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Fresnel beamforming for low-cost, portable ultrasound systems

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Fresnel beamforming for low-cost, portable ultrasound systems

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FRESNEL BEAMFORMING FOR LOW-COST, PORTABLE ULTRASOUND
SYSTEMS

by

Man Nguyen

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
(BIOMEDICAL ENGINEERING)

August 2013

Copyright 2013 Man Nguyen
ii
CONTENTS

LIST OF FIGURES ................................................................................................................... IV
LIST OF TABLES ................................................................................................................... VII
LIST OF ACRONYMS ............................................................................................................ VIII
CHAPTER 1. INTRODUCTION ................................................................................................... 1
1.1. Motivation ................................................................................................................ 1
1.2. Background .............................................................................................................. 2
1.2.1. Beamforming approaches in array ultrasound systems .................................... 4
1.2.2. Low-cost beamforming approaches.................................................................. 5
1.3. Contributions ........................................................................................................... 7
1.4. Publication List ........................................................................................................ 8
1.5. Organization of the Dissertation ............................................................................. 10
CHAPTER 2. FRESNEL BEAMFORMING WITH A REDUCED CHANNEL COUNT ........................... 12
2.1. Introduction ............................................................................................................ 12
2.2. The Design ............................................................................................................. 12
2.3. Methods ................................................................................................................. 17
2.3.1. Simulation ...................................................................................................... 17
2.3.2. Experimental setup ........................................................................................ 18
2.4. Results ................................................................................................................... 20
2.4.1. Simulation results .......................................................................................... 20
2.4.2. Experimental results ...................................................................................... 25
2.5. Summary ................................................................................................................ 29
CHAPTER 3. PERFORMANCE IMPROVEMENT OF FRESNEL BEAMFORMING USING DUAL
APODIZATION WITH CROSS CORRELATION ................................................................ 30
3.1. Introduction ............................................................................................................ 30
3.2. The design .............................................................................................................. 32
3.2.1. Dual apodization with cross-correlation – DAX ............................................ 32
3.2.2. Integration of DAX into Fresnel beamforming ............................................... 33
3.3. Methods ................................................................................................................. 36
3.3.1. Simulation ...................................................................................................... 36
3.3.2. Experimental setup ........................................................................................ 37
3.4. Results ................................................................................................................... 41
3.4.1. Simulation results .......................................................................................... 41
3.4.2. Experimental results – spatial resolution ....................................................... 44
3.4.3. Experimental results - contrast ...................................................................... 47
3.5. Summary ................................................................................................................ 50
CHAPTER 4. HARMONIC IMAGING WITH FRESNEL BEAMFORMING IN THE PRESENCE OF
PHASE ABERRATION ................................................................................................. 51
4.1. Introduction ............................................................................................................ 51
4.2. The Design ............................................................................................................. 52
4.2.1. Harmonic Imaging ......................................................................................... 52
4.2.2. Implementing harmonic imaging in Fresnel beamforming ............................. 54
4.3. Methods ................................................................................................................. 56
iii
4.3.1. Data acquisition – harmonic signal generation and ex-vivo aberrator .......... 56
4.3.2. Data processing – beamforming and contrast enhancement .......................... 57
4.3.3. Contrast-to-noise ratio (CNR) and spatial resolution .................................... 60
4.4. Results ................................................................................................................... 61
4.5. Summary ................................................................................................................ 68
CHAPTER 5. GATED TRANSMIT BEAMFORMER AND MODULAR FRESNEL RECEIVE
BEAMFORMER .......................................................................................................... 70
5.1. Introduction ............................................................................................................ 70
5.2. The Design ............................................................................................................. 72
5.2.1. Gated transmit beamforming ......................................................................... 72
5.2.2. Modular Fresnel receive beamforming .......................................................... 73
5.3. Methods ................................................................................................................. 76
5.3.1. Simulation ...................................................................................................... 76
5.3.2. Experimental setup ........................................................................................ 77
5.3.3. Post-beamforming processing ........................................................................ 78
5.4. Results ................................................................................................................... 79
5.4.1. Simulation results .......................................................................................... 79
5.4.2. Experimental results - spatial resolution ....................................................... 84
5.4.3. Experimental results – contrast ..................................................................... 86
5.5. Summary ................................................................................................................ 90
CHAPTER 6. CONCLUSIONS AND FUTURE WORK ................................................................... 91
6.1. Conclusions ............................................................................................................ 91
6.2. Future Work ........................................................................................................... 93
BIBLIOGRAPHY .................................................................................................................... 94

iv
LIST OF FIGURES
Figure 1-1: Creating a transmit focus for an array transducer. Pulses from elements are
transmitted with specified delays to arrive at the focus at the same time. ...................................... 3
Figure 1-2: Creating a receive focus for an array transducer. Signals received from elements are
applied electronic delays before being summed. ............................................................................ 3
Figure 1-3: Delay profiles (not to scale) for a) traditional geometric focus beamforming, b)
Fresnel beamforming. Each segment corresponds to one period of the signal ............................... 6
Figure 2-1: Delays profiles of Fresnel beamforming and focusing errors in terms of wavelength
compared to DAS geometric focus beamforming for a 64-element linear array .......................... 14
Figure 2-2: A 4-transmit Fresnel (phase and sum) beamforming schematics for an array
transducer ...................................................................................................................................... 14
Figure 2-3: Fresnel (phase and sum) beamforming schematics for a 2-element array. 0
0
phase
shift is applied by closing switch 1, 45
0
by closing switch 1 and 2, 90
0
by closing switch 2.
Inverting amplifiers are used with switches 3 and 4 to obtain 180
0
and 270
0
phase shifts,
respectively. The signals will go through two receiving channels, each of which has an A/D
converter and a digital band pass filter (BPF). ............................................................................. 16
Figure 2-4: Simulated lateral (left) and axial beamplots (right) using three different beamforming
methods with signal bandwidths of 20% (top), 50% (middle), and 80%(bottom). F-number is 2 22
Figure 2-5: Comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-phase Fresnel
in terms of simulated -6 dB lateral beamwidth (a) and axial pulse length (b) with signal
bandwidths of 20%, 35%, 50%, 65%, and 80%. F-number is 2 ................................................... 22
Figure 2-6: Simulated lateral (left) and axial (right) beamplots using three different beamforming
methods with f-numbers of 1 (top), 2 (middle), and 3 (bottom) ................................................... 24
Figure 2-7: Comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-phase Fresnel
in terms of simulated -6 dB lateral beamwidth (a) and axial pulse length (b) with f-numbers of 1,
1.5, 2, 2.5, and 3 ............................................................................................................................ 24
Figure 2-8: Experimental single-wire images using three different beamforming methods with
50% signal bandwidth and f-numbers of 1, 2, 3 ........................................................................... 26
Figure 2-9: Experimental comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-
phase Fresnel in terms of terms of -6 dB lateral beamwidth (a) and axial pulse length (b) with as
a function of f-number .................................................................................................................. 26
Figure 2-10: Experimental 3mm-diameter cyst images using three different beamforming
methods with 50% signal bandwidth and f-numbers of 1, 2, and 3 .............................................. 28
Figure 2-11: Experimental comparison of beamforming algorithms: DAS, 8-phase Fresnel, and
4-phase Fresnel in terms of contrast to noise ratio (CNR) with f-numbers of 1, 1.5, 2, 2.5, and 3
....................................................................................................................................................... 28
v
Figure 3-1: An example of delay profiles of Fresnel beamforming and focusing errors in terms of
wavelength for a 64-element sub-aperture of a linear array (left) and a curvilinear array (right). In
both profiles, the focused point is set at a depth of 50 mm. The curvilinear array has a 40 mm
radius of curvature. Vertical lines indicate the range of elements that are used for specific f-
numbers. ........................................................................................................................................ 31
Figure 3-2: General system block diagram for dual apodization with cross-correlation (DAX)
(Seo, 2008) .................................................................................................................................... 33
Figure 3-3: Pair of receive sub-apertures in Fresnel beamforming at 50 mm depth. ................... 34
Figure 3-4: Fresnel beamforming schematics for a 2-element array combined with DAX .......... 34
Figure 3-5: Simulated spatial resolution of 3 beamforming algorithms without DAX (a, b) and
with DAX (c, d). ........................................................................................................................... 42
Figure 3-6: Simulated lateral beamplots using DAS, 4-phase Fresnel beamforming with and
without DAX at f-number = 2 (a), 3 (b) and 4(c) ......................................................................... 42
Figure 3-7: Experimental single-wire images without DAX using 4-phase Fresnel, 8-phase
Fresnel, and DAS with 50% signal bandwidth and f-numbers of 2, 3, and 4 ............................... 44
Figure 3-8: DAX-applied experimental single-wire images using 4-phase Fresnel, 8-phase
Fresnel, and DAS with 50% signal bandwidth and f-numbers of 2, 3, and 4 ............................... 45
Figure 3-9: Simulated spatial resolution of 3 beamforming algorithms without DAX (a, b) and
with DAX (c, d) ............................................................................................................................ 46
Figure 3-10: Experimental 6-mm-diameter cyst images without DAX using 4-phase Fresnel, 8-
phase Fresnel, and DAS beamforming with 50% signal bandwidth and f-numbers of 2, 3, 4. .... 47
Figure 3-11: DAX-applied experimental 6-mm-diameter cyst images using 4-phase Fresnel, 8-
phase Fresnel, and DAS beamforming with 50% signal bandwidth and f-numbers of 2, 3, and 4
....................................................................................................................................................... 48
Figure 3-12: Experimental comparison of beamforming methods in terms of contrast-to-noise
ratio (CNR): 4-phase Fresnel, 8-phase Fresnel, DAS with and without DAX applied ................ 49
Figure 4-1: Delay profiles for Fresnel beamforming and focusing errors in terms of wavelengths
for a 64-element subaperture at a) the fundamental frequency (1.96 MHz) and b) the 2
nd

harmonic frequency (3.92 MHz)................................................................................................... 55
Figure 4-2: The overall implementation of harmonic imaging in Fresnel beamforming followed
by dual apodization with cross-correlation (DAX) ....................................................................... 56
Figure 4-3: Experimental 6-mm-diameter cyst images without aberrator using DAS and Fresnel
beamforming with and without DAX ........................................................................................... 62
Figure 4-4: Experimental 6-mm-diameter cyst images with weak aberrator (5-mm pork tissue)
using DAS and Fresnel beamforming with and without DAX. .................................................... 63
Figure 4-5: Experimental 6-mm-diameter cyst images with strong aberrator (12-mm pork tissue)
using DAS and Fresnel beamforming with and without DAX ..................................................... 65
vi
Figure 4-6: Frequency spectra of the received RF data for a) conventional imaging at the
fundamental frequency of 1.96 MHz, b) THI, and c) PIHI at the second harmonic frequency. The
frequency response of the band-pass filter is also shown in all 3 cases. ...................................... 66
Figure 5-1: Delays profiles of Fresnel beamforming and focusing errors in terms of wavelength
compared to DAS geometric focus beamforming for a 64-element phased array at a) 0 degree
scan angle and b) 40 degree scan angle ........................................................................................ 72
Figure 5-2: A gated transmit beamforming with 4 transmitters ................................................... 73
Figure 5-3: Delay profiles and focal errors for 2-module (a) and 4-module (b) Fresnel
beamforming ................................................................................................................................. 75
Figure 5-4: A 4-module Fresnel receive beamformer ................................................................... 75
Figure 5-5: Field II simulated images of multiple point targets ................................................... 82
Figure 5-6: Simulated spatial resolution at different scan angles for different beamforming
methods without gated transmit .................................................................................................... 83
Figure 5-7: Simulated spatial resolution at different scan angles for different beamforming
methods with gated transmit ......................................................................................................... 83
Figure 5-8: Experimental multi-wire images using different beamforming methods .................. 85
Figure 5-9: Experimental spatial resolution at different scan angles for different beamforming
methods with gated transmit ......................................................................................................... 85
Figure 5-10: Experimental cyst images using different beamforming methods ........................... 87
Figure 5-11: Comparison of contrast-to-noise ratios for experimental cysts at different scan
angles obtained with different beamforming methods.................................................................. 87
Figure 5-12: Experimental cyst images using 4-module Fresnel beamforming and delay-and-sum
without DAX (left column) and with DAX (right column) .......................................................... 89
Figure 5-13: Comparison of contrast-to-noise ratios for experimental cysts at different scan
angles obtained with 4-module Fresnel beamforming and DAS, with and without DAX. .......... 89
Figure 6-1: Overall design schematic for Fresnel beamforming .................................................. 93

vii
LIST OF TABLES
Table 2-1: Field II simulation parameters ..................................................................................... 18
Table 3-1: Parameters for Simulation and Experimental Setup .................................................... 38
Table 3-2: DAX parameters for Experimental Setup ................................................................... 40
Table 4-1: Parameters for filters designed with Matlab FDATool box ........................................ 58
Table 4-2: Parameters for experimental Setup .............................................................................. 59
Table 4-3: Contrast-to-noise ratio (CNR) values for experimental data ....................................... 67
Table 4-4: -6 dB lateral beamwidth and axial pulse length for wire target (mm) ........................ 67
Table 5-1: Parameters for Simulation and Experimental Setup .................................................... 77
viii
LIST OF ACRONYMS
ADC Analog-Digital Converter
CNR Contrast-to-Noise Ratio
CPLD Complex Programmable Logic Device
DAS Delay-And-Sum
DAX Dual-Apodization with cross-correlation
FIR Finite Impulse Response (
GCF Generalized Coherence Factor
PCB Printed Circuit Board
PIHI Pulse Inversion Harmonic Imaging
SNR Signal-to-Noise Ratio
THI Tissue Harmonic Imaging
VDAS Verasonics Data Acquisition System
1
Chapter 1. INTRODUCTION

