are mainly
to address two issues: (1) making the curing simultaneously so that the fabrication speed
can be increased, and (2) fabricating specific micropatterns that can modify the surface
texture of an object surface. The second issue will be demonstrated in our future work.
Complex Parts with Multiscale Features
In addition to the lattice structures, three more complex parts have been fabricated to
verify the proposed multi-scale tool path planning framework. The fabrication results based
on the accordingly planned tool path are shown in Figure 4-9. The successful fabrication
123
of these parts validates the proposed multi-scale fabrication process. Especially, the part
“Lion” has features ranging from the centimeter’s main body to tens of micrometers’ hairs.

Figure 4-9: The fabricated complex parts with a quarter coin. The left part is a pyramid with the
large sloped surface; the middle one is a turbine with shell-like blades, and the right one is a “Lion”
model with delicate hairs.
Comparison with Other SL Processes
We compare our multi-scale SL process with some representative SL processes in
literature, including the laser-based SLA (LSL) [84], the projection-based micro SLA
(PuSL) [77], the two-photon polymerization (TPP) [130], the continuous interface liquid
production (CLIP) [86], and the large area projection-based micro SLA (LaPuSL) [21].
Table 4-2 lists the details of the comparison. We compared these processes in five major
fabrication metrics, including part size, feature resolution, part-size-to-feature-size ratio,
fabrication speed, and cost.

124
Table 4-2: Comparison between different SL processes
Metric LSL PuSL TPP CLIP LaPuSL Ours
Part Size (mm) 125 3 0.2 141 80 120
Feature Size ( m) 155 3 0.1 75 5 30
Ratio 800 1000 2000 1900 16000 4000
Layer thickness ( m) 25 5 - 1 5 20
Speed (/1cm
3
)
6
hr
300
hr
3000
hr
6
min
6
hr
3
Hr
Cost $$ $$$ $$$$ $$$$ $$$$ $$

The data in Table 4-2 is estimated from the referred website or the published studies.
The fabrication speed is measured as the time to fabricate the Lion model in Figure 4-9.
The ratio is calculated as the ratio part size to feature size. As shown in Table 4-2, the
conventional SL processes face trade-offs among fabrication speed, resolution, scalability,
and cost. On the contrary, the proposed method partially solves these tradeoffs by using
the idea of the multi-scale laser beams in the XY plane and multi-scale layer thicknesses in
the Z direction. The main components of our setup are off-the-shelf, and the total cost of
them is less than two thousand dollars. In comparison, the other SL processes are more
expensive since they use either a more expensive Digital Micromirror Device or a
femtosecond laser, as well as some specially designed components such as an oxygen-
permeable membrane and a customized F-theta focusing lens. To the best of our knowledge,
no other fabrication processes can provide such a combination of large part size, micro-
scale features, fast fabrication speed, and low cost.
125
4.1.5 Concluding Remarks
The section presents a novel dual layer AM process and the related tool path planning
framework for fabricating three-dimensional macroscale objects with microscale features.
A major contribution of our work is to present a multiscale fabrication mechanism across
different layers to optimize the fabrication speed and feature resolution simultaneously.
We use multiscale layer thicknesses in the Z-axis. This novel multiscale curing strategy
enables our fabrication process to be not only fast but also capable of achieving a high
XYZ resolution. The fabrication results based on the developed process have verified the
benefits of the multiscale curing strategy.
The full text of this section has been published on Journal of Micro and Nano
Manufacturing [8].

126
4.2 Adaptive Layer Thickness
3

To scale up an additive manufacturing process means using the same process to
fabricate larger scale 3D objects. As mentioned in the introduction, one key bottleneck that
prevents scaling up is the trade-off between fabrication time and surface quality. For
layered SLA, if a smaller layer thickness is used, it results in more layers, which leads to
longer fabrication time. For example, if a 100mm high part is sliced with 100um layer
thickness, there are 1000 layers. If this part is sliced using 10um layer thickness, the number
of layers is 10000. This results in 10 times long times is required. Here, we improve one
vital approach to scale up the SLA process, i.e., adaptive slicing. By adaptive slicing, one
can guarantee the surface quality in the region of the parts that users care about by using
smaller layer thickness, and at the same time speed up the fabrication by fabricating the
regions that are not sensitive using larger layer thickness.
Adaptive slicing is an important computational task required in the layer-based
manufacturing process. Its purpose is to find an optimal trade-off between the fabrication
time (number of layers) and the surface quality (geometric deviation error). Most of the
traditional adaptive slicing algorithms are computationally expensive or only based on a
local evaluation of errors. To tackle these problems, we introduce a method to efficiently
generate the slicing plans by a new metric profile that can characterize the distribution of
deviation errors along the building direction. By generalizing the conventional error
metrics, the proposed metric profile is a density function of deviation errors, which

3
The full text of this section has been published on the journal of Computer Aided Design, as Mao, H.,
Kwok, T.H., Chen, Y. and Wang, C.C., 2019. Adaptive slicing based on efficient profile analysis. Computer-
Aided Design, 107, pp.89-101.
127
measures the global deviation errors rather than the in-plane local geometry errors used in
most prior methods.
Slicing can be efficiently evaluated based on metric profiles in contrast to the
expensive computation on models in boundary-representation. An efficient algorithm
based on dynamic programming is proposed to find the best slicing plan. Our adaptive
slicing method can also be applied to models with weighted features and can serve as the
inner loop to search for the best building direction. The performance of our approach is
demonstrated by experimental tests on different examples.
4.2.1 Motivation
Over the last thirty years, a new type of manufacturing process, called additive
manufacturing (AM), has been developed
Using the principle of layer-based material accumulation [146]. Many novel AM
processes based on different techniques such as laser curing, nozzle extrusion, jetting,
electron beam, and laser cutter, have been developed [147] [148] [149]. AM is a direct
manufacturing process that can fabricate parts directly from computer-aided design (CAD)
models without part-specific tools or fixtures. Therefore, it can fabricate highly complex
parts effectively. In most of the AM processes, the digital CAD model is sliced by
intersecting it with several horizontal planes. The sliced contours are then transferred to
generate the tool paths for material accumulation.
While the uniform layer thickness is widely used due to its simplicity, it has been
theoretically proven that adaptive layer thickness can produce parts with higher accuracy
128
and shorter building time [100] [101] [150], as shown in Figure 4-10. In adaptive slicing,
the varied thickness of layers is determined by the geometry of input models.

Figure 4-10: Tradeoff between resolution and efficiency.
Most of the existing methods [101] evaluate deviation errors locally by the geometry
at particular slicing planes, which can result in large approximation error when there is
complex geometry between neighboring slices.
To improve the accuracy of geometry error evaluation, different strategies have been
developed, including: 1) slicing the model using the finest layer thickness [114], 2) direct
slicing the designed CAD model (like NURBS [151], CSG [111]) rather than the related
tessellated model (like STL [100]), and 3) refining the slicing plan if sharp geometry
changes are detected within one layer [110]. However, these methods are computationally
129
expensive, and the bottleneck is caused by the process requiring a large number of
intersection operations between the slicing plane and the CAD model.

Figure 4-11. The pipeline of scalable layer thickness. Given a mesh model with weights on faces(a),
the metric profiles (b) are extracted to describe the surface metric distributions along a building
direction. Based on these profiles and the mesh weight, an optimal slicing plan (c) can be computed.
The color scale in (c) represents the layer thickness value, and the smaller the layer thickness is,
the color is closer to the red end. Moreover, all the figures in this study share this same color scale
for layer thickness. The result of the model fabricated by the optimal slicing is shown in (d), and
the comparisons can be found in Figure \ref{fig:fab_results_one}.
In this study, we develop a novel method to overcome this bottleneck by representing
a CAD model as a profile of the geometric error along the building direction. An example
is shown in Figure 4-11.
The evaluation of the geometric deviation error can be done on the profile rather than
intersecting the CAD model intensively. By constructing the metric profiles using GPU-
accelerated methods, the whole process of adaptive slicing can be computed in about one
second.
In summary, our presented adaptive slicing technique is accurate and efficient. The
main contribution is a new profile-based framework for adaptive slicing, which shows the
following properties.
Global: The profile generalizes the conventional error metrics and provides an
implicit representation for the shape of an input model, and it is global information for
130
slicing. Based on that, we design an optimization algorithm based on dynamic
programming to find the best slicing plan.
Efficient: The analysis taken in our algorithm is based on a metric profile that can be
generated by GPU-accelerated techniques. In our tests, the whole process from profile
construction to getting the optimal slicing plan can be completed in around one second.
Benefiting from the efficiency, it can serve as the inner loop to find the best building
direction.
General: The formulation can be easily extended to integrate different, commonly
used error metrics. Moreover, we also show that it can be further generalized to incorporate
the user specified salience.
4.2.2 Adaptive Slicing Based on Metric Profiles
The complexity of the slicing optimization problem mainly arises from the evaluation
of geometry error. This geometry error calculation is time-consuming because most slicing
algorithms are based on NURBS [151], STL [100]or point cloud set [103], and slicing one
3D model based on these representations is computationally expensive.
Instead of directly evaluating the deviation error on input CAD models, we propose
an intermediate metric profile to evaluate the deviation error distribution along the z-axis
(the printing direction).
131

Figure 4-12: Illustration of the metric profile: error density function.
The value of metric profile ϕ(z) is a measure of geometric error density with reference
to the height z.
Based on the definition of metric profile ϕ(z), we can evaluate both the error metric
of each layer and the total error with trivial effort. Specifically, the metric error ε
k
of a
layer k is defined as the integral of a metric profile function along with that layer's height
range [z
k−1
,z
k
] as
ε
k
⁡=∫ ϕ⁡(z)
z
k
z
k−1
⁡⁡dz ,
(36)
Problem Definition: Based on the metric profile (error density function) ϕ(z) and
given the allowed maximal error ϵ of a layer, the optimization objective is to minimize the
total number of layers while assuring each layer's integral error ε
k
is within the given
tolerance ϵ, i.e.

132
min𝐾
(37)
s.t.
ε
k
⁡=∫ ϕ⁡(z)
z
k
z
k−1
⁡⁡dz≤ϵ,k=1,….,K
C1
z
k
=𝑧 𝑘 −1
+𝑡 𝑘 ,𝑘 =1,…,𝐾 C2
t
𝑚𝑖𝑛 ≤𝑡 𝑘 ≤𝑡 𝑚𝑎𝑥
,𝑘 =1,…,𝐾 C3
z
0
=0,𝑧 𝐾 =𝐻 C4
where ϕ⁡(z) is the metric profile function, the unknown variable K is the number of
layers, the unknown variable t
k
is the thickness of layer k, t
min
and t
max
are the
manufacturing constraints of the minimal and maximal layer thickness, and H is the height
of the input model.
To solve this slicing problem, we propose a novel adaptive slicing pipeline, as shown
in Figure 4-13. Different from the traditional adaptive slicing pipeline that directly
performs the slicing on the CAD model (refer to the bottom row of Figure 4-13), our new
pipeline first efficiently samples the input 3D model into structured points and then
constructs the metric profile from the sampled points. Using the metric profile, we can
efficiently obtain the optimal slicing plan, and eventually, export the tool paths for 3D
printers such as Fused Deposition Modeling (FDM) [152]or projection-based
Stereolithography (SLA) [143]). The details of each step in our new framework will be
discussed as follows.
133

Figure 4-13. The framework of the proposed scalable layer. Comparison between the traditional
and our newly proposed adaptive slicing pipelines.
Metric Profile
We introduce ``metric profile'' ϕ(z) to describe the geometry error distribution along
the z-direction (the printing direction). The metric profile is a function to measure the
geometry error density at height z. There are different error metrics can be used to construct
the profile, e.g., cusp height, surface roughness, area deviation, and volume deviation. The
proposed framework is compatible and useful for all these errors and other applications as
long as a metric profile can be defined. In this section, as a widely used metric since its
development [100], the cusp height is picked to explain the algorithm.
The error metric “cusp height'' is to measure geometry error due to the lack or surplus
of materials caused by slicing. The cusp height c of the i
th
layer is calculated by its
thickness t
i
and the normal of the points in the layer. Assume the slicing is along the z
direction and the maximum value of normal in z-axis is n
z
(from a normal vector 𝐧 =
(n
x
,n
y
,n
z
)), the cusp height of the layer can be approximated by
c=|𝑡 𝑖 ⋅𝑛 𝑧 |
∞
(38)
134
As there are many points with different normal values in a layer, the infinity norm is
used (i.e., the maximum value of n
z
is picked as the error density) to conservatively
preserve the sharpest feature. Remarked that, the metric of cusp height is used here just for
the sake of explaining the algorithm, but same concepts can be applied to other metrics.
By definition, the thickness t
i
is always along the printing direction z, so a change in
the value of t
i
can be denoted as Δz. Thus the corresponding change in cusp height is Δc=
Δz⁡|n
z
|
∞
. Therefore, the metric profile for cusp height is defined as the derivative of c w.r.t.
the height z:
ϕ
cusp
(𝑧 )=
𝑑𝑐 𝑑𝑧 = lim
Δz→0
Δc
ΔZ
≈max⁡{𝑛 𝑧 }⁡
(39)

Figure 4-14: Illustration of the error metric. (a)(c) are conventional cusp height, and (b)(d) are the
proposed cusp height calculation. The designed model is a trapezoid shape. The printed shapes are
extruded rectangles. The values of cusp heights C are calculated given small layer's thickness is 1/3
mm. For a simple geometry with linear surface (a)(b), the conventional cusp height measures the
geometry error well, and the big layer's cusp height is equal to the sum of small layers' cusp height
(0.72=0.24+0.24+0.24). For a complex geometry with curved surface, the conventional cusp height
135
results in a poor estimation of the geometry error, while the sum of small layers' cusp height gives
a better estimation.
Based on the above-defined error metric profile, we can easily calculate the metric
error ε
k
of a layer k within the height range [z
k−1
,𝑧 𝑘 ], as the integral of metric profile
ε
k
⁡=∫ ϕ⁡(z)
z
k
z
k−1
⁡⁡dz .
(40)
Noted that, this proposed integral error metric is a generalization of the conventional
slicing algorithm using cusp height. To determine a new slice plane efficiently, the
conventional slicing only considers the normal of the points in the previous slice plane. In
other words, it approximates the surface between the slice planes linearly using the normal
and uses the cusp height for the approximated surface to determine the next position of
slice plane. When the layer is very small or the true surface is indeed linear, such as the
one shown in Figure 4-14, the cusp height is a good estimation of the slicing error.
The idea of our proposed metric profile is illustrated in Figure 4-14 using three smaller
layers. The cusp heights are calculated separately in each small layer, and they are
integrated as the error for the whole layer. In this case, the proposed integral error metric
just recovers the cusp height of the thick layer, i.e., the big layer' cusp height is the sum of
three small layers' one 0.72=0.24+0.24+0.24.
Nevertheless, when the true surface is not linear, simply considering the normal of the
previous plane results in a poor approximated surface and inaccurate error estimation. For
example, if the bottom plane's normal is used for the curve shown in Figure 4-14(c), the
approximated surface is outlined by the dotted line. The real slicing error for this curve
surface should be similar to (probably a bit smaller than) the one in Figure 4-14(a).
136
Unfortunately, because the approximated geometry is different from the true geometry, the
cusp height is computed as $0.86$, which is much higher than the linear one 0.72.
In comparison, our error metric profile records the normal at each height, illustrated
in Figure 4-14(d) using three small layers again. The cusp height of each layer is calculated
using the normal in its own height. The sum of three small layer's cusp height is
0.16+0.24+0.29= 0.69, which is a bit smaller than the linear one. If we further divide the
smaller layers, an even better approximation will be obtained. When the small layers are
infinitesimal, this comes to the idea that we calculate the error by integrating the error
metric profile.
Sampling for Profile Construction
To improve the efficiency of the implementation, the entire range of the metric profile
ϕ(z) is divided into a series of intervals. The bins (intervals) are consecutive and non-
overlapping intervals of the height z, and they have an equal size of b, i.e., ϕ(z)=
{ϕ
̃
(1),…,ϕ
̃
(N)} where N= {model height (H)/ interval size(b)} is the number of bins, and
the size of each interval $b$ is set as a small value (2 um in our test cases; in comparison,
the layer thickness typically used in SLA is 100 um).
We employ the sampling techniques to facilitate the computation of the metric profile
value in each interval. It can be well-structured points, voxels, or rays, and the geometric
error could be easily evaluated by checking all the sampled points falling into the
corresponding interval. This process is efficient compared to the expensive intersection
operation based on the original CAD model.
137
In this study, we choose the Layer Depth Image (LDI) as our sampling approach. LDIs
[153] [154] is an extension of the ray representation (ray-rep) in solid modeling. Based on
a well-structured discrete sampling approach, LDIs can efficiently and robustly perform a
set of complex geometric operations, including offsetting [128] [155], Boolean [144],
regulation [156] [157]and overhang area evaluation [158]. By parallel GPU computing,
LDI could achieve high resolution efficiently (an STL model with 1 million faces can be
sampled into LDI within one second). Comparing to directly slicing a model with similar
complexity in the finest resolution that takes several minutes, it saves a lot of computation
time. Generally, the resolution of the LDI is dense enough for normal models. For a bigger
size model or a higher accuracy is needed, a technique called volume tiling [157] can be
used. That is, the bounding box of a model is first split into smaller tiles. Each tile is then
processed independently, and we construct their LDI models respectively.
Besides the sampling efficiency, LDI is also a rich sampling representation (denoting
a sampled model as P={p
j
}={x
j
,y
j
,z
j
,n
j
x
,n
j
y
,n
j
z
,f
j
,r
j
} ), which includes the point
coordinate (x
j
,y
j
,z
j
), normal (n
j
x
,n
j
y
,n
j
z
), ID of facet f
j
where the point belongs to, and ID
of sampling ray r
j
that has the information of point adjacency and In/Out specification (i.e.,
the intersection point where the ray goes into or gets out from the model).
Among this information, the point coordinates (x
j
,y
j
,z
j
) is always useful, and the facet
ID f
j
is used to retrieve the weight ω
j
⁡. Also, the normal (n
j
x
,n
j
y
,n
j
z
) is used to construct the
profiles of “cusp height” and “surface roughness,” while the ID of sampling ray r
j
is used
138
to build the profiles of “area deviation” and “volume deviation.” The ray r
j
is also useful
in the generation of tool paths/mask-images for fabrication.

Figure 4-15: Sampling for profile construction.
For example, the cusp metric profile requires the normal (n
j
x
,n
j
y
,n
j
z
). The construction
of the metric profile can be performed efficiently by grouping the points into the
corresponding intervals according to their heights. Recall that the metric profile of cusp
height is discretized into N intervals, and for each interval 𝑖 , the metric value ϕ
̃
(i) is the
maximal value of $n_z$ among all the points inside the interval, i.e.,
ϕ
̃
cusp
(𝑖)=max{𝑛 𝑗 𝑧 |⌈
𝑧 𝑗 𝑏 ⌉=𝑖 ,𝑃 𝑗 ∈𝑃 } (41)
Hence, the metric profile value at height $z$ could be approximated as
ϕ
cusp
(𝑧 )≈ϕ
̃
cusp
(⌈
𝑧 𝑏 ⌉) (42)
This profile construction process can be done within 50 ms on GPU for all our tests.
Slicing Algorithm
139
After constructing the metric profile ϕ(z), we have all the information to formulate
the slicing optimization problem of Eq.(\ref{equ:problem}).
We represent the slicing plan (S) as a boolean array with a size equal to the number of
intervals N+1, where the value of $true$ or $false$ stands for if there is a slice on that
particular height or not. There are manufacturing constraints of the minimal and maximal
layer thickness [t
𝑚𝑖𝑛 ⁡,t
𝑚𝑎𝑥
], and the the size of interval b. As the intervals are used to
optimize the location of the slicing planes, if b is a common factor of t
𝑚𝑖𝑛 ⁡and⁡t
𝑚𝑎𝑥
, it is
possible for the algorithm to utilize the whole range of layer thickness. Otherwise, the range
of the layer thickness will be narrowed down, and the minimal and maximal number of
intervals in one layer will be ⌈t
𝑚𝑖𝑛 /𝑏 ⌉and ⌊t
𝑚𝑎𝑥
/𝑏 ⌋.
To find a slicing plan, one may apply a greedy algorithm to assign as many intervals
as possible to a layer until the sum of the metric profile ϕ
̃
(i) exceeds the tolerance ϵ.
However, a greedy heuristic may yield locally optimal solutions and fail to satisfy the
constraints while the minimal layer thickness is restricted. Although it is faster to calculate,
we find that this kind of situation is not rare and appears from time to time. Moreover, such
a greedy algorithm cannot guarantee the result with a minimal number of layers. It
motivated us to design an efficient algorithm based on Dynamic Programming (DP) [159]
to compute a true global optimum.
For a bottom-to-top DP algorithm, it starts from the head and computes sub-solutions
from smaller to bigger problems, and then stores the intermediate results in the memory.
These previously computed solutions are combined to give the best solution for the whole
140
problem. Once it has reached the tail, the optimal slicing plan can be extracted by
backtracking.
The process is illustrated using an example of first 8 intervals {ϕ
̃
(1),…,ϕ
̃
(8} shown
in Figure 4-17. Assume the allowable error of a layer is ϵ=0.6, and the minimal and
maximal number of intervals in a layer are 2 and 3 to satisfy the constraint C3 in Eq.(37),
i.e., ⌈t
𝑚𝑖𝑛 /𝑏 ⌉ = 2 and⌊t
𝑚𝑎𝑥
/𝑏 ⌋ = 3. A weight array K[0,…,8] and an index array D[0,…,8]
for the slicing planes, i.e., K[1] is in between ϕ
̃
(1) and ϕ
̃
(8). The weight array K[…]
stores the least number of layers and the index array D[…] records the index of optimal
slicing positions, which will be used in backtracking. Figure 4-16 shows the core idea of
dynamic programming: memorizing the solutions to small problems.