1.1. Motivation
In recent years, a segment of the ultrasound community has focused on making
ultrasound systems which are smaller, cheaper, and more power-efficient while maintaining
good image quality. These hand-held systems can become “ultrasonic stethoscopes” that allow
physicians to perform ultrasound examinations almost anywhere and anytime (Roelandt 2003;
Hwang et al. 1998; Rosenschein et al. 2000). For instance, a hand-held system can provide point-
of-care diagnosis in remote locations, battlefields, emergency rooms and private clinics. It can
also be used in trauma or minimally invasive ultrasound-guided procedures such as central
catheter insertion (Hwang et al. 1998; Rosenschein et al. 2000). With wide-ranging applications
in clinics, developing countries, and the military, the demand for portable ultrasound systems has
increased rapidly in the last decade. The P10 from Siemens and the VSCAN from GE Healthcare
are examples of recently introduced pocket-size ultrasound systems.
There have been multiple approaches to improve portable ultrasound systems in terms of
size, cost, and quality, such as transducer design, transmit and receive circuitry design, and
beamforming algorithm (Owen et al. 2003; Saijo et al. 2004; Lewis and Olbricht 2008; Khuri-
Yakub et al. 2009). Currently, a significant percentage of the size and power of an ultrasound
system is devoted to the beamformer, which is responsible for focusing the ultrasound beam. The
standard beamformer, which consists of 64 to 128 transmit/receive channels, is straightforward
2
to implement if design constraints such as size and power are relaxed. As ultrasound systems
become more portable, new beamformer architectures with fewer channels and lower power
consumption than standard cart-based systems will be needed.

1.2. Background
The purpose of beamforming in ultrasound is to scan and focus the acoustic beam. In
transmit beamformer, to form a pulse with a large amplitude and with a beamwidth as narrow as
possible at the focus, pulses from all elements must arrive at the focus at the same time. This is
achieved by transmitting the signal from each element with a delay based on the distance
between the element and the focus. Pulses from elements further from the focus must be
transmitted earlier than those nearer to the focus. As shown in Figure 1-1, each transducer
element requires a transmitter to transmit its signal at a certain time based on the delay profile.
As a result, these transmitted signals arrive at the focus at the same time. The time delay for an
element is calculated based on the following equation:

(1.1)
where ∆R is the difference between the path length of that element to the focus and the path
length from the farthest element to the focus.
Similarly, in the receive, in order to obtain a large echo signal from a target at the focus,
the contributions from all elements need to be delayed and aligned before being summed (Figure
1-2). This also results in a receive beam with a narrow beamwidth at the focus, thus improving
3
lateral resolution. The delays in the receiving beamforming are also calculated based on the path
length differences as shown in Equation 1.1.

Figure 1-1: Creating a transmit focus for an array transducer. Pulses from elements are transmitted with
specified delays to arrive at the focus at the same time.

Figure 1-2: Creating a receive focus for an array transducer. Signals received from elements are applied
electronic delays before being summed.
4
1.2.1. Beamforming approaches in array ultrasound systems
Beamforming approaches can be broadly categorized into two methods: analog
beamforming and digital beamforming. In analog beamforming, the images are formed by a
sequence of analog signals which are delayed with analog delay lines, summed in the analog
domain, and then digitized. In digital beamforming, the images are formed by sampling analog
signals from individual array elements, applying digital delays, and then summing digitally
(Steinberg 1992). Current digital beamforming applies time delays to focus digitized data
(traditional delay-and-sum beamforming, or DAS) or combines digital time delays with complex
phase rotation (O’Donnell et al. 1991; Agarwal et al. 2008). In digital DAS beamforming, the
focused data are summed and passed on for envelope detection and further signal processing.
This method is straightforward and intuitive but requires a significant amount of hardware and
processing capability. Digital beamforming can also be achieved by digitizing the incoming RF
data from each element, but then applying a coarse delay, followed by complex demodulation
with phase rotation for fine delay. This method reduces the computational demands compared to
DAS beamforming but still requires redundant hardware for each channel (O’Donnell et al.
1990).
A hybrid approach to beamforming is also possible where different parts of the
beamforming process occur in either analog or digital domains. In one case, echoes from clusters
of elements are delayed and summed in the analog domain and then digitized by a single analog
to digital (A/D) converter. This approach reduces the number of A/D converters compared to a
full digital beamformer (Pesque and Souquet 1999).

5
1.2.2. Low-cost beamforming approaches
To minimize the cost, power, and size of the beamformer, low-cost beamforming
approaches have been previously proposed in the literature. One concept is the direct-sampled
I/Q (DSIQ) beamforming algorithm in which I/Q data are acquired by directly sampling the Q
data one quarter-period after the I data (Ranganathan and Walker 2004). The DSIQ algorithm
relies solely on phase rotation of the I/Q data to provide focusing. The proposed realization uses
only one transmitter with a lower sampling rate and one I/Q channel for each element. When
used with a 2-D array, the DSIQ method can acquire C-scan images at 43 frames per second, B-
scans with arbitrary plane orientation and 3D images (Fuller et al. 2009).
Another concept is known as Fresnel focusing. Originally used in optics, a Fresnel lens is
much thinner and therefore lighter than a conventional lens with the same focal point. In
acoustics, physical Fresnel lenses are fabricated to focus ultrasonic waves for an acoustic
microscopy system, which provides high efficiency and focusing power as well as a simpler
manufacturing process (Hadimioglu et al. 1993; Chan et al. 1996). These physical lenses replace
the spherical focus of a conventional lens with an equivalent phase shift. Used with an array
transducer, the Fresnel focusing technique can reduce the number of delays needed since
different elements may require the same delay. These elements can then be clustered together. In
1980, Richard, Fink and Alias first proposed the use of Fresnel focusing in an array-based
system (Richard et al. 1980). In their experiment for 8-state Fresnel focusing, 8 different delays
were used for transmit mode while four different delays plus inverting amplifiers were used for
receive mode. By imaging a 0.3 mm diameter copper wire, they showed that for a linear array,
6
finer Fresnel phase sampling lowers the side-lobe level and the lateral resolution improves as f-
number decreases (Richard et al. 1980).

Figure 1-3: Delay profiles (not to scale) for a) traditional geometric focus beamforming, b) Fresnel beamforming.
Each segment corresponds to one period of the signal

7
1.3. Contributions
The contributions of this dissertation are proposing, evaluating, and refining a novel
beamforming method that can reduce the size and cost of ultrasound imaging systems while
providing image quality comparable to that of conventional systems. This method, called Fresnel
beamforming, has a delay profile with a shape similar to a physical Fresnel lens (Figure 1-3).
This method uses a unique combination of analog and digital beamforming methods. The
advantage of Fresnel beamforming is that a system with 4 transmit and 2 receive channels with a
network of single-pole/single-throw switches can be used to focus an array with 64 to 128
elements. The main trade-off of this method is the presence of focal errors, leading to image
degradation. Several techniques are presented in this dissertation for overcoming the trade-off of
Fresnel beamforming. These techniques include 1) integrating a novel side-lobe suppression
method, called dual apodization with cross-correlation (DAX); 2) implementing harmonic
imaging; 3) the gated transmit beamforming technique; and 4) the modular Fresnel receive
beamforming technique. These techniques helps improve the performance of Fresnel
beamforming, making it a suitable alternative beamforming method for various transducer arrays
even in the presence of aberration, where differences in sound speed induce additional focal
errors in Fresnel beamforming. In summary, this dissertation demonstrates the suitability and
robustness of Fresnel beamforming in providing ultrasound imaging systems, not only with
reduced cost and size but also with comparable image quality to that of conventional harmonic
imaging systems.

8
1.4. Publication List
During my study, I have authored and co-authored a number of reviewed conference and
journal publications as listed below. Some of them are on different project than the Fresnel
beamforming projects. The diversity of these projects helps expanding my knowledge and
appreciation on ultrasound imaging.
Fresnel beamforming project:
Nguyen M, Junseob J, Yen J. Ultrasound harmonic imaging for Fresnel beamforming in the
presence of phase aberration. Ultrasound in Medicine and Biology, submitted.
Nguyen M, Yen J. Performance improvement of Fresnel beamforming using dual-apodization of
cross-correlation. IEEE Transaction on Ultrasonics, Ferroelectrics, and Frequency Control,
Volume 60, Number 3, pp. 451-462, 2013.
Nguyen M, Mung J, Yen J. Fresnel-based beamforming for low-cost, portable ultrasound. IEEE
Transaction on Ultrasonics, Ferroelectrics, and Frequency Control, Volume 58, Number 1, pp.
112-121, 2011.
Nguyen M, Shin J., Yen J. Fresnel beamforming and dual apodization with cross-correlation for
curvilinear arrays in low-cost, portable ultrasound system. IEEE International Ultrasonics
Symposium Proceedings, Orlando, October 18-21, 2011.
Nguyen M, Mung J, Yen J. Fresnel beamforming for compact, portable ultrasound array
system. IEEE International Ultrasonics Symposium Proceedings, Roma, Italy, September 20-23,
2009.
9
Dual-layer transducer for 3-D ultrasound imaging project:
Chen Y, Nguyen M, Yen J.A 5 MHz cylindrical dual-layer transducer array for 3-D transrectal
ultrasound imaging. Ultrasonic Imaging, Volume 34, Number 3, pp.181-195, 2012.
Chen Y, Nguyen M, Yen J. A 7.5 MHz dual-layer transducer array for 3-D rectilinear imaging.
Ultrasonic Imaging, Volume 33, Number 1, pp.1-12, 2011.
Chen Y, Nguyen M, Yen J. Real-time rectlinear volumetric acquisition with a 7.5 MHz Dual-
layer array transducer – Data acquisition and signal processing. IEEE International Ultrasonics
Symposium Proceedings, Orlando, October 18-21, 2011.
Chen Y, Nguyen M, Yen J. Recent results from dual-layer transducers for 3-D imaging. IEEE
International Ultrasonics Symposium Proceedings, San Diego, October 11-14, 2010.
Ultrasound elastography project (at Philips Research North America)
Nguyen M, Xie H, Paluch K, Stanton D, Ramachandran B. Pulmonary Ultrasound
Elastography: a Feasibility Study with Phantoms and Ex-vivo Tissue. SPIE Medical Imaging,
Orlando, February 9-14, 2013.
Paluch K, Xie H, Nguyen M, Stanton D, Ramachandran B. Development of Balloon-Based
Prototype System for Ultrasound Elastography in the Lungs. International Symposium on
Biomedical Imaging, San Francisco, April 7-11, 2013.

10
1.5. Organization of the Dissertation
The dissertation is divided into 6 chapters:
Chapter 1 provides an introduction to ultrasonic imaging with an emphasis on
beamforming. It presents an overview of general beamforming approaches for array ultrasound
systems as well as low-cost beamforming approaches for low-cost, compact ultrasound systems.
Chapter 2 introduces the basics of Fresnel beamforming and its performance evaluation
using a linear array. Two versions of Fresnel beamforming are presented in this chapter: 4-phase
(4 different time delays or phase shifts) and 8-phase (8 different time delays or phase shifts). The
advantage of Fresnel beamforming is that a system with 4 to 8 transmit channels and 2 receive
channels with a network of switches can be used to focus an array with 64 to 128 elements.
Chapter 3 presents the concept and performance evaluation for the integration of Fresnel
beamforming with a signal processing method called dual-apodization with cross correlation
(DAX). This method helps to suppress the high side lobes due to focal errors in Fresnel
beamforming and allows Fresnel beamforming to be used in arrays which can result in relatively
large focal errors (1 to 6 wavelengths).
Chapter 4 presents the implementation of tissue harmonic imaging in Fresnel
beamforming. With the advantages of lower side lobes and suppressing aberration, harmonic
imaging offers an effective solution to the limitations of Fresnel beamforming. The results
suggest the effectiveness of harmonic imaging in improving image quality for Fresnel
beamforming, especially in the presence of phase aberration.
11
Chapter 5 introduces and evaluates two new techniques that can further improve the
performance of Fresnel beamforming. One technique is called gated transmit beamforming. This
technique allows an ultrasound system with only 4 transmitters to achieve an ideal transmit
focusing, which normally requires 64-128 transmitters. The other technique is the modular
Fresnel receive beamforming technique, which can considerably reduce the focal errors in
Fresnel receive beamforming, especially in phased arrays where beam steering is needed.
Chapter 6 concludes the dissertation and describes the future work on Fresnel
beamforming.
12
Chapter 2. FRESNEL BEAMFORMING WITH
A REDUCED CHANNEL COUNT

2.1. Introduction
This chapter presents the use of a modified electronic Fresnel-based beamforming
method for low-cost portable ultrasound systems. This method is based on the concept of the
optical Fresnel lens which was applied using ultrasound array transducers in the 1980s (Richard
et al. 1980). Fresnel beamforming uses a unique combination of analog and digital beamforming
methods. Two versions of the Fresnel beamforming are presented in this chapter: 4-phase (4
different time delays or phase shifts) and 8-phase (8 different time delays or phase shifts). The
novel electronic Fresnel beamforming method can reduce the number of channels in an
ultrasound system, normally 64 to 128, down to only 4 to 8 transmit and 2 receive channels. This
chapter presents initial simulation and experimental results to evaluate the feasibility of this
approach.

2.2. The Design
The goal of beamforming is to focus ultrasound energy at one location. In array
transducers, this is achieved by applying time delays or phase shifts corresponding to the path
length differences between elements. Here, I propose a hybrid beamforming approach called
Fresnel-based beamforming. In transmit mode, time delays are applied to transmit elements.
13
Elements requiring the same time delay are clustered together using a network of switches. Here,
I present a system which can have either 4 or 8 transmit channels. In receive mode, phase shifts
are applied using a combination of the analog and digital domains. Up to 8 different phase shifts
are possible, but only 2 A/D converters are needed in the proposed implementation.
With Fresnel focusing, the standard geometric time delay ∆t is replaced by a new delay
∆t
F
given by:
T t t
F
mod    (2.1)

where mod indicates the modulo operation and T is the period of the ultrasound signal based on
the center frequency.
F
t  is the remainder after integer multiples of the ultrasound period T have
been subtracted from t  (Nguyen et al. 2011; Nguyen and Yen 2013; Richard et al. 1980) . This
process is illustrated in Figure 2-1 where a delay profile with geometric focusing is used. A new
delay profile is also shown after integer multiples of the period have been subtracted. The new
delay profile for the Fresnel beamforming method will have a shape similar to a physical Fresnel
lens (Figure 2-1). Each segment corresponds to a period T or a 360
0
phase offset. Using
F
t 
results in a focusing error where the error is always an integer multiple of T. Focusing errors are
also plotted in Figure 2-1 as the dotted lines. Elements which are further away from the focus
have greater focal errors. These focal errors will result in larger beamwidths, higher clutter, and
longer pulse lengths.
In the case of a 4-transmit system, excitation signals can be generated by 4 transmitters
with different time delays corresponding to quarter-period shifts up to one full period. Using 4
switches per element, I can control the time delay of the signal emitted by each element (Figure
14
2-2). For an 8-transmit system, I will use 8 transmitters to generate signals with 8 different time
delays in increments of one-eighth of a period.

Figure 2-1: Delays profiles of Fresnel beamforming and focusing errors in terms of wavelength compared
to DAS geometric focus beamforming for a 64-element linear array

Figure 2-2: A 4-transmit Fresnel (phase and sum) beamforming schematics for an array transducer
15
On the receive side, incoming RF data are subject to phase shifts which are also selected
based on the principle of Fresnel focusing. In narrowband applications, the time delay Δt
associated with each element is replaced with an equivalent phase shift Ɵ that ranges from 0
0
to
360
0
based on the following relationship
θ = -ω * ∆t (2.2)
where ω is the angular frequency. The delay profile is converted into discrete phase shifts and
never exceeds 360
0
. When a phase shift greater than 360
0
is required, the phase shift wraps
around and starts back at 0
0
.
As shown in Figure 2-3, the phase delays in a 4-phase system will be applied to the
received signals using 4 switches per element. The signals with phase shifts of 0
0
, 90
0
, 180
0
, 270
0
correspond to switches 1, 2, 3, and 4, respectively. In a 4-phase system, only one of the four
switches is closed. A 180
0
phase shift is accomplished using an inverting amplifier. All 0
0
and
180
0
phase-shifted data across all elements are summed with one summer and all 90
0
and 270
0

phase-shifted data across all elements are summed with a second summer. These summations are
performed in the analog domain. The resultant waveforms are then digitized by only 2 analog-to-
digital (A/D) converters. The data from the second A/D converter are phase-shifted 90
0
via a
digital Hilbert transform, and the resultant data are summed digitally. This phase shift can be
incorporated into the coefficients of a digital finite impulse response (FIR) band-pass filter.
Finer phase shifts can be achieved by selectively summing combinations of two phase-
shifted signals. For instance, an element requiring a 45
0

phase shift can be achieved by applying
both 0
0
and 90
0
phase shifts followed by summation. In this case, switches 1 and 2 are closed
simultaneously. Another example is that closing switches 2 and 3 results in a 135
0
phase shift.
16
Applying phase shifts in this manner will also increase the signal magnitude by a factor of √ , or
3 dB.

Figure 2-3: Fresnel (phase and sum) beamforming schematics for a 2-element array. 0
0
phase shift is
applied by closing switch 1, 45
0
by closing switch 1 and 2, 90
0
by closing switch 2. Inverting amplifiers
are used with switches 3 and 4 to obtain 180
0
and 270
0
phase shifts, respectively. The signals will go
through two receiving channels, each of which has an A/D converter and a digital band pass filter (BPF).
The primary advantage of this technique is that a system with 4 to 8 transmit channels
and 2 receive channels can be used to focus an array with as many as 128 elements. Each
channel is assigned a different time delay (transmit) or phase shift (receive). Single-pole/single-
throw switches can be used to cluster elements with identical time delays and phase shifts.
However, while ultrasound signals are broadband, the Fresnel receive beamformer makes a
narrowband assumption about the signal, which can limit the beamformer performance.
Undesirable side-lobe levels and large main-lobe widths may be potential problems. To quantify
17
performance, simulations and experiments were performed to evaluate the proposed Fresnel
beamforming method.

2.3. Methods
2.3.1. Simulation
Using Field II, I performed computer simulations to evaluate the performance of Fresnel
beamforming compared to DAS beamforming in terms of lateral beamwidths, axial pulse length,
and contrast (Jensen and Svendsen 1992). I also examined the robustness of Fresnel
beamforming by varying the signal bandwidth and the array f-number. A temporal sampling rate
of 200 MHz was used with a fixed transmit center frequency of 5 MHz.
I investigated the effect of signal bandwidth on the performance of Fresnel beamforming
with a 5 MHz Gaussian pulse with -6 dB fractional signal bandwidths of 20%, 35%, 50%, 65%,
and 80%. Since the receive side of the proposed Fresnel beamforming makes a narrowband
assumption of the signal, the performance is likely to degrade as bandwidth increases. I also
investigated the effect of f-number on the performance of Fresnel beamformer by implementing
f-numbers of 1, 1.5, 2, 2.5, and 3. Using a DAS beamformer with a larger aperture results in
better lateral resolution. However, the Fresnel beamformer uses time delays within one period or
phase shifts which always range from 0
0
to 360
0
. This results in a greater number of integer
wavelength offsets as the aperture size increases. The signals from the edge elements can
deteriorate the image quality by increasing the main-lobe width and side-lobe levels.
18
Table 2-1: Field II simulation parameters
Parameters Value
Center frequency 5 MHz
Sampling frequency 200 MHz
Azimuthal element pitch 0.3 mm
Elevation element height 5 mm
Sound speed 1540 m/s
Transmit focus 22 mm

2.3.2. Experimental setup
For the experimental setup, full synthetic aperture RF data sets were collected and
sampled at 40 MHz using an Ultrasonix Sonix RP ultrasound system (Ultrasonix Medical
Corporation, Richmond, BC, Canada) with a 128 element, 300 μm pitch linear array. A 2-cycle 5
MHz transmit pulse was used in this experiment. Data from each channel were collected 32
times and averaged to minimize effects of electronic noise. The data sets were then beamformed
using Matlab (The MathWorks, Inc. Natick, MA) with offline DAS, 8-phase Fresnel, and 4-
phase Fresnel beamforming methods. The transmit focusing was fixed at 22 mm while the
dynamic receiving focusing was updated every 0.1 mm. The image line spacing was 50 µm. I
evaluated the performance of Fresnel beamforming in terms of spatial resolution and contrast-to-
noise ratio. The effect of varying f-number was also investigated with f-numbers of 1, 1.5, 2, 2.5,
and 3.
19
Spatial resolution
I imaged a 0.1 mm diameter custom-made nylon wire target immersed at 20 mm depth in
degassed water. The -6 dB lateral and axial target sizes were measured to serve as metrics for
spatial resolution.
Contrast-to-noise ratio (CNR)
A full synthetic aperture RF data set of an ATS ultrasound phantom (Model 539, ATS
Laboratories, Bridgeport, CT) containing a 3 mm diameter cylindrical anechoic cyst at 20 mm
depth was collected and beamformed with offline DAS beamforming and the proposed Fresnel
focusing techniques. Contrast-to-noise ratio (CNR) is defined as the difference between the mean
of the background and the cyst in dB divided by the standard deviation of the background in dB
(Krishnan et al. 1997):

̅̅̅

̅̅̅̅

(3)
where

̅
is the mean of the signal from the target (dB),

̅̅̅
is the mean of the signal coming from
the background (dB), and σ
b
is the standard deviation of the background (dB).

20
2.4. Results
2.4.1. Simulation results
Effect of bandwidth
Figure 2-4 shows the lateral and axial beamplots simulated with Field II using 4-phase
Fresnel and 8-phase Fresnel beamforming techniques compared to DAS. From these figures, the
lateral main lobes are found to be minimally affected by the signal bandwidths. As signal
bandwidth increases from 20% to 80%, there is little difference between lateral beamwidths
using Fresnel beamforming methods and those using DAS. For instance, at 50% signal
bandwidth, the -6 dB lateral beamwidths using 8-phase Fresnel and 4-phase Fresnel
beamformers are 0.52 mm and 0.55 mm, which are about 2% and 8% higher compared to a
beamwidth of 0.51 mm using DAS. However, small increase in the differences between the
lateral beamwidths using Fresnel beamforming methods and those using DAS was found as
signal bandwidth increases. At 20% bandwidth, the side-lobe levels with Fresnel beamforming
are about 2 dB lower than those with DAS at lateral locations x= ±0.85 mm (Figure 2-4a).
However, the 8-phase and 4-phase beamformers have greater total off-axis energy than the DAS
beamformer indicating poorer cystic contrast when using Fresnel beamforming. At 50% and
80% bandwidths, the peak side-lobe levels are 5.4 dB and 7.2 dB higher with Fresnel
beamforming than with DAS beamforming (Figure 2-4b, c). For all bandwidths, the peak side-
lobe with Fresnel focusing is closer to the main lobe compared to DAS focusing.
Using 4-phase Fresnel beamforming method, the axial pulse lengths are 0.86, 0.65, 0.59,
0.56, and 0.55 mm for signal bandwidths of 20%, 35%, 50%, 65%, and 80%, respectively. For
21
the 8-phase Fresnel beamforming method, the axial pulse lengths are 0.86, 0.64, 0.58, 0.55, and
0.54 mm, respectively. While the 4-phase and 8-phase beamforming methods have pulse lengths
comparable to each other, they are about 0.10 to 0.15 mm higher than the pulse lengths using
DAS. For example, at 50% signal bandwidth, the -6 dB axial pulse lengths using 8-phase and 4-
phase Fresnel beamformers are 0.58 mm and 0.59 mm, which are about 31% and 33% larger
than -6 dB axial beamwidth of 0.45 mm using DAS, respectively. The differences in axial pulse
lengths produced by Fresnel beamforming compared to DAS increase as the signal bandwidth
increases. Fresnel beamforming also results in higher side-lobe levels at higher bandwidth.
Figure 2-5 summaries the plot of lateral beamwidths (Figure 2-5a) and axial pulse lengths
(Figure 2-5b) against signal bandwidths for three beamforming methods. It confirms the
relationship between the performance of Fresnel beamforming method and signal bandwidths:
increasing signal bandwidth has little effect on lateral beamwidth while reducing axial pulse
length. These trends in performance of Fresnel beamforming compared to DAS can be explained
by the violation of the narrowband assumption as the signal bandwidth increases.
22

Figure 2-4: Simulated lateral (left) and axial beamplots (right) using three different beamforming
methods with signal bandwidths of 20% (top), 50% (middle), and 80%(bottom). F-number is 2

Figure 2-5: Comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-phase Fresnel in terms
of simulated -6 dB lateral beamwidth (a) and axial pulse length (b) with signal bandwidths of 20%, 35%,
50%, 65%, and 80%. F-number is 2
23
Effect of f-number
Figure 2-6 depicts the effects of f-number on the performance of 4-phase and 8-phase
Fresnel beamforming method compared to DAS. As f-number incrementally increases from 1 to
3, the -6 dB lateral beamwidth also incrementally increases from 0.47 mm to 0.81 mm for 4-
phase Fresnel beamforming method, from 0.40 mm to 0.81 mm for 8-phase Fresnel
beamforming method, and from 0.34 mm to 0.80 mm for DAS beamforming. At f-number = 1,
high sidelobes of -15 dB are seen for Fresnel beamforming, which are –11dB higher than the
side lobe for DAS beamforming (Figure 2-6a). These side-lobe magnitudes for Fresnel
beamforming decrease to -20 dB for f-number = 2 (Figure 2-6b). At f-number = 3, the side-lobe
levels for Fresnel and DAS beamforming are quite comparable, which are about -30 dB. The
opposite effect of f-number on pulse length is seen on axial beamplots using Fresnel
beamforming methods: increasing f-number results in smaller axial pulse lengths (Figure 2-6d, e,
f). This effect on axial pulse length is only seen with Fresnel beamforming methods, but not with
traditional DAS beamforming. As the f-number increases, the amount of focal error decreases.
Therefore, the effect of wrapping phase shifts in Fresnel beamforming is reduced as the number
of integer wavelength offsets decrease. In fact, at f-number = 3, since the path length difference
between the outer and center elements is about one wavelength, there is no phase wraparound in
the delay profiles for Fresnel beamformers and the differences in the performance of 3
beamformers are due solely to the quantization of the delays and phase shifts. As shown in
Figure 2-7, both the lateral beamwidths (Figure 2-7a) and axial pulse lengths (Figure 2-7b)
generated by Fresnel beamformers approach those generated by traditional DAS beamformer as
the f-number approaches 3.