Figure 4-16: Illustration of Dynamic Programming: Memorize solutions for small problems and
reuse them
141

Figure 4-17: An example to show the scalable layer algorithm with the first 8 intervals in the metric
profile is used to illustrate the Dynamic Programming based slicing process. SP\# means the slice
plane number. S[i] is the resulted optimal slicing plan.
Starting from the head (0
th
), it is initialized with K[0]=0 and D[0]=NA$as the first
slice plane to satisfy C4 in Eq.(37). The 1
st
-plane is initialized with K[1]=∞ and D[1]=NA
as for the minimal number of intervals to form a layer is 2, it is not allowed to put a slice
plane here. For the 2
nd
-plane, it can form a layer only with 0
th
-plane including ϕ
̃
(1) and
ϕ
̃
(2), so K[2]=K[0]+1=1, where the `+1' means one layer, and D[2]=0, meaning 0
th
-plane.
In other words, if there is a slice plane on 2
nd
-plane, this layer is optimal forming by the
0
th
-plane and itself.
As the minimal and maximal number of intervals are 2 and 3, there are two possible
positions to form a layer with the 3
rd
-plane, which are the 0
th
- and 1
st
-plane. A
comparison can be done to find the optimal one, and this sub-solution will be stored in the
memory. Specifically, two cases of forming a layer with the 0
st
-plane including ϕ
̃
(1) to
ϕ
̃
(3) and with 1
st
-plane including ϕ
̃
(2) to ϕ
̃
(3) are compared, and the minimum one is
picked. For 0
th
-plane, it is K[0]+1=1; and for 1
st
-plane, it is K[1]+1=1+1=2. In this case
the 0
th
-plane wins, and this sub-solution is stored as K[3]=1 and D[3]=0. Similarly, the
4th-plane will store K[4]=2 and D[4]=2.
142
For the 5th-plane, the two cases are with the 3
rd
-plane and the 4th-plane. However,
both ϕ
̃
(3)+ϕ
̃
(4) + ϕ
̃
(5) =0.9 and ϕ
̃
(4) + ϕ
̃
(5)=0.7 exceeds the allowable error of a
layer ϵ=0.6. Therefore, none of them is feasible, so the weight is set as K[5]=∞ and
D[5]=NA to prevent a plane is placed at this position. The iteration continues, and the rest
are K[6]=3 and D[6]=4; K[7]=∞⁡and D[7]=NA; K[8]=4 and D[8]=6.
The key of DP algorithm is making use of the stored sub-solutions (e.g., K[0…7]) to
compute the later ones until the last (K[8]). Once it has been done, the optimal slice plan
can be extracted by backtracking using the index array D[0…8]. Starting from D[8], which
records the optimal one to form a layer should be the 6th-plane, and recursively D[6]
returns 4, D[4] returns 2, and D[2] returns 0, which reaches the head. As a result, the slice
plan S[0] = S[2] = S[4] = S[6] = S[8] = True, and there are four layers: (ϕ
̃
(1),ϕ
̃
(2)),
(ϕ
̃
(3),ϕ
̃
(4)), (ϕ
̃
(5),ϕ
̃
(6)), and (ϕ
̃
(7),ϕ
̃
(8)).
The slice plan is valid and each of the layers has an error smaller than the allowable
error, so the DP algorithm can find a global optimum where the greedy algorithm probably
will take the first three intervals (ϕ
̃
(1),ϕ
̃
(2),ϕ
̃
(3)) and get a local optimum for the first
layer, and then being stuck with (ϕ
̃
(4),ϕ
̃
(5)) as the sum of them (0.7) is greater than the
allowable error⁡ϵ = 0.6.
Note that, if there is no feasible solution, the tail will store invalid values, e.g., K[8]=∞
and D[8]=NA, and the system will study and ask for a revision of the constraints. Otherwise,
the backtracking will never reach any of the invalid values in the middle until the head.
A general version of the slicing algorithm is summarized in Figure 4-18.
143

Figure 4-18: Adaptive slicing algorithm based on dynamic programming
It takes a linear time O(N) to compute and track the optimal slicing plan, where N is
the number of intervals (the worst case is quadratic time O(N
2
) for the range of minimal
and maximal interval number in a layer equals to the total number of intervals). In all of
our test cases, this slicing algorithm takes less than 5 ms.
The optimization based on the integral of metric profile works very well in the general
models as will be shown in the result section. Moreover, we can optionally insert some
must-slicing plane heuristically. For some special cases that a general flat metric profile
has some sharp changes, the integration may not exceed the allowable limit even a sharp
change is included because its neighborhood is very low in value. For instance, the CAD
144
model shown in Figure 4-18 has two such kind of sharp changes in the profile (marked as
A and B) due to the transitions between the cube and the cylinder.
Fortunately, the sharp changes can be easily detected in the profile, and thus, the
special case can be easily handled. We introduce one more step before applying the
optimization, and it is simply to go through the profile from the bottom to the top and
compute the difference for each consecutive interval. If the difference is greater than a
threshold (i.e., 0.5), a slice is placed in the upper interval, and the profile is separated into
two segments by the slice. After that, the optimization can be performed separately in
different segments, and they are assembled to a final result. Figure 4-19 has shown the
detail of this step.

Figure 4-19: Example of the scalable layers. Based on the metric profile of a given CAD model,
sharp changes (located at A and B, which are the sharp transitions between the cube and the
cylinder) can be detected. Our algorithm can successfully place slicing planes on these positions
with sharp changes.
Tool Path/Image Generation
After obtaining the optimal slicing plan, we can generate the projection images for
SLA printers, or the tool paths for FDM printers. Traditionally, the contours for the images
are directly computed from the intersection between the z planes and the CAD model,
145
which usually needs triangulation of the contour to generate the images. On the contrary,
because LDI is a kind of ray representation, we can easily determine whether a certain pixel
is black/white by checking the position of this pixel. Specifically, given the height of an
image plane, and that the resolution of the image is the same as that of LDI in the z-
direction, we can go through every ray of the LDI in each pixel and find the least sampling
point that is greater than the given height, and then the black/white of the pixel can be
determined by the In/Out specification of the sampling point. As the sampling point is the
next intersection point along the ray in the z direction, if it is specified as Out, then the
position of the pixel has to be inside the model, and the pixel should be white, and vice
versa. This can generate the images in a very efficient way.
The tool paths are then designed by the sequence for accumulating material to fill up
the whole image.
4.2.3 Adaptive Slicing of Weighted CAD Model
In some cases, the features of a CAD model are not equally important, and a
straightforward idea is that the more salient features will be sliced with smaller thickness.
For example, in the CAD model of Figure 4-20, the face of David model is considered as
more salient than the rest part. By adding a weight (whose value ranges from 0 to 1) to
each face, we can adjust the importance of each feature (face). In this study, two methods
of generating the weights are combined. Lee [160] introduced a multi-scale mesh saliency
computation method, which is the basis of our salient mesh. This multi-scale mesh weights
gives us another perspective of importance of features with different scales. It emphasizes
more on small scale features.
146
We also develop an interactive interface for the user to explicitly assign saliency level
to each mesh facet or region. Then, a combined mesh weight map will be generated by the
per-face product of geometry and user-specified saliency. An example can be found in
Figure 4-20. The saliency map for geometry-based method has high weight everywhere
along the z-axis, while by specifying the high weight only in the face of David model, we
can focus our saliency weight onto the portion that the user prefers.

Figure 4-20:CAD model with weighted surface, and the right salient map is a combination of
geometry saliency map (left) and user-defined saliency map (middle)
Moreover, each sampled point p
j
in our LDI model will inherit the weight value from
its belonged face. As there are numerous sampled points at each height, in this work, we
conservatively pick the maximal weight at a height to indicate the importance of the feature
at that height. Multiplying by this conservative weight, the original metric profile is
adjusted according to the height's importance. A weighted metric profile can be
reformulated as
ϕ
w
cusp
(z)=ϕ⁡(z)⋅⁡ω(z),
(43)
147
where ϕ(z) is the original metric profile, and ω(z) is the maximal value among all
weights at height z, i.e. ω(z)⁡=⁡max{ω
j
|z
j
=z,p
j
∈⁡P}, which conservatively preserve
the features with the highest weight.
Our original algorithm could be easily extended to considering the weighted features.
We design a GUI to assign a weight to each face of the CAD model, in which the larger
weight means the more salient. As the LDI sampled point provides the face ID it belongs
to, we can retrieve the weight of the face. Thus, a weight map for all the features can be
imported to our slicing algorithm, and the original metric profile will be adjusted as the
weighted metric profile as shown in Figure 4-21. After the weighted profile is computed,
the rest of the slicing algorithm is the same. Figure 4-21 shows the optimal slicing plan of
the weighted model.

Figure 4-21: Slicing comparison between weighted and non-weighted CAD model. The top part of
the figure is a general slicing plan, which is almost uniform slicing, and the slicing in the bottom
148
has small thicknesses in high weight positions. The colors in the slicing plan range from red to blue,
indicating from the smallest thickness (50um) to the largest thickness (150um). The very right
column shows the weighted result in the bottom has smaller cusps, and the scale bar is 200um.
The fabrication results demonstrate that the slicing with a weight map has a smoother
surface on the David's face than the one without a weight map. Comparing with the non-
weighted CAD model, the weighted model has large weight values in the face region.
Correspondingly, the weighted metric profile has a large value at the height of the face.
Therefore, in the optimal slicing plans, the slicing result of weighted CAD model has
smaller layer thickness (red lines) in the area of David's face. Eventually, this finer slicing
yields a smoother David's face with finer layers. i.e., with smaller cusps and staircases.