24

Figure 2-6: Simulated lateral (left) and axial (right) beamplots using three different beamforming
methods with f-numbers of 1 (top), 2 (middle), and 3 (bottom)

Figure 2-7: Comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-phase Fresnel in terms
of simulated -6 dB lateral beamwidth (a) and axial pulse length (b) with f-numbers of 1, 1.5, 2, 2.5, and 3
25
2.4.2. Experimental results
Spatial resolution:
Figure 2-8 shows the experimental images of a custom-made nylon wire target immersed
in degassed water using the three different beamforming approaches. The relatively high side-
lobe levels seen in simulated lateral beamplots using Fresnel beamforming can also be seen in
the experimental images with dynamic range of 40 dB. As f-number increases, -6 dB lateral wire
size becomes larger while the noise caused by high side-lobe levels in Fresnel beamforming is
reduced. At f-number = 3, the wire images beamformed by three different methods are very
similar. This observation also coincides with the lateral and axial pulse lengths which also
converge as f-number approaches 3 shown in Figure 2-9. These trends are in good agreement
with those predicted by simulation shown in Figure 2-7.
26

Figure 2-8: Experimental single-wire images using three different beamforming methods with 50%
signal bandwidth and f-numbers of 1, 2, 3

Figure 2-9: Experimental comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-phase
Fresnel in terms of terms of -6 dB lateral beamwidth (a) and axial pulse length (b) with as a function of f-
number

27
Contrast-to-noise ratio (CNR):
Figure 2-11 shows the experimental images of the ATS tissue-mimicking phantom
containing anechoic cysts using the three different beamforming approaches. All images are
shown on a 40 dB dynamic range. The transmit focus is always set to a 22 mm depth. As shown
in Figure 2-11, the performance of Fresnel beamformers in terms of contrast-to-noise ratio is
highest at an f-number of 2. This can be explained by the compromise between the beamwidths
and the integer wavelength offsets caused by Fresnel beamformers. Increasing f-number
increases the lateral beamwidth while reducing the integer wavelength offset. The CNR for the
3mm diameter cyst images using traditional DAS, 8-phase Fresnel, and 4-phase Fresnel
beamformers at f-number of 2 are 4.66, 4.42, and 3.98, respectively.

28

Figure 2-10: Experimental 3mm-diameter cyst images using three different beamforming methods with
50% signal bandwidth and f-numbers of 1, 2, and 3

Figure 2-11: Experimental comparison of beamforming algorithms: DAS, 8-phase Fresnel, and 4-phase
Fresnel in terms of contrast to noise ratio (CNR) with f-numbers of 1, 1.5, 2, 2.5, and 3
29
2.5. Summary
This chapter presents the concept and performance evaluation of a novel Fresnel
beamforming method for low-cost portable ultrasound system. The advantage of the proposed
method is that a system with 4 to 8 transmit channels and 2 receive channels with a network of
single-pole/single-throw switches can be used to focus an array with 64 to 128 elements. This
beamforming technique can dramatically reduce the complexity, size, and cost of the system.
However, the trade-off in image quality should also be considered.
The simulation and experimental results show that Fresnel beamforming image quality is
comparable to DAS beamforming in terms of spatial resolution and contrast-to-noise ratio under
certain conditions: f-number = 2 and 50% signal bandwidth. Fresnel beamforming is shown to be
able to provide adequate image quality compared to DAS for different signal bandwidths. The
lateral beamwidths using Fresnel beamforming are only 0.04 mm larger than those using DAS
while the axial pulse lengths using Fresnel beamforming are about 0.10 mm to 0.15 mm larger
than those using DAS while for a wide range of signal bandwidths. The results also show that f-
number has a significant effect on the performance of Fresnel beamforming. The optimal CNR
using Fresnel beamforming occurs at f-number = 2, at which the CNRs using 8-phase and 4-
phase Fresnel beamforming are about 5.1% and 14.6% lower than CNR using DAS, respectively.
Despite the fact that 4-phase Fresnel beamforming uses half of the number of time delays and
phase shifts in 8-phase Fresnel beamforming, the performance of these two methods are
comparable.

30
Chapter 3. PERFORMANCE IMPROVEMENT
OF FRESNEL BEAMFORMING USING DUAL
APODIZATION WITH CROSS CORRELATION

3.1. Introduction
Chapter 2 investigates a Fresnel-based beamforming method, which has the advantage of
reducing channel count from 64-128 channels down to 4-8 transmit channels and 2 receive
channels, thus reducing the number of analog-to-digital converters (ADC), time-gain-
compensation circuits, and potentially size, cost, and power. However, the trade-off of this
approach is the presence of focal errors, leading to image quality reduction. In the case of linear
arrays, these focal errors limit the use of Fresnel beamforming to certain conditions: f-number =
2 and 50% signal bandwidth (Nguyen et al. 2011). At these conditions, Fresnel beamforming
was shown to yield a performance comparable to conventional delay-and-sum (DAS)
beamforming. To suppress the effects of focal errors inherent in Fresnel beamforming, I propose
the use of dual apodization with cross-correlation (DAX), which is a signal processing method
that suppresses side lobes and clutter, thus improving contrast without compromising spatial
resolution (Seo and Yen 2008, 2009).
This chapter proposes the integration of DAX with Fresnel beamforming. A curvilinear
array was used to evaluate the proposed usage of DAX for Fresnel beamforming, for two main
reasons. Firstly, due to the curvature, curvilinear arrays have larger path length differences
31
compared to linear arrays. These differences between curvilinear arrays and linear arrays
decrease with deeper focus depths. As an example, in Figure 3-1, a curvilinear array with a 40
mm radius of curvature has about two times larger path length differences at 50 mm depth
compared to a linear array. These larger path length differences lead to higher focusing errors in
Fresnel beamforming (Figure 3-1), degrading image quality. Therefore, DAX is useful to
suppress the side lobes caused by these focusing errors. Secondly, given the same number of
elements and the same pitch, curvilinear arrays have the advantage of an increasing field of view
with depth compared to linear arrays (Whittingham and Martin 2010). With their trapezoidal
shaped field of view, curvilinear array transducers can be used for a wide range of applications
such as abdominal, obstetrics and gynecologic imaging or detecting internal bleeding (Thijssen
et al. 2008; Kirkpatrick et al. 2007; Iwashita et al. 2012).

Figure 3-1: An example of delay profiles of Fresnel beamforming and focusing errors in terms of
wavelength for a 64-element sub-aperture of a linear array (left) and a curvilinear array (right). In both
profiles, the focused point is set at a depth of 50 mm. The curvilinear array has a 40 mm radius of
curvature. Vertical lines indicate the range of elements that are used for specific f-numbers.

32

3.2. The design
3.2.1. Dual apodization with cross-correlation – DAX
DAX is a signal processing method that suppresses side lobes and clutter, thus improving
contrast without compromising spatial resolution (Seo and Yen 2008, 2009). Assuming linearity,
an ultrasound signal is composed of 2 signals: one is from the main lobe and one is from the side
lobes, grating lobes and other undesirable forms of clutter (other than main lobe). The purpose of
DAX is to distinguish side-lobe-dominated signals and minimize their contribution to the image.
This approach is achieved by using two receive aperture functions that give similar main lobe
and different clutter or side-lobe patterns. Some examples of these aperture functions are
uniform, Hanning, Hamming, or alternating functions (Stankwitz et al. 1995; Wang et al. 2002).
The signals comprised primarily of main lobe components will have cross correlation
coefficients close to 1, while those comprised mainly of clutter will have cross-correlation
coefficients close to or less than 0. A weighting matrix for the beamformed RF data is generated
as shown in Figure 3-2. For each pixel, axial segments of the two beamformed RF data sets are
cross correlated. If the coefficient is less than a set threshold value ε > 0, that pixel signal is
considered side-lobe-dominated and assigned a minimal weighting. This threshold is selected
based on the level of decorrelation of the signals that need to be detected and suppressed. In Yen
et al. (Seo and Yen 2008, 2009), the weighting for side-lobe-dominated signals equals to the
threshold, which is set to 0.001, equivalent to a 60 dB magnitude reduction. This level of
reduction prevents these signals from contributing to the images, normally displayed in a 30-50
33
dB dynamic range. The weighting matrix essentially is the matrix of cross-correlation
coefficients after passing through the threshold. The combined, beamformed data are obtained by
adding two data sets from the two apertures. If the two aperture functions are complementary,
i.e. an element is only used in one of the two receive apertures but not in both, the combined data
is the same as the data from a standard receive aperture. This combined data is then multiplied
with the weighting matrix, envelope detected and log compressed to generate a display image.

Figure 3-2: General system block diagram for dual apodization with cross-correlation (DAX) (Seo, 2008)

3.2.2. Integration of DAX into Fresnel beamforming
In the case of Fresnel beamforming, the two receive channels contain RF signals coming
from 2 different apertures. These two apertures can be completely complementary in the case of
a 4-phase Fresnel system, where the signal from each element is passed to only one of the two
channels through a network of switches. Which channel the signals are passed to is determined
by the Fresnel beamforming delay profile and whether the signals require a 0-degree or 90-
degree phase shift. Thus, the apodization functions are dynamically changed with different
receive foci. As an illustrative example, Figure 3-3 shows a pair of apodization functions at a
34
focus of 50 mm depth. On average, for a 64-element sub-aperture, there is a slightly higher
number of elements in the apodization function for receive channel 1 (34±4 elements) than for
receive channel 2 (30±4 elements).These aperture functions have similar mainlobe signals and
different side-lobe signals, and thus DAX can be an approach to distinguish and suppress side-
lobe signals to improve image contrast.

Figure 3-3: Pair of receive sub-apertures in Fresnel beamforming at 50 mm depth.

Figure 3-4: Fresnel beamforming schematics for a 2-element array combined with DAX
35

Figure 3-4 shows the receive Fresnel beamforming followed by DAX. Here, the resultant
data from two channels will go through A/D converters and band-pass filters (BPF1s) with phase
shifts. BPF1s bandpass the RF signals, first to isolate the selected frequency range within the
transducer bandwidth to construct the image, and secondly to filter out signal noise. For the
experiment, BPF1s have a 50% bandwidth around the transducer center frequency of 3.3 MHz.
The data will then be used in two parallel processes. In the first process, the data sets are digitally
summed to get the combined, beamformed RF data. In the second process where DAX is
applied, these data sets are used to construct a weighting matrix that can identify and suppress
side-lobe-dominated signals. Due to the inherent focal errors in Fresnel beamforming when used
with broadband signals, the side lobes of Fresnel beamforming are higher than those of DAS,
which reduces image contrast. These side-lobe levels increase as the signal bandwidth increases
due to increasing focal errors (Nguyen et al. 2011). In broadband applications, side-lobe-
dominated signals are also highly correlated between the two aperture functions of Fresnel
beamforming due to the violation of narrowband assumption. This correlated attribute of these
sidelobes can limit the capability of DAX to identify and suppress them. However, with another
set of narrow band-pass filters (BPF2s) to reduce focal errors caused by the violation of
narrowband assumption, this correlation attribute of the sidelobes can be reduced, thus allowing
sidelobe-dominated signals to be better distinguished and suppressed by DAX. As a trade-off,
the axial pulse length becomes longer as the signal bandwidth decreases. The elongation of axial
pulse can increase the correlation between signals above and below the cyst and the side-lobe-
dominated signals inside the cyst. This limits the efficiency of side-lobe suppression using DAX.
Since axial pulse length and side-lobe levels both affect CNR, an optimal bandwidth for BPF2
36
needs to be determined to maximize CNRs. In this study, the optimal -6 dB fractional bandwidth
for BPF2 is empirically found to be 15%.
After filtered by BPF2, the resultant data sets are then cross-correlated. The matrix of
cross-correlation coefficients subsequently passes through a threshold and functions as a
weighting matrix. Finally, a DAX-applied image is obtained after the beamformed RF data is
multiplied with this weighting matrix, envelope detected and log compressed.