4.2.4 Result
Our slicing pipeline is implemented in C++, built on the open source package LDI
[154]. All tests are run by a PC computer with Intel(R) Core(TM) i5-3450 CPU @3.10GHz,
12GB RAM, and NVIDIA GeForce GT 640. The LDI sampling resolution is set as 2048.
The heights of all the tested CAD models range from 17.8 mm to 62.4 mm. All the
fabrication results are built using the SLA process. We modified a Projet 1000 printer from
3D Systems to function with different layer thickness. The layer thickness is controlled by
a Z-stage, and the practical thickness for a layer is from t
min
=50⁡μm (0.002 inch) to
t
max
=150⁡μm⁡(0.006 inch). The photocuring time of one single layer varies from 1 to 2
seconds respectively, while the overhead of transition between layers takes around 14
seconds.
149
From the slicing results, our new pipeline consumes less than 1 second in total
including sampling, constructing a profile, generating and optimizing the slicing plan, and
image generation. In contrast, the direct slicing algorithms need around 5 seconds for
coarsest layer thickness and 15 seconds for finest layer thickness. It is worth reminding
that the slicing time for the local greedy adaptive slicing algorithm [100] is only one single
evaluation of a slicing plan, but our adaptive slicing algorithm evaluates all the possible
slicing plans with the ultra-fine resolution and outputs the global optimal one. For
comparison, we have also shown the needed time for slicing plan optimization that is
directly computed on the CAD model using the ultra-fine resolution, denoted as T
𝑢𝑙𝑡𝑟𝑎 in
Table 4-3. On average, our algorithm could achieve 100 times faster than the direct slicing.
The effect is more significant when a large number of slicing will be performed to optimize
the fabrication orientation. In our orientation optimization experiment, it takes us less than
15 minutes to search among 1000 directions, while the slicing method directly computed
on the CAD model needs more than 1 day.
Table 4-3: Slicing Efficiency Comparison

The time units are in seconds. #Tri is the number of triangles in each STL model. #L
is the number of layers by our slicing algorithm. T
our
,T
co
.,T
loc
.,T
fine
⁡,T
ultra
represent
150
slicing time of our algorithm, coarsest uniform, local greedy, finest uniform, ultra
resolution slicing. This result is also visualized in Figure 4-22.

Figure 4-22: Slicing Efficiency Comparison Visualization.
Slicing Quality
Table 4-4: Slicing performance comparison with other slicing algorithms

We compare our method with the finest uniform slicing, greedy adaptive slicing [100],
and coarsest uniform slicing, denoted as “Finest,” “Greedy” and “Coarsest” in the table. A
set of models with various heights are sliced, and the results are compared in terms of the
number of layers (the middle part of the table) and the geometric error (maximum layer's
151
integral error among all layers, unit: mm, the right part of the table). The height unit is mm,
\#Tri means the number of triangles in each STL model, and the geometric error uses the
metric “Cusp Height.” This result is also visualized as below:

Figure 4-23: Visualize the slicing performance of different slicing algorithms
In Table 4-4, we compare our method with other slicing algorithms, including slicing
methods using uniform layer thickness and a greedy adaptive slicing method proposed in
[100]. The error metric used in Table 4-4 is ``Cusp Height". The left part of Table 4-4
shows the number of layers in the results computed by different slicing algorithms. It also
reflects the printing time as the printing time is almost proportional to the number of layers.
The right part of Table 4-4 shows the geometry error computed by the maximum error
among all layers, i.e., max{ε
k
⁡}. Here, the cusp height is used as the error metric, and thus,
this geometric error is also the maximum cusp height among all layers. Without any
surprise, the coarsest uniform slicing always gives the smallest number of layers but has
the largest geometric error, and the finest one always has the smallest geometric error but
152
gives the largest number of layers. They are used as the upper bound and the lower bound
for comparing the adaptive slicing algorithms. Both of our proposed and the greedy
adaptive slicing algorithm has set the allowable geometric error as the cusp height of ⁡ϵ⁡=
⁡65⁡μm for one layer.
From the table, we can see that the two methods fall right inside the upper and the
lower bound in terms of the layer number and geometric error. The results verify that both
of the methods are effective. However, our algorithm can achieve a smaller number of
layers under the same tolerance, and thus a smaller printing time (save up to 16\% printing
time). Moreover, due to the geometric complexity of the model and the fabrication
constraints, the greedy algorithm fails to distribute the errors evenly on the layers. Hence
their results are not optimal, and even cannot always satisfy the given tolerance for all the
layers. In contrast, our algorithm has global information for the planning, and our results
can successfully satisfy the given tolerance in all cases.
Last but not least, it is found that our adaptive slicing can get very competitive results
with the finest slicing, but our results have a much fewer number of layers and can save up
to 49 percent printing time. It validates our proposed method is not only efficient but also
promising.
Other Examples and Fabrication Results
We have applied our adaptive slicing algorithm using ``Cusp Height" error metric on
various models as shown in Figure 4-24. These slicing results reveal an intuition that the
layer thickness gets smaller at the height with increased geometry error density (i.e., with
a larger value in the metric profile). This intuition results from the error constraint in each
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layer that is the error of each layer cannot exceed the limit ϵ. Hence, if the error density of
a layer is large, then the layer thickness should be small so that the total integral error in
the layer does not exceed the limit ϵ.

Figure 4-24: Adaptive slicing results of various models
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Figure 4-25: Fabrication results of hearing aid model by different slicing methods.

Figure 4-26: Fabrication results of hand model by different slicing methods.
Figure 4-25 displays the physical fabrication results using different slicing algorithms.
From the microscope images (the bottom row of Figure 4-25), we can see that the results
from our slicing algorithm using ``Cusp Height" error metric is very close to the one
produced by the slicing with the finest layer thickness (the very left image in Figure 4-25).
Compared with the results of the uniform slicing and local adaptive slicing, our result has
a better surface finish, i.e., our result has less noticeable cusps and staircases. Figure 4-26
is another example to validate our slicing method. Similar to Figure 4-25, the result using
our method has fewer staircase defects comparing with other slicing algorithms like greedy
and uniform slicing.
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4.2.5 Extension: Different Metric and Optimal Orientations
Our slicing pipeline is a general slicing framework based on the sampling approach.
In this section, we extend our adaptive slicing framework by considering other factors
rather than cusp heights: 1) other commonly used error metrics are shown to be compatible
with our framework, 2) the mesh saliency map is integrated into the metric profile to
preserve the salient feature, and 3) the proposed slicing algorithm can be served as a
building block in searching the optimal fabrication direction efficiently.
Different Metric Profiles
In physical modeling, the commonly used geometry deviation error metrics include
cusp height, surface roughness, area deviation, volume deviation, etc. We show that our
framework is general to incorporate these metrics. Figure 4-27 shows all the metric profiles
and their corresponding slicing plans. We have already demonstrated our framework using
cusp heights, and we will briefly describe the details of formulation for others in below.

Figure 4-27: Metric Profiles with different geometric error are shown in the top and the
corresponding slicing plans are shown in the bottom. The colors in the slicing plan range from red
to blue, indicating from the smallest thickness (50um) to the largest thickness (150um)
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Figure 4-27 compares metric profiles and slicing results of different error metrics. The
metric profiles reflect the features of the users' interest. For example, the volume deviation
metric cares about the portion that has a large amount of volume error, and the bottom half
part has a large volume, and thus the bottom half of error metric profile is larger than the
up half part. In comparison, the cusp height metric measures the cusps which are not related
to the contour size, and hence it has a relatively balanced metric profile compared to the
volume deviation metric profile.
The exemplary “hearing aid" model in Figure 4-27 has surfaces facing up around the
middle height. These surfaces introduce large staircase error. We also notice that all these
error metric profiles have the large error density value at the height of these surfaces.
Accordingly, all the four optimal slicing results have a smaller layer thickness at the height
of these surfaces, i.e. the red lines in the middle height.
We should mention that all the three error metrics, including “cusp height”, “surface
roughness” and “area deviation”, have the “additive” property: the error for a thick layer is
the sum of the errors evaluated on the thinner layers that are combined into the thicker
layer. However, the formulation of volume deviation calculation indicates that this
“additive” property does not hold for the volume deviation.
Optimal Fabrication Orientation
Determining an optimal printing orientation can further improve the printing
performance, and it can be based on a different criterion.
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Figure 4-28: Optimizing the printing orientation. (a) We uniformly sample the directions on a
Gaussian sphere, and visualize the distribution of energy in a Gaussian sphere. Both the front view
(b) and the back view (c) are displayed. The three of best building orientations are shown in (d),
(e), and (f).
As will be demonstrated in the result section, our proposed slicing algorithm is very
efficient that can complete the slicing plan for all the models within one second. Such
efficiency plays an important role in finding the optimal fabrication orientation, which
requires a large number of slicing evaluations along different orientations (normally about
1000 direction candidates). In this study, we present a nested loop to find the optimal
building orientation based on the fabrication time and surface quality. In the outer loop, we
uniformly sample the orientation space into 1000 directions (Figure 4-28(a)). For each
orientation, given the allowable maximum cusp height, we run our adaptive slicing
algorithm as the inner loop and obtain the optimal slicing plan with the corresponding
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fabrication time and surface quality. We use the weighted summation of fabrication time
and surface roughness as the objective energy function:
F(𝐎 )⁡=α⁡|K(𝐎 )|⁡+⁡(1−α)|ε(𝐎 )| (44)
K(𝐎 ) is the number of layers at orientation 𝐎 , which is normalized by dividing the
maximum of layer numbers over all orientations. K(𝐎 ) is the geometric error at the
orientation 𝐎 , which is also normalized by dividing the maximum geometric error over all
orientations. The weighted ratio α is set as 0.5.
We use the “Pig” model as an example to show the usage of metric profile to find the
optimal building orientation. This “Pig” model's height is 58mm. We uniformly sample the
orientation space into 1000 directions (Figure 4-28 (a)). For each orientation, given the
allowable maximum cusp height, we run our adaptive slicing algorithm and obtain an
optimal slicing plan and corresponding fabrication time and surface roughness. Moreover,
the weighted objective energy is visualized in a Gaussian sphere as shown in Figure 4-28
(b) and (c), where the front-view and back-view of the Gaussian sphere are displayed with
red and blue in color represent large and small energy respectively. Three local best
fabrication directions are identified as (d)(e)(f) in Figure 4-28.
4.2.6 Concluding Remarks
This section presents a novel adaptive slicing algorithm for layer-based additive
manufacturing. Traditional adaptive slicing algorithms suffer from long computation time
or yield sub-optimal slicing result based on local geometry error. To generate the global
optimal slicing plan efficiently, we introduce a novel algorithm based on a “metric profile”,
which is a measure of geometry error distribution along a given building direction. The
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efficiency and effectiveness of our algorithm are enabled by three key ideas in our study:
1) the new representation of metric profile provides us the global geometry deviation along
the z-direction, rather than only geometry error on the slicing planes that are used in most
traditional methods, 2) we efficiently construct the metric profile using a GPU-accelerated
sampling approach, and 3) an optimization algorithm based on dynamic programming is
proposed to find the global optimal slicing plan efficiently. Such advantages have been
validated by comparing the computational time and fabrication quality with other slicing
algorithms.
Our slicing method is a general adaptive slicing framework, and we have extended it
to consider weighted features of a CAD model and to incorporate the commonly used
surface quality metrics, such as cusp height, surface roughness, area deviation, and volume
deviation. Our slicing algorithm can also serve as a building block for computing the
optimal printing direction. The full text of this section has been published on Computer
Aided Design [7].

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4.3 Transferring Layers for High-Resolution Channel
The previous layer planning methods are mainly focused on the quality of the outward
surface. In comparison, there is another crucial type of surface, channel, that is critical and
difficult for current AM processes. The challenge of printing channels results from three
aspects. Firstly, channels have overhang “roof” structures which may need support.
Secondly, the penetration of the light through the roof may cure the resin left in the
channels, blocking the channels. Most importantly, various functional channels have a very
small cross-section profile, whose height is only several micrometers, while the overall
footprint of the part is in centimeters. This again is the scalability issue. In this section, we
propose a new layer planning method, specifically to address the fabrication of channels
with scalable height.

Figure 4-29: Comparing scalable layers and scalable channels.
Before introducing the proposed scalable channel, we would like to review the related
work and issues on 3D printing micro channels. Microfluid channels are important
biomedical devices [161] [162] [163]. They have a lot applications [164] [165] [166] [167]
[168] [169] [170]. For example, the droplet generator can generate microdroplet for the
drug study. The flow cell microchip can be used for single cell study. Also, there is more
other microfluid channels that have tremendous applications. Typical micro-fluid channel
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height ranges from 10 um to 50um. However, conventional fabrication methods have many
drawbacks. They are very expensive due to the mode fabrication, and also they are mostly
just one layer or two.
Currently, the 3D version of microfluid is becoming more popular due to its
effectiveness and efficiency. For example, people find that 3D mixture has a better mixture
performance. Also, the 3D micro channels can also enable integrated devices which reduce
the burden for connector and assembly [161].
However, Current 3D printing has limitation to fabricate the micro channels. The
major reason is the resolution. Most 3D printers can only print channels with more than
200 um width and height [170]. Among them, SLA is a promising method for printing
high-resolution features.
However, SLA has a significant issue when printing transparent resin, which is so-
called over curing. Due to the transparency, the curing light will penetrate to cure the
residual resin left in the channel, hence to block the channel. By fine-tuning the parameters,
researchers find the minimum feasible height for a given resin, that is 2.3 times of the light
penetration depth. This value is huge. For a commonly used resin, E-glass, the minimum
height for a channel is about 554 um, which is not possible for printing usable channels.
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Figure 4-30: Challenges of printing transparent micro-fluid channels. a) shows our printing
transparent channels with red liquid flowing through the channels. b) shows the curing
characteristic of the used resin, whose penetration depth is 241um. c) shows that the channels
printed by conventional SLA are blocked due to the over curing issue.
In this project, we report a method to produce transparent micro-fluid channels with
less than 5um, which is not reported, to the best knowledge of us. Figure 4-30 a) shows our
printed result. Figure 4-30 b) shows that the E-glass resin’s curing characteristics, which
has a large penetration depth, around 254um. Figure 4-30 c) shows that the conventional
SLA process cannot produce clear channels using this E-glass resin.
4.3.1 Printing Channels with Double Platforms
To illustrate the principle of the proposed method, suppose we want to print this three
layer’s channel. The middle layer contains two channels. As shown in Figure 4-31 a), we
print the first two layers using standard methods. For the last layer, we use another aux
platform to build the roof for the channels first. Moreover, the remove the aux platform
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and print the rest region of that layer. In this way, we can prevent the curing light to cure
the resin in the channel, so that to print arbitrary height of channels.

Figure 4-31: Fabrication method of scalable channels. a) demonstrates the key steps of our methods.
b) shows a simple micro chip design. c) shows the mask images planning method.
4.3.2 Mask Image Planning Algorithm
We also design the image planning algorithm to handle complex geometries. The basic
idea is printing the roof first to protect the channels, as shown in Figure 4-31 c). Here, we
summarize the idea into an algorithm:
Image Planning Algorithm
Step 1: Slicing the 3D model into N layers, each layer has an image pattern L
i
.
Step 2: For i=1:N
Step 3: L
i
1
=L
i
−L
i
∩L
i−1

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Step 4: L
i
2
=L
i
∩L
i−1

Step 5: End for
4.3.3 Separation Force
An enabling technique is the fabrication of the channel “roof.” In this technique, an
aux platform is used to constrain the height of the roof. The key challenge is to ensure that
the printed “roof” is left in the resin tank, rather than attached to the aux platform when the
aux platform is removed. This requires that the bonding force between the “roof” and the
resin tank is much larger than the bonding force between the “roof” and the aux platform.
Noted that in our implementation, both the resin tank and the aux platform are coated with
Teflon film. The resin tank is coated with Teflon film because we expect that a relative
lower bonding force so that the printed part can be printed on the regular platform. However,
for the “roof” printing, we expect the printed part is left in the resin tank. To ensure this,
we integrated four mechanisms so that the printed roof can be left in the resin tank, and the
printed part can be attached to the regular platform.
First, we notice that in the printing of the “roof,” the bonding between the “roof” and
the resin tank is naturally stronger than the bonding between the “roof” and the aux
platform due to the former one received more energy. Moreover, more energy means the
bonding is stronger. This is verified by the data shown in Figure 4-32 c) and d).
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Figure 4-32: Detaching mechanism in scalable channels. a) shows the forces involved in the
fabrication of channel “roof.” b) is the schematic drawing of sensing the detaching force. c)
compares the real-time force at different curing time. d) gives the force compassion at different
curing time.
Second, the gravity let the printed “roof” tend to stay in the resin tank, rather than to
attach to the aux platform.
Third, the contact area of the bonding between the “roof” and the resin tank is larger
than the bonding between the “roof” and the aux platform.
Lastly, we could also pick different Teflon film for the resin tank and the aux platform,
so that the bonding force between the “roof” and the resin tank is larger than the bonding
force between the “roof” and the aux platform.
4.3.4 Bounding between two exposures
In the proposed method, a layer is printed with two connected exposures. A natural
question for this method is how good the bounding between two exposure is. We did a set
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of mechanical test and found out that the two connected exposure has no significant
difference with the part using single exposure.

Figure 4-33: Bounding force test.
4.3.5 Fabrication Result
Simple Channels
Here, we show some preliminary results of the proposed method. Using the above
method, we first printed straight channels to validate the feasibility of the proposed method.
Figure 4-34 a) shows the printed results. Figure 4-34b) gives the detailed profile of the
printed channels. The height of the channels measures at 70um, which verify that our
method can fabricate channels with height much thinner than the penetration depth. We
drop some liquid to test the functionality of the channels. Figure 4-34e) shows how the
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liquid flow through the channels. During the testing, we notice an interesting phenomenon
that the liquid flows much faster for the first time, we drop the liquid compare that when
the liquid already wets the channel.

Figure 4-34: Simple channel fabrication and testing. a) shows two micro channels with 70um
height. b)-d) shows the profile of the channels. e) shows how a droplet is flowing through the
channel.
Channels with 5um Height
We try to figure out what the minimum height we can print for channels. It turns out
we can print a fully functional channel with the only 5um. To the best of our knowledge,
this is the first time that 5um transparent channels can be 3D printed.
Figure 4-35 a) gives the design of the tested patterned, which contains five channels
with a height of 200um, 100um, 50um, 25um, and 5um. Figure 4-35 b) and c) shows a
microscopic image of the printed results. It shows that all the channels are clear, and the
liquid can flow through easily. Figure 4-35 g)-i) reveals the printed 5um channels.
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Figure 4-35: Printing channel with different height. a) shows the design pattern with different height
channels. b)-c) shows the printed results. d)-f) show the profile of a 25um channel. g)-i) shows a
channel with only 5um height.
An integrated micro fluid mixture
Then, we try to print an integrated micro fluid device to demo the benefit of 3D
structure for less connector and assembly. Figure 4-36 shows the printed part and how we
test the functionality of the printed device.
The channels in Figure 4-36 is 400um wide and 50 um high, which is proper for most
microfluid experiments.
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Figure 4-36: An integrated 3D printed device
3D structures with micro fluid channels
To verify that the proposed method can fabricate complex 3D structures with multiple
layers of channels, we design a 3D structure with two layers of channels, shown in Figure
4-37a). Figure 4-37 c) shows the microscope image of the channels, which demonstrate
that the two layers of channels are separated clearly. Figure 4-37 b) show that liquid can
flow through the channels. Figure 4-37 d) and e) depicts that the two layers channel is
separated as designed, and each channel is connected and functional. This structure gives
a proof of the concept that the process could fabricate complex 3D structures with micro
fluid channels.
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Figure 4-37: 3D structures with micro fluid channels.
4.3.6 Concluding Remarks
This subsection reported a novel method to 3D print transparent micro fluid channels.
The key idea is to print the “roof” of the channel individually to avoid the over curing issue
in conventional SLA process. Using this method, we have successfully produced
transparent channels with only 5um height, which is very difficult for conventional SLA.
Moreover, to ensure the reliability of the process, we study the bonding forces in the
process and integrated different mechanism to improve the printing reliability. Also, we
have printed several parts to validate the feasibility of the process.

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Chapter 5 Application: Mimicking the Shark Skin
4

Several experimental parts were printed to verify the effectiveness of the proposed
SAM processes. Also, we fabricated a functional multiscale structure, i.e., the structure
inspired by shark skin.
Nature is an exceptional source of structures that have superb functions. Self-cleaning
and super-hydrophobicity property of lotus leaf is well known. Other than that, spinules or
micro-hairs on Geckos, insects, spiders keep them water repellent and dry. Fine structures
at inner walls of wood conduits help water transport in the plant. The scales on Lepidoptera
serves dual purposes. Scales on their wings generate eye-catching effect with structural
color, and certain scales on some moth creates ultrasonic signals for intraspecific
communication [1]. Many structures from nature can be transferred into technologies that
have significant engineering and economic potential. The skin on fast swimming sharks
has been drawing attention for three decades. The superficial structure on shark skin
consists of skin teeth that are multi-functional. They prevent sharks from biofouling and,
more importantly, reduces fluid friction drag making the swimming more efficiently
through the water. Such structure can also be applied to ships, underwater vehicles,
airplanes and pipelines with relatively flat sides for which friction drag accounts for a major
part of total drag.