3.3. Methods
The performance of Fresnel beamforming with and without DAX was investigated in
terms of spatial resolution and CNR. Without DAX, the higher number of focal errors for a
curvilinear array compared to a linear array potentially results in higher sidelobe levels, higher
clutter, and longer pulse length for Fresnel beamforming. However, by applying DAX, I expect
to reduce the amount of clutter and lower sidelobe levels without compromising lateral
beamwidth and axial pulse length. To quantify the performance, I have performed simulations
and experiments to evaluate the proposed integration of DAX into Fresnel beamforming for
curvilinear arrays.
3.3.1. Simulation
I performed Field II simulation to evaluate the performance of Fresnel beamforming on a
curvilinear array with and without DAX (Jensen 1992). The lateral beamwidth and axial pulse
37
lengths of Fresnel beamforming were examined with different f-numbers. The results of Fresnel
beamforming were then compared to those of DAS, which served as the gold standard. A 3.3
MHz Gaussian pulse with 50% bandwidth was used as the transmit pulse.
3.3.2. Experimental setup
For the experimental setup, full synthetic aperture RF data sets were collected and
sampled at 20 MHz, using Verasonics Data Acquisition System (VDAS) with an ATL C4-2
curvilinear array. This 128-element array has a radius of 40 mm and an aperture angle of 75°.
The data was then beamformed offline with DAS beamforming and the proposed Fresnel
focusing techniques. For the Fresnel beamforming techniques, the transmit delays applied to the
signals only take 4 values, ranging from 0 to a period T (Equation 1.1). These delay values were
implemented in Matlab by delaying the signals in terms of samples. On the receive, the signals
are subjected to 0, 90, 180, 270 degree phase shifts, which can be implemented offline by
multiplying the signals with -1 and/or Hilbert transform. The performance of Fresnel
beamforming with and without DAX was evaluated in terms of spatial resolution and CNR. The
robustness of Fresnel beamforming was also assessed by using f-numbers ranging from 2 to 4.
The lateral beam spacing is 0.14°, which results in a 0.225 mm lateral beam spacing at 50 mm
depth. The transmit focusing was fixed at 50 mm, which is at the center of the cyst and wire
targets while the dynamic receive focusing was updated every 1 mm.
Table 3-1 presents the parameters used for Field II simulation and experimental setup.
The pitch, element height, radius of curvature, aperture angle and center frequency were chosen
according to the ATL C4-2 curvilinear array transducer. The sound speed of 1480 m/s, which is
38
that of water, was used in simulation, providing a better context for relating the simulation
results and experimental results.
Table 3-1: Parameters for Simulation and Experimental Setup
Parameters Value
Radius of curvature 40mm
Aperture angle 75 degrees
Center frequency 3.3 MHz
Sampling frequency 20 MHz
Azimuthal element pitch 0.409 mm
Elevation element height 13 mm
Sound speed 1480 m/s (water)
1450 m/s (phantom)
Transmit focus 50 mm
Lateral beam spacing 0.14 degrees (0.225mm at 50 mm depth)
Receive focal delay step 1 mm

1. Spatial resolution
I imaged a 0.05 mm diameter human hair target immersed at 50 mm depth in degassed
water. The full synthetic data set was collected within two hours after the hair was submerged in
water. The -6 dB lateral and axial target sizes were measured to serve as metrics for spatial
resolution.

39
2. Contrast-to-noise ratio (CNR)
A full synthetic aperture RF data set of an ATS ultrasound phantom (Model 539, ATS
Laboratories, Bridgeport, CT) containing a 6 mm diameter cylindrical anechoic cyst at 50 mm
depth was collected. The data was then beamformed with offline DAS beamforming and the
proposed Fresnel focusing techniques. CNR is defined as the difference between the mean of the
background (the area surrounding the cyst) and the cyst in decibels divided by the standard
deviation of the background in decibels (after beamforming and log compression) (Krishnan et
al. 1997):

̅

̅̅̅̅

(3.1)
where

̅
is the mean of the signal amplitude from the target (in decibels),

̅̅̅
is the mean of the
signal amplitude coming from the background (in decibels), and σ
b
is the standard deviation of
the signal amplitude from the background (in decibels).
Using the Verasonics Data Acquisition System (VDAS), I used a sampling frequency of
20 MHz for experiments. At this frequency, signals of a 3.3 MHz transducer are sampled at a
rate of 6 samples per wavelength. The delays applied to the 4 transmitters ideally are 0, ¼, ½,
and ¾ of a period, which are equivalent to 0, 1.5, 3, and 4.5 samples. Without interpolation,
instead of having a 3- or 6-transmitter Fresnel system, I implemented Fresnel beamforming with
4 transmitters which have unequally spaced delays of 0, 1, 3, and 4 samples to preserve the same
number of switches and transmitters of the system. By comparing with a system with equally
spaced delay transmitters, I found that the additional focal errors caused by unequally spaced
delays have minor effects on Fresnel beamforming, with less than 2% discrepancies in terms of
40
CNR and resolution. Furthermore, this sampling rate of 6 samples per wavelength does not affect
the receive side of a 4 or 8-phase Fresnel beamforming, where phase shifts are applied.
As described earlier, there are several parameters in the DAX algorithm that can be
adjusted to provide the optimal performance of the system when DAX is combined with Fresnel
beamforming. These parameters include the threshold for the cross-correlation matrix, the size of
median filter, the segment length for cross-correlation, and the band-pass filter used for DAX.
By varying these parameters, the following values empirically provide the best performance in
terms of CNR for Fresnel beamforming with DAX.
Table 3-2: DAX parameters for Experimental Setup
Parameters Values
Threshold 0.001
Cross corr. segment size 6 samples
Median filter size 4λ x 4λ
Filter bandwidth (BPF2) 15%

41
3.4. Results
3.4.1. Simulation results
Figure 3-5 shows the effect of f-number on the performance of 4-phase and 8-phase
Fresnel beamforming methods compared to delay-and-sum (DAS), without dual apodization
with cross correlation (DAX) (Figure 3-5a,b) and with DAX (Figure 3-5c,d). Applying DAX
minimally affects the spatial resolution of Fresnel beamforming with the largest differences
being 0.03 mm for axial pulse length and 0.08 mm for lateral beamwidths. This is expected since
DAX was shown to suppress the side lobes without broadening the main lobes (Seo, 2008 &
2009). With DAX, as the f-number increases from 2 to 4, the -6 dB lateral beamwidth also
increases, changing from 1.06 mm to 1.50 mm for 4-phase Fresnel beamforming, from 1.18 mm
to 1.46 mm for 8-phase Fresnel beamforming, and from 0.90 mm to 1.57 mm for DAS
beamforming, as shown in Figure 3-5c. As a result, the discrepancies in lateral beamwidth
between Fresnel and DAS beamforming also decrease, from 0.28 mm to 0.11 mm for 8-phase
Fresnel beamforming for example. Furthermore, the discrepancies in axial pulse length between
Fresnel and DAS beamforming decrease from about 1.3 mm to 0.1 mm as the f-number increases
from 2 to 4 (Figure 3-5b,d). To explicate, axial pulse length for 8-phase Fresnel beamforming
with DAX decreases from 1.92 mm at f-number = 2 to 0.71 mm at f-number = 4, approaching
the axial pulse length of 0.59 mm for DAS beamforming with DAX.

42

Figure 3-5: Simulated spatial resolution of 3 beamforming algorithms without DAX (a, b) and with DAX
(c, d).

Figure 3-6: Simulated lateral beamplots using DAS, 4-phase Fresnel beamforming with and without
DAX at f-number = 2 (a), 3 (b) and 4(c)
43
The decreasing discrepancies in spatial resolution between Fresnel and DAS
beamforming with increasing f-numbers can be explained by the decreasing number of focal
errors in Fresnel beamforming. In fact, the maximum path length difference between outer and
center elements is reduced from 6 wavelengths to 2 wavelengths as f-number goes from 2 to 4 as
shown in Figure 3-1. This results in a maximum focal error of 1 wavelength for Fresnel
beamforming at f-number = 4.
Figure 3-6 shows the lateral beamplots simulated with Field II, using DAS and 4-phase
Fresnel beamforming with and without DAX at f-number = 2 (Figure 3-6a), 3 (Figure 3-6b) and
4 (Figure 3-6c). Even though the main-lobe beamwidths for Fresnel beamforming are
comparable with those for DAS, the side-lobe levels for Fresnel beamforming is about 6 to 15
dB higher than those for DAS, which can deteriorate image contrast. As the f-number increases,
these side-lobe levels of Fresnel beamforming become lower due to smaller focal errors. In the
case of 4-phase Fresnel beamforming, the side-lobe level is lowered from -9 dB at f-number = 2
to -20 dB at f-number = 4. Using DAX, signals away from the main lobe are more suppressed
than the ones near the main lobe. For instance, at f-number = 2, the clutter at a lateral distance 2
mm away from the main lobe is suppressed from -17 dB to -21 dB, while the clutter at a lateral
distance 4 mm away from the main lobe is suppressed from -26 dB to -51 dB. These effects are
later seen in experimental single-wire images (Figure 3-7 and Figure 3-8).

44
3.4.2. Experimental results – spatial resolution

Figure 3-7: Experimental single-wire images without DAX using 4-phase Fresnel, 8-phase Fresnel, and
DAS with 50% signal bandwidth and f-numbers of 2, 3, and 4
Figure 3-7 and Figure 3-8 show the experimental images of a target of human hair, using the
three different beamforming techniques without DAX (Figure 3-7 and with DAX (Figure 3-8) in
a 60 dB dynamic range. As seen in Figure 3-7, the clutter in Fresnel beamforming becomes less
noticeable, with a trade-off of enlarging lateral beamwidths as the f-number increases. The
clutter, especially beyond 3 mm laterally away from the main beam, is suppressed with DAX as
shown in Figure 3-8. These results agree with the simulated results, where the clutter in these
regions is suppressed by about 20 dB.
45

Figure 3-8: DAX-applied experimental single-wire images using 4-phase Fresnel, 8-phase Fresnel, and
DAS with 50% signal bandwidth and f-numbers of 2, 3, and 4
Figure 3-9 quantifies the plots of experimental lateral beamwidths and axial pulse lengths
against f-numbers without DAX (Figure 3-9a, b) and with DAX (Figure 3-9c, d). Similar to the
simulated results, these results show that applying DAX does not affect spatial resolution, with a
maximum difference of 0.02 mm for lateral beamwidths. This maximum difference is 0.07 mm
for axial pulse length. Regarding spatial resolution for Fresnel beamforming, the same trends are
seen in experimental results as in simulation results. As the f-number increases from 2 to 4, the -
6 dB lateral beamwidth enlarges from 1.38 mm to 1.69 mm for 4-phase Fresnel beamforming,
and from 1.24 mm to 1.66 mm for 8-phase Fresnel beamforming. The axial pulse length
decreases from 1.92 mm to 0.83 mm for 4-phase Fresnel beamforming, and from 1.89mm to 0.84
mm for 8-phase Fresnel beamforming. The resolution of Fresnel beamforming and DAS
46
beamforming also converges to within a 5% discrepancy as the f-number increases to 4, where
the focal errors are reduced to about 1 wavelength.

Figure 3-9: Simulated spatial resolution of 3 beamforming algorithms without DAX (a, b) and with DAX
(c, d)

47
3.4.3. Experimental results - contrast

Figure 3-10: Experimental 6-mm-diameter cyst images without DAX using 4-phase Fresnel, 8-phase
Fresnel, and DAS beamforming with 50% signal bandwidth and f-numbers of 2, 3, 4.
Figure 3-10 shows the experimental images of 6-mm diameter cylindrical anechoic cysts
in the ATS tissue mimicking phantom. Here, the clutter inside the cyst and the non-circular
shape of the cyst in the images for Fresnel beamforming are the results of high side-lobe levels
due to focal errors as seen in Figure 3-6, , and Figure 3-8. As the f-number increases, the cyst
appears more circular with less clutter. In fact, the CNRs increase from 3.0 at f-number = 2 to 3.8
at f-number = 4 for 4-phase Fresnel beamforming, and from 3.0 to 3.9 for 8-phase Fresnel
beamforming, approaching CNRs for DAS beamforming.

48

Figure 3-11: DAX-applied experimental 6-mm-diameter cyst images using 4-phase Fresnel, 8-phase
Fresnel, and DAS beamforming with 50% signal bandwidth and f-numbers of 2, 3, and 4
Figure 3-11 shows the experimental images of the same cysts with DAX applied. Shown
in the same dynamic range of 40 dB as those in Figure 3-10, these cysts appear darker with less
clutter. These visual improvements are quantified with the CNR measurements, which have
improved by at least 100%. For instance, applying DAX on DAS beamforming improves the
CNR from 5.2 to 11.2 at f-number = 3, and from 4.9 to 11.4 at f-number = 4. For 4-phase Fresnel
beamforming, the CNRs are improved from 3.7 to 10.6 at f-number = 3, and from 3.8 to 9.1 at f-
number = 4. These improvements are expected due the reduction of side-lobe levels when DAX
is applied as previously shown in Figure 3-6.

49

Figure 3-12: Experimental comparison of beamforming methods in terms of contrast-to-noise ratio
(CNR): 4-phase Fresnel, 8-phase Fresnel, DAS with and without DAX applied
Figure 3-12 summarizes the plots of CNRs against different f-numbers for DAS and
Fresnel beamforming with and without DAX. As the f-number increases from 2 to 4, the CNRs
for Fresnel beamforming without DAX slightly improve slightly from 3.0 to 3.8, approaching the
CNRs for DAS beamforming, which decreases from 5.3 to 5.0. This is expected due to the
decreasing side-lobe levels in Fresnel beamforming. The CNRs are also compatible within 10%
for 4-phase and 8-phase Fresnel beamforming across all f-numbers. The CNRs of Fresnel
beamforming with DAX are highest at f-number = 3, where CNRs for 4-phase Fresnel with DAX
and 8-phase Fresnel with DAX are 10.6 and 10.9. These CNRs are 5.2% and 2.4% lower than the
CNR of 11.2 from DAS beamforming with DAX, respectively. F-number = 3 is also the point
where the spatial resolution for Fresnel beamforming is comparable with those of DAS (Figure
3-5 and Figure 3-9).

50
3.5. Summary
This chapter presents the concept and performance evaluation of Fresnel beamforming
followed by a novel side-lobe suppression method, called dual apodization with cross-correlation
(DAX), for curvilinear array transducers. Fresnel beamforming technique allows a system with 4
to 8 transmit channels and 2 receive channels with a network of single-pole/single-throw
switches to focus an array. It is shown that combining DAX with Fresnel beamforming can result
in a 4 to 20 dB of clutter suppression, and at least a 100% improvement in CNR. Therefore, the
proposed integration of DAX into Fresnel beamforming suppresses the effects of focal errors in
Fresnel beamforming, allowing it to be used in curvilinear arrays. In fact, even though the results
shown in this chapter come from a curvilinear array with the radius of 40 mm, similar analysis
can be used for arrays with different radii. For instance, the performance of Fresnel beamforming
is expected to improve for curvilinear arrays with larger radii as a result of decreasing focal
errors. On the other hand, bigger f-numbers may be needed to reduce the number of focal errors
for arrays with smaller radii.

51
Chapter 4. HARMONIC IMAGING WITH
FRESNEL BEAMFORMING IN THE PRESENCE
OF PHASE ABERRATION

4.1. Introduction
In previous chapters, Fresnel beamforming is introduced as a beamforming method that
can reduce the size and cost of ultrasound systems (Nguyen et al. 2011; Nguyen and Yen 2013).
Having a delay profile with a shape similar to a physical Fresnel lens, Fresnel beamforming has
the advantage of reducing channel count from 64-128 channels down to 4-8 transmit and 2
receive channels. The drawback of Fresnel beamforming is the presence of high side lobes and
grating lobes due to focal errors which result from phase wraparound and quantization of the
delay profile of Fresnel beamforming. To suppress high side lobes and grating lobes in Fresnel
beamforming, I previously proposed the integration of a novel clutter-suppression method called
dual apodization with cross-correlation (DAX) in Fresnel beamforming (Nguyen and Yen 2013).
DAX is a signal processing method that suppresses side lobes and clutter, thus improving
contrast without compromising spatial resolution (Seo and Yen 2008, 2009). While allowing
Fresnel beamforming to be used in cases where focal errors are large (up to 7 wavelengths), this
integration still needs improvement for clinical use in large patients. In these patients, sound
speed aberration can induce additional focal errors in Fresnel beamforming. The improvement
presented in this chapter is achieved by implementing harmonic imaging in Fresnel beamforming
to suppress side lobes and aberration effects.
52
4.2. The Design
4.2.1. Harmonic Imaging
Introduced in 1997 by Averkiou et al., harmonic imaging has become a popular and
important diagnostic tool in many clinical applications (Averkiou et al. 1997; Tranquart et al.
1999). These applications include detecting subtle lesions in organs such as thyroid and breast,
delineating endocardial borders and visualization of cardiac chambers, as well as abdominal
imaging (Kornbluth 1998; Shaprio et al. 1998; Szopinski et al. 2003a, 2003b). Harmonic
imaging offers several benefits over conventional fundamental imaging. First, ultrasound
beamwidth is reduced at harmonic frequencies (Starritt et al. 1986; Ward et al. 1997). Second,
studies have shown that the side lobes generated from harmonic frequency signals are much
lower than those generated from fundamental frequency signals (Christopher 1997; Christopher
et al. 1998; Rubin et al. 1998). Furthermore, the amplitudes for second harmonic signals vary in
proportion to the square of the amplitudes of fundamental signals. Therefore, small regional
variations in the amplitudes of fundamental signals will result in larger variations in harmonic
signals (Desser and Jeffrey 2001). This characteristic, along with lower side-lobe levels, provides
harmonic imaging the ability to improve image contrast and to detect and characterize lesions.
Lastly, harmonic signals originate within tissues, and therefore pass through tissue layers only
once instead of twice as in the case of fundamental frequency signals. This makes harmonic
imaging less prone to distortion in the presence of aberration (Desser and Jeffrey 2001). Due to
the characteristics of lower side-lobe levels and aberration effect suppression, harmonic imaging
provides an effective solution to the limitations of Fresnel beamforming.
53
Unlike conventional ultrasound imaging, where images are formed from echoes of the
transmit frequency (fundamental), tissue harmonic imaging (THI) utilizes echoes at twice the
transmit frequency (second harmonic). These tissue harmonic signals are generated by the
nonlinearity of the imaged target and the propagation medium (Averkiou et al. 1997; Desser and
Jeffrey 2001; Tranquart et al. 1999). To explicate, in ultrasound imaging, tissues behave like
linear systems only when the applied acoustic pressure is very small. However, when higher
pressures are applied, tissues are no longer completely elastic and behave nonlinearly, resulting
in faster sound speeds through compressed tissues than through relaxed tissues. As a result,
ultrasound waveforms are distorted, resulting in the generation of harmonic signals (Beyer and
Letcher 1969; Duck 2002; Li and Shen 1999). These harmonic signals have amplitudes lower
than those of fundamental signals. However, dynamic transmit focusing was demonstrated to
increase harmonic signal generation as well as to improve the sensitivity and penetration of
harmonic imaging (Li and Shen 1999).
There are two main approaches in harmonic imaging. One method, called tissue harmonic
imaging (THI), uses band-pass filters to extract harmonic content from the received echoes. The
other method is based on pulse inversion sequence, also known as pulse inversion harmonic
imaging (PIHI) (Chapman and Lazenby 1997; Ma et al. 2005). While THI is simple and can be
efficiently implemented, it is prone to potential contrast degradation due to spectral overlap
(Shen and Li 2001). This spectral overlap in THI can be reduced with a narrower transmit
bandwidth, at the expense of lengthened axial resolution. On the other hand, PIHI method can
avoid the potential spectral overlap even when used with a relatively broad transmit bandwidth.
In this method, two transmit pulses, 180
0
out of phase relative to each other, are required for each
scan line. The echoes from both transmits are added, resulting in a cancellation of signals at the
54
fundamental frequency (Chapman and Lazenby 1997; Ma et al. 2005). Since PIHI requires two
transmit pulses per scan line, the drawbacks of PIHI include frame rate reduction and motion
artifacts. In this work, I implement and evaluate both THI and PIHI approaches in Fresnel
beamforming.

4.2.2. Implementing harmonic imaging in Fresnel beamforming
In Fresnel beamforming, the standard geometric delay ∆t is replaced by a new delay ∆t
F

given by:
T t t
F
mod    (4.1)

where mod indicates the modulo operation and T is the period of ultrasound signals based on the
center frequency of the signals. ∆t
F
is the remainder after integer multiples of the ultrasound
period T have been subtracted from ∆t (Nguyen et al. 2011; Richard et al. 1980). ∆t
F
is then
quantized into equally spaced discrete values. For instance, for a 4-phase Fresnel beamforming,
∆t
F
takes the values of 0, 1/4, 2/4, and 3/4 of the period T. To illustrate, Figure 4-1 shows the
delay profiles ∆t for a 64-element sub-aperture when geometric focusing is used. These delay
profiles are calculated from a curvilinear array with a 40-mm radius of curvature and a focus
depth of 50 mm. These delay profiles are plotted in terms of signal periods based on the
fundamental frequency (Figure 4-1a) and the 2
nd
harmonic frequency (Figure 4-1b). The new
delay profiles ∆t
F
for Fresnel beamforming are plotted as the bold lines. These delay profiles
have shapes similar to a physical Fresnel lens. Each segment corresponds to a period T offset.
Using ∆t
F
results in a focal error which is equal to an integer multiple of T plus the error caused
55
by quantization. Focusing errors, plotted as the dotted lines, show that the number of focal errors,
in terms of wavelengths, for Fresnel beamforming doubles as the frequency goes from
fundamental to 2nd harmonic.

Figure 4-1: Delay profiles for Fresnel beamforming and focusing errors in terms of wavelengths for a 64-
element subaperture at a) the fundamental frequency (1.96 MHz) and b) the 2
nd
harmonic frequency (3.92
MHz)

Figure 4-2 depicts the overall process of implementing harmonic imaging for Fresnel
beamforming followed by the contrast enhancement technique, DAX. As the radio frequency
(RF) signal arrives at each element, the signal is passed to one of the two receive channels,
Rx1(+) and Rx2(+), through a network of switches, as shown previously in Figure 2-3. These
signals will be band-pass filtered and phase shifted. The center frequencies of these filters are
either at the fundamental frequency, f
0
, as in the case of fundamental imaging, or at the 2
nd

harmonic frequency, 2f
0
, as in the case of harmonic imaging (THI and PIHI). For PIHI, after the
first transmit, an additional transmit with inverted pulse is required for each image line. The
receive signals from these two transmits will be summed and subsequently band-pass filtered at
the harmonic frequency 2f
0
. For each pair of receive channels, DAX will be applied to form
DAX-applied images for fundamental, tissue harmonic, and pulse inversion harmonic imaging,
respectively.
56

Figure 4-2: The overall implementation of harmonic imaging in Fresnel beamforming followed by dual apodization
with cross-correlation (DAX)

4.3. Methods
4.3.1. Data acquisition – harmonic signal generation and ex-vivo aberrator
For the experimental setup, radio frequency (RF) data sets of an ATS ultrasound phantom
(Model 539, ATS Laboratories, Bridgeport, CT) were acquired and sampled at 45 MHz, using
Verasonics Data Acquisition System (VDAS). The phantom contains a 6-mm diameter anechoic
cyst, used for image contrast evaluation, and a 0.05-mm diameter monofilament nylon, used for
spatial resolution evaluation. These targets are located at a 50 mm depth. A 128-element C4-2
curvilinear array transducer was used for this experiment. This array has a radius of curvature of
40 mm, an aperture angle of 75 degrees, and a pitch of 409 um. A 2-cycle 1.97 MHz transmit
pulse was used in this experiment. RF data sets were acquired with and without the presence of
near-field phase aberrators. These aberrators were mimicked by 5-mm and 12-mm thick pork
tissue layers. Transmit focusing was implemented to improve the generation of harmonic signals.
57
The transmit foci were set at 50 mm depth in the case without the pork layer, and shifted down to
55 mm and 62 mm in the presence of the 5-mm and 12-mm thick pork layers, respectively. For
each acquisition, data from each channel were collected 12 times and averaged. To obtain a data
set with pulse inversion harmonic signals, another data set was obtained, using a transmit pulse
with the same amplitude but inverted, and then summed with the data set from the first transmit.
4.3.2. Data processing – beamforming and contrast enhancement
The channel data sets were then beamformed with DAS beamforming and Fresnel
beamforming using Matlab (The MathWorks Inc., Natick, MA). The dynamic receive focusing
was updated every 1 mm. The image line spacing is 0.14 degrees. The delay profiles for Fresnel
beamforming were calculated based on 1.96 MHz center frequency for fundamental frequency
imaging, and on 3.92 MHz for harmonic imaging. These delays, ranging from 0 to ¾ of a period
T, were implemented in Matlab by multiplying the signals with -1 and/or Hilbert transform. For
example, a signal requiring a delay of 2.75 wavelengths based on 1.96 MHz center frequency
was subjected to a 0.75 * 360 = 270-degree phase shift. This phase shift was implemented by
first multiplying the signal with -1, equivalent to a 180-degree phase shift, and then passing it
through the Hilbert transform, which associates with a 90-degree phase shift. This delay of 2.75
wavelengths based on 1.96 MHz fundamental frequency is equivalent to a delay of 5.5
wavelengths based on 3.92 MHZ harmonic frequency. In this case, the delay was wrapped
around to be 0.5 wavelengths, which was implemented by a 180-degree phase shift. All the data
were band-pass filtered around 1.96 MHz for fundamental imaging and around 3.92 MHz for
both THI and PIHI. The filters were designed using the Matlab Filter Design and Analysis Tool
58
(FDATool) box. The parameters used in the FDATool box are presented in Table 4-1. To further
improve image contrast, DAX was applied to the RF channel data, after band-pass filtering, for
both DAS and Fresnel beamforming at all aberration levels. Table 4-2 presents the parameters
used for the experimental setup.

Table 4-1: Parameters for filters designed with Matlab FDATool box
Parameters Value
Response Type Bandpass
Design Method FIR – Least-squares
Filter Order 64
Fstop1 2.8 MHz
Fstop2 4.1 MHz
Sampling frequency 45 MHz
Weight value1 (Wstop1) 1000000
Weight value 2 (Wstop2) 1

59
Table 4-2: Parameters for experimental Setup
Parameters Value
Radius of curvature 40mm
Number of elements 128
Aperture angle 75 degrees
Elevation element height 13 mm
Azimuthal element pitch 0.409 mm
Transmit center frequency 1.96 MHz
Sampling frequency 45 MHz
Sound speed 1480 m/s (water)
1450 m/s (phantom)
Transmit focus 50 mm (no pork)
55 mm (5 mm pork)
62 mm (12 mm pork)
Lateral beam spacing 0.14 degrees
Receive focal delay step
Threshold (DAX)
Median filter (DAX)
1 mm
0.001
4λ x 4λ

60
4.3.3. Contrast-to-noise ratio (CNR) and spatial resolution
The quality of the cyst images beamformed with DAS beamforming and Fresnel
beamforming was quantified in terms of contrast-to-noise ratio (CNR). CNR is defined as the
difference between the mean of the background (the area surrounding the cyst) and the cyst in
decibels divided by the standard deviation of the background in decibels (after beamforming and
log compression) (Krishman et al. 1997):

̅

̅̅̅̅

(4.2)
where

̅
is the mean of the signal amplitude from the target (in decibels),

̅̅̅
is the mean of the
signal amplitude coming from the background (in decibels), and σ
b
is the standard deviation of
the signal amplitude from the background (in decibels). On the wire-target images, the -6 dB
lateral and axial target sizes were measured to serve as metrics for spatial resolution.