4
The full text of this chapter has been published on the journal of Advanced Material Technologies, as Li,
Y., Mao, H., Hu, P., Hermes, M., Lim, H., Yoon, J., Luhar, M., Chen, Y. and Wu, W., 2019. Bioinspired
Functional Surfaces Enabled by Multiscale Stereolithography. Advanced Materials Technologies,
p.1800638.
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Figure 5-1: Mimicking shark skin.
5.1 Reduced Drag Force in Multiscale-Structured Shark Skin
Saif, M, and Koury, E studied drag in pipes lined with riblets film and observed 5 - 7%
drag reduction [2, 3]. Bixler et al. used molding to duplicate from a real shark skin sample,
and the replica got 29% drag reduction with superhydrophobic coating [171]. Bechert et al.
fabricated 3D interlocked riblet structure using micro casting and printing and observed
7.3% drag reduction [172]. Lauder and Li et al. did a series of the study of drag effect of
shark skin denticles under a dynamic self-propellant condition which involved real shark
skin membrane, 3D printed solid denticles on the flexible membrane as well as laser cut
membrane [135] [134] [173]. The membrane made of real shark skin sample achieved a
12.3% drag reduction, and the 3D printed sample achieved 9.6% drag reduction.
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The complete mechanism of how the riblets interact with fluid is complex and not yet
fully understood. Typically, in laminar flow, the riblets increase friction drag due to the
increased surface area. The drag reduction usually happens in the turbulent flow region. A
simplified explanation [174] is that when vortices form, the riblets keep them away from
the valleys between the riblets and only the tips of the riblets are in contact with the high-
speed flow in the vertices. The majority of the surface area is in the valleys, and low-
velocity flow in them only produce very low sheer stress. Numerical simulations [175] also
shows such velocity distribution on riblets covered surface.
The low drag property is very promising in many emerging areas such as microfluidic
devices, unmanned aerial vehicle(UAV), autonomous underwater vehicles(AUV), etc. Up
to now, the majority of the manufacturing technology in previous studies are limited to
molding and micromachining, which is a natural result of the characteristics of shark skin
texture. The texture involves riblets that have a pitch of a fraction of a millimeter and
smallest feature of sub 100-micrometer size. To duplicate the feature, high-resolution
fabrication technique is required. However, if we want to apply the texture to applications
above, a few challenges will arise. First, the area to be covered is much larger compared to
the minimum feature size of the riblets which prevents some high resolution, low
throughput technologies, such as two-photon lithography [139] and electron beam
lithography from being used in fabricating shark skin texture. Second, the surface to which
the riblets attach is not always flat and can be highly customized geometry which the
technologies such as molding, laser cutting, and micromachining are hard to accommodate
to.
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The flexibility of stereolithography makes it very appealing in realizing artificial shark
skin texture on the customized surface shape. However, there is an issue that needs to be
solved. As the micro-texture and the whole printed object are many magnitudes different
in size, the manufacturing is inherently multiscale. Any stereolithography machine with a
fixed voxel size will not execute the multiscale process very well. For example, most
commercially available 3D printers that are capable of printing objects larger than
centimeter size only have a resolution of 100 um at best [176] which is far from the optical
limit of the printing resolution and not fine enough for fabricating the riblets. Wen Li and
colleagues studied a shark skin structure fabricated by 3D printer [134], but the features
were scaled up due to printing resolution, which limited the study. The reason behind it is
a trade-off between the overall size of the object and the total number of voxels that can be
handled practically. To have a fine resolution in 3D lithography, not only we need to have
a small x-y plane resolution. A small layer thickness in the vertical Z direction is required
as well. Therefore, if the size of the voxel is shrunk linearly to increase resolution, the total
number of the voxel will have a cubic growth which will result in a significant increase in
fabrication time and workload of modeling in a computer system. Some technique has been
developed for high-resolution printing [139] [176] [177] [178], but the volume per minute
throughput was very low that only tiny object could be demonstrated. Lauder et al.
fabricated a high-resolution shark skin denticle using two-photon lithography [173],
however, no large area sample could be fabricated for fluid mechanics study. DMD based
stereolithography machine has been a popular option in fabricating microscale objects [179]
[88] with the benefit that the whole cross-section can be cured with one exposure. The
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smallest feature they can build is defined by the image of a single pixel on the DMD. To
achieve a smaller resolution, the whole exposure area needs to be demagnified due to the
fixed number of pixels available on the device. In other words, these machines have to
either print small high-resolution objects or big low-resolution objects. As there was a gap
between microscale fabrication and macro-scale applications, we proposed a multiscale 3D
printing technology to bridge it.
We proposed to fabricate large area objects covered with shark skin riblets using a low
cost (built under $2500), scanning mirror based multiscale stereolithography technology.
To demonstrate the concept, several pipes with riblets covered interior were printed, and
their pipe flow friction reduction effect was measured. The multiscale printing was
achieved by a variable size voxel. A large voxel can fill most solid volume in the pipe wall
quickly and a small voxel can build detailed riblets features. Pipes with shark skin texture
which are about 19 cm long with sub 40 um features were printed with a printing speed
that was more than 4 times faster than the traditional fixed voxel process.
Other than printing shark skin riblets, multiscale stereolithography can also have big
impact in several aspects. First, for non-multiscale objects, as small voxel can be used in
printing objects’ surface, their surface finish can be improved significantly, eliminating the
necessity for time-consuming polishing process. Second, the designer can have various
porosity or microstructure in a different part of the object. Hence by using a single material,
the various mechanical property can be realized by using a single material and machine.
Last but now least, it is a powerful tool to integrate more functionality in a given volume
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for additive manufacturing, which is a trend we have seen in the semiconductor industry in
the last 5 decades.
The resonance grating filter consists of TiO2 gratings on a fused silica substrate. It is
selected in this work due to its high reflectivity and small thickness, which makes it
possible to stack multiple layers together to have more than two beam shapes similar to
shaped-beam electron-beam lithography [180]. The grating fabrication process includes
nanoimprint lithography, reactive ion etching. The grating structure inside a 25 um
diameter circular area at the filter center was removed by photolithography followed by
reactive ion etching which creates an aperture for the 405nm laser. Details on fabrication
were explained in our previous publication [10].

Figure 5-2: Multiscale toolpath planning for shark skins. Cross-sections of 3D printed pipes with
the smooth wall (a) and riblets on the interior with various riblets heights (b) – (d). The riblets
heights are 88 um in (b), 142 um in (c), 222 um in (d). The zoom-in SEM image in (d) shows the
smallest feature size to be 37um. The scale bars in the SEM images are 100 um. (e) – (f) Multiscale
model slicing and printing path. (f) High-resolution riblets feature (red) is sliced into small-scale
layers of 20 um thick. The low-resolution structure is sliced into large-scale layers of 100 um thick
(blue). Five small-scale layers are printed consecutively without recoating process in between.
After that, the cross-section is recoated by moving the stage up and down, and a large scale layer
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is printed. (e) Cross-section view of laser spots printing path. The low-resolution feature is printed
by the large laser spot while the small-scale feature is printed by the small laser spot.
For the digital model, we developed a process to handle the multiscale printing of
pipes with riblet texture (Figure 5-2 (e) – (f)). Using the proposed algorithm in this study
[8], large features and small features are processed separately using the different x-y
resolution and layer thickness. Comparing with fixed voxel stereolithography, the time
saving of our printing process comes from two parts. First, the large laser spot size and
large layer thickness make the low-resolution area being printed much faster. Second, since
the high-resolution features have small cross-section area and it is easy for the resin to flow
in, the recoating operation is not necessary between each small-scale layers and is therefore
removed.
5.2 Fabricating Shark Skin by Combining In- and Inter-Layer Methods
This section describes how the previously developed methods are used to fabricate the
shark skin inspired pipes. Figure 5-3 shows the fabrication methods. In this test case, we
combine the “down-scale” energy in Chapter 3.1 with “dual layer thickness” methods in
Chapter 4.1.
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Figure 5-3: Fabricating shark skin. 3D model of denticles. b) Printed denticles. c) The cross-section
of a sample which shows the suspended area of printed denticles. d,e) Multiscale printing of
denticles: (d) adaptive layer thickness. Different colors denote different layers during printing. (e)
Cross-section view of a layer showing beam switching within a single layer. For the denticle
features in the inner surface, the small laser beam was used for high resolution. For the pipe wall,
the large laser beam was used for high throughput.

As shown Figure 5-3 d), different portions of the part have different layer thickness.
The major body of the pipe uses thicker layer thickness while the high-resolution region
has thinner layer thickness. By doing so, the microstructures of the pipe are preserved, and
so the fabrication speed is not sacrificed due to that the major region is using thickness
layer thickness. Also, as described in Chapter 4.1, there is no up-and-down separation
motion for the thinner layer thickness, which saves a large amount of time. This elimination
of separation for thin layer is possible because when fabricating the thin layers, only the
boundary with micro structures is contacted with the resin vat. This small contact area
enables resin self-refilling, hence no separation is required.
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Besides, within a layer, the “scale-down” energy has two sizes of laser beam: large
beam and small beam. The large beam scans the inner portion efficiently while the small
beam draws the high-resolution microstructures. By doing so, the efficiency and resolution
are both maximized.
Tool Path Planning Method Combining Shaped Laser Beam and Dual Layer
Thickness
We developed a general tool path planning method to dynamically switch laser spot
size between 300 μm and 25 μm, so that the high-resolution features can be preserved by
using the small laser spot and the fabrication speed can be largely improved by the large
laser spot scanning. The task of tool path planning is generating the scanning paths for the
scanner and lasers’ ON/OFF status, given a three-dimensional (3D) object, formatted as an
STL file. The 3D model is first sliced into a set of layers with 20 μm layer thickness. For
every five layers, compute their common area, noted as A. The interior of this common
area is calculated by offsetting A inwards with distance r (r is set as 0.5 mm in all our tests).
Notice that this interior is the common interior for all the five layers, and it is filled by
scanning the large laser spot, hence the major area of the part can be efficiently solidified.
Then, each small layer is only required to fill the boundary region using the small laser
spot, and the boundary for each small layer is computed as the whole layer subtracting the
common interior. This method can be summarized as
Algorithm:
Input: a 3D model (STL format)
Output: the tool path (gcode)
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Steps:
01: Initialize the output as an empty set P={}.
02: Slice the input 3D model into a set of layers using 20 μm layer thickness,
noted each layer as 𝐿 𝑖 .
03: For every 5 layers
04: Compute the common area of these 5 layers, denoted as A
05: Calculate the interior of A by offsetting A inwards with distance r, noted as
I=A↓r.
06: For each layer 𝐿 𝑗 in these 5 layers
07: Calculate the boundary of each layer as the whole layer subtracting the
interior (𝐿 𝑗 −𝐼 ).
08: Generate the scanning path for the small laser spot to fill this boundary,
and add the path to P.
09: End For
10: Generate the scanning path for the large laser spot to fill the common interior
A, and add this scanning path to set P.
11: End For
12: Return the tool path P