61
4.4. Results
Figure 4-3 shows the experimental images of a 6-mm diameter anechoic cyst from the ATS
tissue-mimicking phantom with no aberrator using delay-and-sum (DAS) and Fresnel
beamforming. Similar sets of images, acquired with 5-mm and 12-mm pork tissues, are presented
in Figure 4-4 and Figure 4-5, respectively. These images are shown in a 40-dB dynamic range.
Table 4-3 shows the CNR values for these images. For comparison, the regions for CNR
calculation are identical for DAS and Fresnel beamforming.
Harmonic imaging without DAX
Harmonic imaging provided superior image contrast compared to fundamental
imaging at all aberration levels for both DAS and Fresnel beamforming. However, as the
aberration level increased, image contrast for both fundamental and harmonic imaging degraded.
For DAS beamforming, the CNR values for fundamental imaging decreased from 6.02 in the
case without aberrator to 3.65 and 0.93 in the cases of 5-mm and 12-mm pork aberrators,
respectively. Similar degradation was found with Fresnel beamforming, where the CNR
decreased from 5.83 to 3.17 and 1.38, respectively. While both THI and PIHI improved the
image contrast for all aberration levels, the impact of harmonic imaging became more
pronounced as the aberration level increased. For example, in the case of no aberrator, THI and
PIHI improved CNR by 14% and 21% (from 6.02 to 6.84 and 7.28) for DAS beamforming, and
by 14% and 26% (from 5.83 to 6.65 and 7.35) for Fresnel beamforming, respectively (Figure
4-3). In the case of weak aberrator, these percentage improvements were 83% and 84% for DAS
beamforming, and 72% and 81% for Fresnel beamforming, respectively (Figure 4-4). The impact
of harmonic imaging was most obvious in the case of strong aberrator, where the cysts were not
62
visible with fundamental imaging for both DAS and Fresnel beamforming. With harmonic
imaging, these cysts became visible, although with some clutter caused by aberration effects
(Figure 4-5, first column). The CNR improvements seen with harmonic imaging are the results
of the suppression of aberration effects at the second harmonic.

Figure 4-3: Experimental 6-mm-diameter cyst images without aberrator using DAS and Fresnel
beamforming with and without DAX

Harmonic imaging with DAX
Harmonic imaging improved the image contrast in the presence of weak aberrator with
CNRs comparable to those of unaberrated cysts using fundamental imaging. However, in the
case of strong aberrator, while harmonic imaging improved the cyst visibility with CNR
improvements of at least 350% and 145% for DAS and Fresnel beamforming, respectively, these
cysts still appeared with clutter, and the CNRs were below those of unaberrated cysts. Similarly,
63
although DAX improved image contrast at all aberration levels, applying DAX on fundamental
imaging for the case of strong aberrator still resulted in cysts with noncircular appearance and
low detectability (Figure 4-5). However, combining DAX with harmonic imaging suppressed
most of the aberration effects and resulted in circular cysts with CNR improvements of at least
790% and 370% for DAS and Fresnel beamforming compared to conventional imaging,
respectively.

Figure 4-4: Experimental 6-mm-diameter cyst images with weak aberrator (5-mm pork tissue) using
DAS and Fresnel beamforming with and without DAX.

Fresnel beamforming vs. delay-and-sum (DAS) beamforming
In all cases, Fresnel beamforming was outperformed by DAS beamforming. As the
aberration level increased, the discrepancies between DAS and Fresnel beamforming increased.
For example, in the case of no aberrator at the fundamental frequency, the CNRs were 6.02 and
5.83, equivalent to a 3% discrepancy, for DAS and Fresnel beamforming, respectively. This
64
difference increased to 13% in the case of a 5-mm pork aberrator. However, harmonic imaging
improved the CNRs for Fresnel beamforming, making them higher than those of DAS using
fundamental imaging by 10%, 50% and 264%, but still lower than those of DAS using THI by
3%, 19% and 20% in the cases of no aberrator, weak aberrator, and strong aberrator,
respectively. Applying DAX improved CNRs for both DAS and Fresnel beamforming. The CNR
improvements due to DAX were slightly higher for DAS beamforming than those for Fresnel
beamforming. At the fundamental frequency, these CNR improvements using DAX were 89%,
53%, and 119% for DAS beamforming and 65%, 54%, and 55% for Fresnel beamforming in the
cases of no aberrator, weak aberrator, and strong aberrator, respectively. For THI, applying DAX
improved the CNRs by 118%, 79%, 98% for DAS, and 63%, 84%, 92% for Fresnel
beamforming, respectively. Similar improvements were found when DAX was applied on
images using PIHI. The discrepancies in CNR improvements when applying DAX on DAS and
Fresnel beamforming can be explained by the apodization pairs. DAS used an 8-8 apodization
pair, which was shown to be the most effective in suppressing side lobe and clutter, while
Fresnel beamforming used the apodization pairs that were dynamically changed based on the
delay profile of Fresnel beamforming (Nguyen and Yen 2013; Seo and Yen 2008, 2009).
THI vs. PHI for Fresnel beamforming
Both THI and PIHI improved image contrast and suppressed aberration effects in the
cases of weak and strong aberrators for both DAS and Fresnel beamforming (Figure 4-4 and
Figure 4-5). However, PIHI provided the best improvement in every case. For example, in the
case of no aberrator, the CNRs are 6.84 and 7.28 for DAS beamforming, and 6.65 and 7.35 for
Fresnel beamforming with THI and PIHI, respectively. These CNRs are 4.21, 4.56, 3.38 and 4.19
in the case of strong aberrator, respectively. The superior performance of PIHI over THI can be
65
explained due to the removal of spectral overlap using PIHI. Figure 4-6 shows the frequency
spectra of the receive RF data for fundamental imaging (Figure 4-6a), THI (Figure 4-6b) and
PIHI (Figure 4-6 c). Using THI, the spectral overlap between fundamental and second harmonic
bands could not be completely separated (Figure 4-6b). On the other hand, PIHI effectively
suppressed fundamental frequency signals to minimize the contribution of spectral overlap to the
harmonic images (Figure 4-6c). However, the drawbacks of PIHI include frame rate reduction
and motion artifacts. While artifacts due to axial motion can be effectively removed, little
improvement can be obtained with lateral motion correction (Shen and Li 2002).

Figure 4-5: Experimental 6-mm-diameter cyst images with strong aberrator (12-mm pork tissue) using
DAS and Fresnel beamforming with and without DAX

Effects of harmonic imaging on spatial resolution
The -6 dB lateral beamwidths and axial pulse lengths for DAS and Fresnel
beamforming using different imaging approaches are also summarized in Table 4-4. Both
66
harmonic imaging methods, THI and PIHI, improved spatial resolution for DAS and Fresnel
beamforming at all aberration levels. In most cases, THI and PIHI provide comparable
improvements in spatial resolution. However, the improvements in axial pulse length are slightly
better with PIHI compared to THI. This can be due to the removal of spectral overlap using
PIHI. Furthermore, the impact of harmonic imaging due to its ability to suppress aberration
effects became more pronounced as the aberration level increased. The biggest improvement in
spatial resolution was found when using PIHI in the case of strong aberrator, where -6 dB lateral
beamwidths were reduced by 46% and 45%, and axial pulse lengths were shortened by 39% and
45% for DAS and Fresnel beamforming, respectively. These percentage improvements were
slightly less in the cases without aberrator and with weak aberrator. To explicate, in the case
without aberrator, using PIHI resulted in reductions of 40% and 25% in lateral beamwidth (from
1.54 to 0.92 mm, and from 1.79 to 1.34 mm) and 35% and 22 % in axial pulse length (from 1.48
to 0.96 mm and from 1.47 to 1.15 mm) for DAS and Fresnel beamforming. Furthermore, I also
found that applying DAX did not change the spatial resolution in all cases, which is consistent
with the previous studies on DAX (Nguyen and Yen 2013; Seo and Yen 2008, 2009).

Figure 4-6: Frequency spectra of the received RF data for a) conventional imaging at the fundamental
frequency of 1.96 MHz, b) THI, and c) PIHI at the second harmonic frequency. The frequency response
of the band-pass filter is also shown in all 3 cases.
67
Table 4-3: Contrast-to-noise ratio (CNR) values for experimental data
Delay and Sum Fresnel
No DAX DAX No DAX DAX
Fund. THI PIHI Fund. THI PIHI Fund. THI PIHI Fund. THI PIHI
No Aberrator 6.02 6.84 7.28 11.39 14.90 15.23 5.83 6.65 7.35 9.63 10.81 10.81
5-mm Pork 3.65 6.70 6.66 5.60 11.99 12.72 3.17 5.45 5.75 4.86 10.01 10.16
12-mm Pork 0.93 4.21 4.56 2.03 8.35 10.17 1.38 3.38 4.19 2.14 6.48 6.80

Table 4-4: -6 dB lateral beamwidth and axial pulse length for wire target (mm)
Delay and Sum Fresnel
Lateral Axial Lateral Axial
Fund. THI PIHI Fund. THI PIHI Fund. THI PIHI Fund. THI PIHI
No Aberrator 1.54 0.9 0.92 1.48 1.15 0.96 1.79 1.29 1.34 1.47 1.32 1.15
5-mm Pork 1.84 1.09 1.09 1.46 1.11 1.00 2.07 1.22 1.19 1.88 1.42 1.18
10-mm Pork 2.15 1.15 1.17 1.54 1.07 0.94 2.23 1.27 1.23 1.9 1.24 1.04

68
4.5. Summary
This chapter presents the implementation and performance evaluation of tissue harmonic
imaging (THI) and pulse inversion harmonic imaging (PIHI) in Fresnel beamforming. Even
though the number of focal errors in terms of wavelengths for Fresnel beamforming doubles at
the 2
nd
harmonic frequency compared to that at the fundamental frequency, there is an
improvement in terms of CNR and spatial resolution when implementing harmonic imaging in
Fresnel beamforming. This is due to the suppression of side lobe levels and aberration effects as
well as shorter wavelengths, as the results of harmonic imaging. DAX was shown to improve the
CNRs of Fresnel beamforming by at least 47%, without compromising spatial resolution, in both
fundamental and harmonic imaging at all 3 different aberration levels. PIHI followed by DAX
was shown to improve image contrast the most. This integration improved the CNRs of Fresnel
beamforming by 86%, 221%, and 394% compared to Fresnel beamforming using fundamental
imaging in the cases of no aberrator, weak aberrator, and strong aberrator, respectively. In terms
of resolution, these improvements are 25%, 42%, and 44% for lateral beam reduction, and 22%,
37% and 45% for axial pulse length shortening, respectively.
This chapter also illustrates the increasing impact of harmonic imaging, in terms of
percentage improvements in both CNRs and spatial resolution, for both DAS and Fresnel
beamforming, as the aberration strengthens. However, considerations are needed in choosing
THI vs. PIHI. While PIHI provides the best performance, it requires two transmit pulses per scan
line, resulting in frame rate reduction and motion artifacts. On the other hand, THI can be simply
implemented with harmonic band-pass filters and can still provide decent image quality
improvements.
69
In conclusion, the advantage of Fresnel beamforming is the reduced channel count at the
cost of high side lobes, which can be counteracted by the advantages of lower side lobes and
suppressed aberration effects offered by harmonic imaging. As harmonic imaging has become
widely used in clinics, this chapter illustrates the compatibility of harmonic imaging and Fresnel
beamforming in providing ultrasound imaging systems, not only with reduced cost and size but
also with image quality comparable to that of conventional harmonic imaging systems.
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Chapter 5. GATED TRANSMIT
BEAMFORMER AND MODULAR FRESNEL
RECEIVE BEAMFORMER

5.1. Introduction
In previous chapters, Fresnel beamforming and its benefit of reducing the number of
channels have been introduced and evaluated. In the case of linear arrays where the maximum
focal errors are about 3 wavelengths, Fresnel beamforming performance is comparable to that of
delay-and-sum (DAS) beamforming. However, the performance of Fresnel beamforming is
degraded when the focal errors are larger than 3 wavelengths as in the case of curvilinear arrays.
In this case, the dual apodization with cross-correlation (DAX) method is required to suppress
high side lobes caused by the increasing number of focal errors. This chapter presents two new
techniques – one on transmit beamforming and one on receive beamforming – that can further
improve the performance of Fresnel beamforming.
The first technique, called the gated transmit beamforming method, uses 4 transmitters
with a set of single-pole/single-throw switches to achieve an ideal transmit focusing beam, which
normally requires 64-128 transmitters. Since Fresnel beamforming method already includes a set
of single-pole/single-throw switches, no additional components are needed to implement this
gated transmit beamforming technique. The second technique is the modular receive Fresnel
beamforming method which is a modified version of Fresnel beamforming presented in previous
71
chapters. In this receive beamforming technique, transducer elements are subdivided into smaller
sub-apertures containing consecutive elements. Each sub-aperture has one module of Fresnel
beamforming, which includes 2 receive channels. As a result, the ranges of delays required for
each sub-aperture are reduced, leading to a reduced number of focal errors in each Fresnel
beamforming module. Since each Fresnel beamforming module has two receive channels, the
trade-off of this technique is the increase in the total number of receive channels in Fresnel
beamforming.
In the case of phased arrays where beam steering is needed, the path length differences
among elements increase as the steering angle increases, resulting in delay profiles with
increased ranges. As a result, the number of focal errors in Fresnel beamforming also increases.
Figure 5-1 shows the ideal delay profiles of delay-and-sum beamforming and of Fresnel
beamforming at 0 degree (a), where the delays range from 0 to 2 wavelengths, and at 40 degree
scan angles (b), where the delay profile ranges from -15 to 15 wavelengths. For ultrasound
systems that require a large range of delay values, such as those with phased arrays, the
implementation of gated transmit beamforming and modular Fresnel beamforming becomes
critical for Fresnel beamforming to achieve image quality comparable to that of delay-and-sum
beamforming.