181
5.3 Results and Discussions
To demonstrate the utility of our multiscale printing process, we conducted
hydrodynamic experiments measuring fluid friction in pipes with varying shark skin
inspired textures. Several pipes with different microstructures on their inner walls (Figure
5-4 d) were printed so that they could be tested in a standard pipe flow pressure drop
experiment as shown in Figure 5-4 f. Details of the experiment is included in the
Experimental Section. The length of all four pipes was 18.7 cm and the internal diameter
was 9.4 mm. Figure 5-4 e shows the overall size of one of the pipes. One of the pipes had
a smooth bore (no microstructure); this was used as the baseline reference. The second pipe
had riblets with a height of 142 μm, which proved to be optimal for drag reduction. An
additional two pipes with riblet height 88 μm and 222 μm were also printed to test the effect
of texture size on drag reduction. The maximum feature resolution was 37 μm as shown in
Figure 5-4 d. It’s worth mentioning that higher resolution can be easily realized by using
lenses with larger numerical aperture which is not necessary for this work and may increase
the setup cost.
Friction factor estimates for the smooth bore pipe and the pipe with the optimal 142
μm riblets are plotted in Figure 5-4 g) as a function of the Reynolds number, 𝑅𝑒 =
𝜌 <𝑈 >𝐷 𝜇 ,
in which 𝜇 is the dynamic viscosity of water. Note that the Reynolds numbers in the
experiment ranged between 𝑅𝑒 ≈5000 and 𝑅𝑒 ≈12000. Over this entire range of
Reynolds number, the pipe with riblets had a smaller friction coefficient compared to the
smooth bore pipe, indicating drag reduction. The degree of drag reduction varied with
Reynolds number. On average, the friction coefficient was 0.046∓0.0017 for the smooth
182
pipe and 0.042∓0.0016 for the pipe with riblets, which yields an average drag reduction of
9.6%. To study how riblet geometry affects drag, both taller and shorter riblets were also
tested. The measured friction factors are shown in Figure 5-4 h). The measurements
demonstrate that, for the conditions tested, the 142 μm riblets yielded the best performance.
Both increasing and reducing the riblet height worsened performance.
The observations described above are in broad agreement with previous results, which
demonstrate that riblets can generate as much as 10% drag reduction [172]. Further,
previous experimental and numerical studies [172] also demonstrate a clear optimum in
riblet size for given flow conditions. However, the exact numbers obtained here must be
treated with some caution. This is because the average friction factor observed for the
present smooth bore pipe, 𝑓 𝐷 = 0.0463 is higher than that observed in previous smooth pipe
experiments. Specifically, the friction factor typically ranges between 0.04 and 0.03 over
the range of Reynolds numbers tested. We attribute this to potential roughness effects since
the 3D-printing process with a minimum layer thickness of 20 μm yields a rougher surface
than that in finely polished or honed pipes. Nevertheless, the current measurements
provide a nice demonstration of potential applications.
To demonstrate the advantage in throughput of the multiscale printing process. Several
pipes with different dimension scales were printed and the printing time was recorded
(Figure 5-4 i). At scale 1, the pipe was of 200 mm length, 12 mm diameter, 1.5 mm wall
thickness, 237 μm riblet pitch and 142 μm riblet height. In other words, the scale 1 pipe
has dimensions similar to the samples used in pipe flow testing, as shown in Figure 5-4 f).
For the other scales, riblet dimensions remained the same while the overall size of the pipe
183
changed in every direction. This test was carried out to simulate the situation in which
larger samples are needed for real-world application, but the high-resolution features need
to be maintained to ensure surface function. As shown in Figure 5-4 i), at scale 0.5, the
multiscale process is about 3.8x faster than the fixed voxel process. The speedup ratio
increases to 4.4 at scale 1 and 11 at scale 5. Note that data for scale 2 and 5 were
extrapolated from printing time of pipes shorter than required. The results shown in Figure
5-4 i) demonstrate that the multiscale process becomes more advantageous as the object
scale increases.
184

Figure 5-4: Small-scale features can change the large-scale object’s surface property. a) 3D diagram
of the complete multiscale stereolithography setup. The two lasers have wavelength of 405 nm and
445 nm respectively. b-c) Schematics of beam profile switching process with resonance grating
filter. The optical filter has different transmission properties for different wavelengths: b) For λ1 =
445 nm the filter is transparent and gives a larger laser spot (~300 μm) on the resin surface. c) For
λ2 = 405 nm, only the central area is transparent. The filter works as an aperture and gives a smaller
(~25 μm) laser spot on the resin surface. d) Cross-section view of four pipes with different interior
textures. Scale bar for the SEM images, 200 μm. e) Comparison of the overall size of a printed
multiscale pipe with a quarter dollar coin. f) Schematic of pipe flow setup. g) Measured friction
factors for the smooth pipe and the pipe with 142 μm riblets. h) Comparison of friction factors of
the pipes with different riblet height. i) Printing time of fixed voxel process and variable voxel
multiscale process at different object size scale.
With the help of multiscale stereolithography process, many other biomimetic
structures may be fabricated and studied experimentally. As an example, Figure 5-5 b)
185
shows an artificial lotus leaf with micropillars which has water repellent function, printed
using the same process. A contact angle of 139° was measured on the artificial lotus leaf
with 300 μm pillar pitch using a water droplet of 10 μL volume. Although the angle is
smaller than that on a lotus leaf in nature(Figure 5-5a) which can be larger than 150°, it is
a preliminary result showing that similar structure can be easily fabricated with the process.
Structure optimization and detailed characterization will be included in future works.

Figure 5-5: A drop of water on the surface of, a) a lotus leaf in nature, image from (http://www.hk-
phy.org/atomic_world/lotus/lotus01_e.html) and b) an artificial lotus leaf printed by the multiscale
stereolithography process. The pitch between the micropillars is 300 μm.
5.4 Concluding Remarks
In this application, we fabricated large area shark skin riblet texture that had a drag
reduction effect using multiscale stereolithography technology. The new technology was
realized by a variable laser spot size that depends on the wavelength and a model slicing
strategy that separates low and high-resolution features. The traditional stereolithography
process took more than 4X time in fabricating test sample compared with the new process.
Being able to provide high resolution and high throughput at the same time with relatively
186
low cost, the multiscale stereolithography process has the potential of achieving many
untapped applications for 3D printing technology.
The full text of this Chapter has been published on the journal of Advanced Material
Technologies [181].
187
Chapter 6 Conclusion and Recommendation for Future Research
6.1 Answering the Research Questions/Testing Hypotheses
As stated in Chapter 1, the Primary research question is

how can we improve the scalability⁡of polymerization additive
manufacturing?

As additive manufacturing processes are mostly layered manufacturing, the above
research problem can be further divided into two subproblems:

Q1: Within one layer, how can we improve the scalability of
polymerization additive manufacturing?

and

Q2: Across different layers, how can we improve the scalability of
polymerization additive manufacturing?

To answer these two questions, we proposed the following hypotheses:

188
H1: Advanced spatial and temporal polymerization energy control could
improve the in-layer scalability.
H2: Optimized layer planning methods could improve the inter-layer
scalability.

Moreover, these two hypotheses are further decomposed into six sub-hypotheses as:

Table 6-1: Six tested hypotheses
H1.1: Adding spatial modulation to the laser-based temporal energy
control system would improve the in-layer scalability.
H1.2: Adding temporal modulation to the projection-based spatial energy
control system would improve the in-layer scalability.
H1.3: Combining the spatial energy control system and temporal energy
control system would improve the in-layer scalability.
H2.1: Dual layer thickness could improve the fabrication efficiency and
resolution, and hence improve the inter-layer scalability.
H2.2: Adaptive layer thickness could improve the fabrication efficiency
and inter-layer scalability.
H2.3: Transferring layers method could fabricate ultra-thin layers and
improve the inter-layer scalability.

189
Hypothesis H1.1, H1.2, and H1.3 are tested in Chapter 3, which are dealing with the
scalability within one layer.
Hypothesis H1.1 is tested in Chapter 3.1, in which an additional small-scale 25 um
(one-tenth of the original laser spot size) is added to a laser-based additive manufacturing
setup. Therefore, the resolution is improved by 10 times. Meanwhile, an optimized
multiscale tool path planning is proposed and implemented, which can improve the
fabrication speed by more than 2 times on the test cases.
Hypothesis H1.2 is tested in Chapter 3.2, in which we use an XY linear stage to
continuously translate the projector to cover a larger area. Each layer is divided into 100
sections, and each section has the same size as the projector’s image size. By doing so, the
size is improved by 10 times. Moreover, compared with conventional discrete movement,
i.e., the projector is stopped when projecting, we continuously move the projector during
the XY stage translating, which can speed up about 3 times by eliminating the wasted time
on stage acceleration and deacceleration.
Hypothesis H1.3 is tested in Chapter 3.3, in which a 50-um laser spot and a projector
with 128mmX80mm image size are combined in a single setup. The boundary of each layer
is printed by the laser spot which has higher resolution than the projector, and the inner
portion of each layer is printed by the projector. The test cases show that efficiency is
improved to more than 2 times than the laser-based system while maintaining the same
resolution.
Hypothesis H2.1, H2.2, and H2.3 are tested in Chapter 4, which mainly improves the
scalability across layers.
190
Hypothesis H2.1 is tested in Chapter 4.1, in which a 3D object is decomposed into the
boundary portion and an inner portion. The boundary portion is fabricated using 10 um
layer thickness, while the inner portion uses 100 um layer thickness. Due to the boundary
can be recoated with fresh resin in near instant time (several milliseconds), we eliminate
the separation time and the stage’s up and down motion, hence to improve the efficiency
by more than 3 times on average on the tested parts.
Hypothesis H2.2 is tested in Chapter 4.2, in which the layer thickness is not uniform
but adaptive to the geometry error. The layer in the region that is sensitive to layer thickness
has a smaller layer thickness and vice versa. By doing so, about more than half layers are
eliminated without sacrificing the critical features. We formulate the problem as
minimizing the total number of layers while maintaining the surface quality requirement.
Dynamic programming based optimized algorithm is proposed to find the global best layer
planning. Therefore, the fabrication efficiency is improved by 2 times.
Hypothesis H2.3 is tested in Chapter 4.3, in which an auxiliary platform is added to
the setup to fabricate the “roof” of the ultra-thin channels (for example, 5 um channels in
microfluidics) and the “roof” is then transferred to a normal SLA process. With the same
resin, conventional AM methods could only print channels with 500um height, due to the
over curing issues. We treat these channels differently with other layers and achieve the
scalability required for fabricating the objects with these channels. The tested part verified
that the resolution for channels could be improved by 100 times.
Table 6-2 summarizes the improved scalability in tested hypotheses. From this table,
we can see that all the six hypotheses are well tested and verified.
191

Table 6-2: Scalability Improvement by SAMs
SAMs Hypothesis Size Resolution Efficiency
Within one
Layer
(Chapter 2)
Scale Down H1.1 10X 1X 2X
Scale Up H1.2 1X 10X 3X
Scale Integration H1.3 1X 1X 2X
Across Layers
(Chapter 3)
Dual Layer H2.1 1X 10X 3X
Scalable Layer H2.2 1X 1X 2X
Scalable Channel H2.3 1X 100X 1X

6.2 Engineering Achievements and Scientific Contributions
6.2.1 Engineering Achievements
The engineering achievements of this dissertation are listed as follow:
1. Proposed the concept of scalability Δ to quantify the capability to efficiently
fabricate macro objects with microscale features, which could be utilized to
compare different AM processes and to guide the development of next-generation
AM processes.
2. Fundamentally improve the scalability in three ways, by coupling the “spatial” and
“temporal” energy control methods.
a) Adding the “spatial” modulation to the laser beam can dynamically change
the laser spot size when needed. The laser-based SLA process is scaled down
by combing a scale-down 25 um laser spot and a large-scale 300um laser spot.
Optimized multiscale tool path planning to improve resolution and efficiency.
192
b) Adding the “temporal” modulation to the projection-based system enables the
projection energy control to cover a large area by scanning. The projection-
based SLA is scaled up to the printing size by utilizing an XY linear stage to
translate the projector continuously. A rotating mirror synchronized to correct
the motion blur to enable the projector’s continuous movement, which speeds
up the fabrication by eliminating the wasted time on stage acceleration and
deacceleration.
c) Directly combining the two energy control systems mitigates the drawbacks
of each method. I integrated a 50-um laser spot and a projector with a
128mmX80mm image size in a single setup. Scalable energy delivery is
achieved by curing the boundary of each layer with the laser spot and curing
the inner portion of each layer using the projector.
3. Proposed three layer-planning methods to improve the inter-layer scalability.
a) Dual layer thickness improves the resolution and efficiency. A 3D object is
decomposed into the boundary and an inner portion, where the boundary
portion is fabricated using 10 um layer thickness with instant resin recoating,
while the inner portion uses 100 um layer thickness.
b) Adaptive layer thickness improves the efficiency. The layer thickness is not
uniform but scalable to the geometry requirement. Formulated the problem
as minimizing the total number of layers while maintaining the surface
quality requirement. A dynamic programming-based algorithm is proposed
to find the global best layer planning.
193
c) Ultra-thin channels via transferring layers improved the resolution in printing
channels. Added an auxiliary platform to fabricate the “roof” of the ultra-thin
channels and printed ultra-high resolution (5um) channels for microfluidics,
comparing with only 500um channels achieved in conventional AM with
same resin due to the over curing issues.
4. Applied the proposed methods to fabricate large-area shark-skin riblet texture that
had a drag reduction effect. We observed the drag reduction of the printed parts
comparing with smooth surfaces. A lotus leaf’s multiscale structure is also
mimicked, and the printed parts exhibit superhydrophobic property.

These engineering achievements are also summarized and visualized in the following
Figure.
194

Figure 6-1: Illustration of contributions: expanding the scalability Δ within one layer and across
different layers.
6.2.2 Scientific Contributions
When seeking answers to the question: how we can effectively and efficiently fabricate
macroscale objects with microscale features, new knowledge is discovered and listed as
below:
1. Spatial and temporal polymerization energy control. This dissertation couples
spatial and temporal modulation of the polymerization.
a) Nano grated filter modulates the spatial distribution of laser beams. The
mechanism using Nanograting to change the shape of laser beams is
discovered and studied.
195
b) Spatially and temporally cumulative energy polymerization model is
proposed and validated. Multiple exposures lead to results with an equivalent
one-exposure.
2. Layer planning optimization. This dissertation studies the physical phenomena at
different scales, based on which the layer planning problems are mathematically
formulated as optimization problems.
a) The liquid resin recoating process is modeled by the Hele-Shaw flow, which
shows resin recoating time is in a non-linear relationship with the width of
the layer.
b) Adaptive slicing problem is mathematically formulated as a constrained
minimization problem. Dynamic programming finds the global optimal
slicing solution in linear time complexity.
196
6.3 Limitation and Future Research Recommendations
Scalability is one of the most challenging problems that prevent Additive
Manufacturing to be widely adopted for industrial applications. In this research, we have
proposed three methods to achieve scalable energy delivery and three methods to optimize
the layer planning, which significantly improved the scalability of the stereolithography,
which is so-called scalable additive manufacturing.
However, there are lots of limitations that need to be improved and addressed. To
name a few as below:
1. The fundamental philosophy in this research is treating features at different scales
differently. It is critical to study and improve the performance of the bonding
interface between features at different scales. We have tested that the bonding
interface has a statistically similar mechanical property with normal cured parts.
However, it is not clear how the other properties, such as optical property
(transmission rate, reflective index), and conductivity are affected by the multiple
exposures.
2. The additive manufacturing principle in this research mainly focusses on
photopolymerized. Most methods are specifically designed and proposed for light
energy. Besides polymerization, many other AM principles are widely used, such
as FDM and SLS, which are excluded in this research.
3. The scalability problems are decomposed into subproblems within one layer and
across layers. These two subproblems are studied individually in this research.
However, if the scalability issues could be considered in a three-dimensional
197
context, and these two subproblems are integrated, then even better scalability
could be achieved.
4. The layer considered in this research is flat, which is typical for most AM
processes. It is believed that the non-flat layer might bring in more benefit, such
as better surface quality, less support, and higher efficiency. If considered, we
would expect a bigger scalability Δ.
5. Besides the scalability, there are other important issues in AM, such as material
property, deformation, support structure, and fabrication reliability. Our research
optimizes the scalability as a single objective. However, if considered other issues
in SAM, then we could have high-quality scalability.
Besides addressing the above limitations, other future work also includes but not
limited to:
1. Fabricating the biomimetic structures using the proposed process and researching
on its functions in enhancing mechanics, electricity, and energy. The hybrid-
source would prototype designed micro-textures efficiently, assisting the future
investigation on micro-scale texture functionality. More applications should be
identified, for example, fabricating lenses and printing gecko-inspired structure
with directional adhesion property.
2. Applying the layer planning optimization framework to other geometric
computation tasks that are required in the pre-fabrication pipeline of AM processes,
and speeding up the process planning for AM applications like mass customization.
198
3. Applying the techniques proposed in this dissertation to other AM processes and
for example, using different sizes of nozzles in FDM processes to improve its
scalability. Also, the proposed dual layer thickness could be used in metal additive
manufacturing.
199
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Abstract (if available)

Abstract After nature’s millions of years’ evolutions, multiscale structures in plants and animals, such as lotus leaves, shark skin, butterfly wings, and human bone, exhibit splendid advantageous functionalities, including superhydrophobicity, drag reduction, structural color, and light-weight strength and many more. Various fabrication methods have been developed to duplicate these multiscale structures. As a major additive manufacturing process, stereolithography (SLA) has become a prevalent fabrication method for complex structures with high resolution. In SLA, three-dimensional structures are fabricated layer by layer, and each layer is patterned through the dynamic mask for polymerization. The dynamic mask enables SLA with flexible manufacturing capability compared with lithography and micro-machining. ❧ However, it is still challengable for current SLA processes to effectively and efficiently fabricate multiscale structures. Through thirty years’ research, two types of dynamic mask generation methods are developed: laser scanning and mask image projection. The laser scanning deposits energy for resin polymerization sequentially, referred as “temporal” energy control. The mask image projection utilizes a digital micromirror device (DMD) to project a mask image for resin polymerization simultaneously, referred as “spatial” energy control. The fixed laser spot size results in a trade-off between the fabrication efficiency and the laser spot resolution, while the fixed number of pixels in DMD chips leads to a trade-off between the printing size and the pixel resolution. Both “temporal” energy from scanning laser and “spatial” energy from DMD chips cannot effectively and efficiently pattern layers for multiscale structures. ❧ To fill this research gap between the multiscale structures and ineffective fabrication methods, we developed advanced “spatial and temporal” polymerization energy control to effectively and efficiently fabricate multiscale structures. By coupling the “spatial” and “temporal” energy control methods, we fundamentally improve the scalability in three ways. Firstly, adding the “spatial” modulation to the laser beam can dynamically change the laser spot size when needed. Secondly, adding the “temporal” modulation to the projection-based system enables the projection energy control to cover a large area by scanning. Thirdly, directly combining the two energy control systems mitigates the drawbacks of each method individually. ❧ Besides the critical challenges in patterning one layer, AMs fabricate 3D structures layer by layer and use very thin layer thickness to ensure the high-resolution features are printed, which leads to a largely increased number of layers and hence impractical long fabrication time. Based on the philosophy of treating features at different scales differently, three layer-planning methods are proposed to effectively and efficiently fabricate multiscale structures. ❧ The first layer planning method is dual layer thickness where the interior is printed using a large layer thickness, and the boundary is printed using small layer thickness. The second approach is adaptive slicing, where the layer thickness is not uniform but adaptive to the geometry error. The third method is transferring layers, which adds an auxiliary platform to fabricate the “roof” of the ultra-thin channels and transfer the roof to normal SLA process. All these three layer-planning methods could improve the efficiency, size, and resolution without any tradeoff among each other. ❧ By utilizing the advanced polymerization energy control and optimized layer planning, the scalability of AM processes could be largely improved. Currently, as a proof of concept, we have already developed hardware prototypes and software algorithms. Several test cases are fabricated to verify the effectiveness and efficiency of the proposed scalable additive manufacturing. Also, two applications are identified to show the benefit of the multiscale structures. A lotus leaf’s multiscale structure is mimicked, and the printed parts exhibit superhydrophobic property. Moreover, the multiscale of shark skin is designed and fabricated. The drag reduction of the printed parts is observed compared with smooth surfaces.

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Asset Metadata

Creator Mao, Huachao (author)

Core Title Scalable polymerization additive manufacturing: principle and optimization

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Industrial and Systems Engineering

Publication Date 07/25/2019

Defense Date 06/05/2019

Publisher University of Southern California (original), University of Southern California. Libraries (digital)

Tag 3D printing,additive manufacturing,bioinspired,high resolution,large area,multiscale,OAI-PMH Harvest,scalability,spatial and temporal,stereolithography

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Chen, Yong (committee chair), Gupta, Satyandra K. (committee member), Lu, Stephen (committee member), Wu, Wei (committee member)

Creator Email huachaom@usc.edu,mossmao@gmail.com

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c89-190571

Unique identifier UC11663262

Identifier etd-MaoHuachao-7611.pdf (filename),usctheses-c89-190571 (legacy record id)

Legacy Identifier etd-MaoHuachao-7611.pdf

Dmrecord 190571

Document Type Dissertation

Format application/pdf (imt)

Rights Mao, Huachao

Type texts

Source University of Southern California (contributing entity), University of Southern California Dissertations and Theses (collection)

Access Conditions The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the a...

Repository Name University of Southern California Digital Library

Repository Location USC Digital Library, University of Southern California, University Park Campus MC 2810, 3434 South Grand Avenue, 2nd Floor, Los Angeles, California 90089-2810, USA