72

Figure 5-1: Delays profiles of Fresnel beamforming and focusing errors in terms of wavelength
compared to DAS geometric focus beamforming for a 64-element phased array at a) 0 degree scan angle
and b) 40 degree scan angle

5.2. The Design
5.2.1. Gated transmit beamforming
In a traditional transmit beamformer, each element of an array requires a separate
transmit channel, resulting in 64-128 transmit channels to focus the transmit beam of a 64-128
element transducer. With the proposed gated transmit beamforming method, an ideal transmit
focusing can be achieved with the use of 4 transmit channels and a set of switches. The key
concepts of this design are described as follows. For each transmit event, each transmitter
produces one pulse with multiple cycles as shown in Figure 5-2: A . The pulse duration should
be at least equal to the range of the delay profile. For example, in the case of a 3.3 MHz phased
array where the delay profile ranges from -9 to +9 wavelengths at 20-degree scan angle, the
transmitters should generate pulses with at least 18 cycles. The pulses from four transmitters
73
have 0, 90, 180, and 270 degree phase shifts relative to each other. These pulses will be sent to
all transducer elements through a set of 4:1 multiplexers, with one multiplexer per element. By
closing 1 of the 4 switches in the multiplexer at the specified time, the transmit pulse for each
element can be generated with delays as precise as ¼ wavelength.

Figure 5-2: A gated transmit beamforming with 4 transmitters

5.2.2. Modular Fresnel receive beamforming
As described in previous chapters, Fresnel beamforming requires 2 receive channels.
However, the main trade-off of Fresnel beamforming is the presence of focal errors, which
increase with increasing path length differences. As a result, the image degradation becomes
74
more pronounced with smaller f-numbers or, equivalently, larger apertures for a given depth. For
beam steering in phased arrays, the delays at 40-degree steering angle can range from -13 to +15
wavelengths, resulting in focal errors ranging approximately from -13 to +14 wavelengths. In
order to reduce the number of focal errors, the modular Fresnel beamforming method divides the
array elements into smaller groups with consecutive elements. Each sub-aperture has its separate
module of Fresnel beamforming with two receive channels. The appropriate delays will be
applied to these receive channels. This will significantly reduce the number of focal errors for
each element. For example, the first 16 elements shown in b have delays ranging approximately
from 8 to 15 wavelengths. If one module of Fresnel beamforming is used for the entire
transducer, the receive signals of these elements can be delayed by a maximum delay of one
wavelength. This results in focal errors ranging from 7 to 15 wavelengths. However, by grouping
these elements into a separate sub-aperture and applying an additional coarse delay of, for
example, 11 wavelengths, the focal errors will be reduced to a range of -4 to 3 wavelengths
(Figure 5-3b). An increasing number of Fresnel beamforming modules can be used to reduce the
number of focal errors. To explicate, Figure 5-3 shows the delay profiles and focal errors when
2-module Fresnel beamforming is used (Figure 5-3a), and when 4-module Fresnel beamforming
is used (Figure 5-3b). Figure 5-4 depicts a 4-module Fresnel beamformer for a 64-element
phased array. This modular Fresnel beamformer has 4 sub-apertures, each of which has 16
elements controlled by a pair of 2 receive channels and 4 transmit channels. Different coarse
delays ( 
1
, 
2,

3,

4
)

can be applied to each pair of receive channels to reduce the total number of
focal errors in Fresnel beamforming.
75

Figure 5-3: Delay profiles and focal errors for 2-module (a) and 4-module (b) Fresnel beamforming

Figure 5-4: A 4-module Fresnel receive beamformer
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5.3. Methods
In both simulation and experiments, I evaluated the performance of Fresnel beamforming
in 4 different configurations: 1) unmodified (1-module Fresnel beamforming and no gated
transmit beamforming), 2) with only gated transmit beamforming, 3) with only modular Fresnel
receive beamforming, and 4) with both gated transmit beamforming and modular Fresnel receive
beamforming. In all cases, the performance of Fresnel beamforming was compared with that of
delay-and-sum beamforming in terms of spatial resolution and contrast-to-noise ratios. The PA4-
2/20 phased array was used. This transducer has 64 elements with a pitch of 0.3 mm. For both
simulation and experimental setup, the single transmit focus was fixed at 50 mm depth and the
dynamic receive focusing was updated every 1 mm. The field of view was set to a 90 degree
angle, which is a conventional field of view for most phased arrays. The lateral beam spacing of
0.46 degrees (0.008 radians) was selected to meet the spatial sampling requirement at the focus
depth. Table 5-1 includes the parameters used in simulation and experimental setup.

5.3.1. Simulation
Computer simulation for a point target was performed using Field II (Jensen 1992). The
locations of the targets were at 0, 10, 20, 30 and 40 degree scan angles. Spatial resolution of
Fresnel beamforming was then evaluated by measuring -6 dB lateral beamwidths and axial pulse
lengths.
77
Table 5-1: Parameters for Simulation and Experimental Setup
Parameters Value
Number of elements 64
Center frequency MHz
Sampling frequency 40 MHz
Azimuthal element pitch 0.300 mm
Elevation element height 14 mm
Sound speed 1450 m/s (phantom)
Transmit focus 50 mm
Lateral beam spacing 0.008 radian (0.225mm at 50 mm depth)
Receive focal delay step 1 mm

5.3.2. Experimental setup
For the experimental setup, Ultrasonix Sonix RP ultrasound system (Ultrasonix Medical
Corp., Richmond, BC, Canada) was used to collect full synthetic RF data sets at a 40 MHz
sampling frequency. A PA4-2 phased array transducer with a 2-cycle 3.3 MHz transmit pulse
was used in the experiments. For each channel, the data was collected 16 times and averaged to
minimize the effects of electrical noise. Fresnel beamforming was then performed offline, which
took about 15 minutes for each data set. To evaluate the performance of Fresnel beamforming, I
imaged an ATS ultrasound phantom (Model 539, ATS laboratories, Bridgeport, CT) containing
wires and cysts at different angles. For the images of wires, the -6 dB lateral and axial wire sizes
were measured to serve as metrics for spatial resolution. For the images of cysts, the contrast-to-
noise ratios were calculated using the following equation (Krishnan et al. 1997):
78

̅

̅̅̅̅

(5-1)
where

̅
is the mean of the signal amplitude from the target (in decibels),

̅̅̅
is the mean of the
signal amplitude coming from the background (in decibels), and σ
b
is the standard deviation of
the signal amplitude from the background (in decibels).

5.3.3. Post-beamforming processing
Ultrasound signals attenuate as they travel through the medium. This behavior results in a
decrease in signal magnitudes with depth, which can make images erroneously appear darker at
deeper depths. To better display the images, time gain compensation function was applied to the
images. These gain functions were empirically generated according to the rate at which the
signal magnitude attenuated. Furthermore, as the scan angle increases, there is a reduction in
signal sensitivity in Fresnel beamforming due to the increasing focal errors. To compensate for
this sensitivity reduction, the signals from each scan line were multiplied with a correction
factor. This factor was calculated as the ratio of signal magnitudes between the signals at 0
degree scan line and those at the scan line that needed to be compensated. The beamformed RF
data, after being compensated for depths and scan angles were then log compressed and scan
converted to generate a display image.

79
5.4. Results
For all of the images shown below, the image quality gets worse with increasing scan
angles. This is due to several factors:
1. As the steering angle increases, the effective transducer size corresponding to the
steering angle decreases. This results in larger lateral beamwidths, thus reducing lateral
resolution.
2. Transducer elements are most efficient in transmitting to and receiving from the
perpendicular direction of the element surface, where the scan angle equals zero.
Therefore, as the steering angle increases, the element sensitivity decreases.
3. Image degradation can also be caused by the effects of grating lobes. Since beam
steering redirects main lobes as well as grating lobes, steering the main lobes to one side
will also move the grating lobes toward the straight-ahead direction of the transducer,
where the elements are most efficient in transmitting and receiving. The close spacing of
elements in phased arrays can reduce the effects of grating lobes. However, there will be
degradation effects from grating-lobes, which result from the high frequency
components of the ultrasound signals.

5.4.1. Simulation results
Figure 5-5 shows the Field II simulated images of multiple point targets using delay-and-
sum beamforming (Figure 5-5g) and Fresnel beamforming with different combinations of
transmit and receive beamforming (Figure 5-5a-f). Figures 5-5a, c, and e (left column) show the
80
images beamformed with 1-module, 2-module, and 4-module receive Fresnel beamforming
without gated transmit beamforming, respectively. Similarly, Figures 5-5b, d, and f (right
column) show the images beamformed with 1-module, 2-module, and 4-module receive Fresnel
beamforming with gated transmit beamforming, respectively. The lateral beamwidths and axial
pulse lengths of these images are shown in Figure 5-6 and Figure 5-7, respectively.
Effects of modular Fresnel receive beamforming:
Increasing the number of Fresnel beamforming modules resulted in a noticeable
improvement in both lateral resolution (Figure 5-6a vs. Figure 5-7a) and axial resolution (Figure
5-6b vs. Figure 5-7b). For example, in the case with gated transmit beamforming, as the number
of modules in Fresnel receive beamforming increased from 1 to 4, the lateral beamwidths at 40-
degree scan angle and 50-mm depth reduced from 2.21 to 1.59 mm, a 28 % reduction and the
axial pulse lengths were shortened from 1.50 to 5.75 mm, a 74 % reduction.
In the case without gated transmit, increasing the number of Fresnel beamforming
modules had a more pronounced impact on lateral resolution than on axial resolution. For
example, going from 1-module Fresnel beamforming to 2-module Fresnel beamforming reduced
the lateral beamwidths at 40-degree scan angle from 10.2 down to 2.46 mm, a 76 % reduction
(Figure 5-6a), while it barely shortened axial pulse length from 5.59 to 5.58 mm (Figure 5-6b).
However, when the transmit beam was better focused with the gated transmit beamforming
method, increasing the number of receive channels resulted in a noticeable improvement in axial
resolution (Figure 5-7b). For example, at 30-degree scan angle, the axial resolution improved
from 4.41 mm with 1-module Fresnel beamforming to 2.36 mm and 1.20 mm with 2-module and
4-module Fresnel beamforming, respectively.
81
Effects of gated transmit beamforming:
In all cases, gated transmit beamforming improved spatial resolution. For example, as in
the case of 1-module Fresnel beamforming, the gated transmit beamforming method reduced the
lateral beamwidth by 80% at 40-degree scan angle. For a 4-module Fresnel beamforming, using
gated transmit beamforming narrowed the lateral beamwidth by 2.4%, 28.0%, and 28.4%, and
shortened the axial pulse length by 11.9%, 71%, and 74% at scan angles of 0, 20, and 40 degrees
respectively. Furthermore, the impact of increasing number of Fresnel beamforming modules on
axial resolution was also improved when the gated transmit beamforming technique was used in
conjunction (Figure 5-6b vs. Figure 5-7b).
In all cases, the performances of Fresnel beamforming and delay-and-sum beamforming
were comparable at 0-degree scan angle, with the largest discrepancies of 6.7% for lateral
beamwidths and 29.3% for axial beamwidths. However, these discrepancies increased as the
scan angle increased due to the increasing number of focal errors (Figure 5-6 and Figure 5-7).
The combination of 4-module Fresnel receive beamforming and gated transmit beamforming had
spatial resolution most comparable to that of delay-and-sum beamforming. Their differences
gradually increased from 2.3% at 0 degree scan angle to 5.9% at 40 degree scan angle for lateral
beamwidths and from 12% at 0-degree scan angle to 74% at 40-degree scan angle for axial pulse
lengths.

82

Figure 5-5: Field II simulated images of multiple point targets
83

Figure 5-6: Simulated spatial resolution at different scan angles for different beamforming methods
without gated transmit

Figure 5-7: Simulated spatial resolution at different scan angles for different beamforming methods with
gated transmit

84
5.4.2. Experimental results - spatial resolution
Figure 5-8 shows the experimental images of multi-wire phantoms with different
beamforming methods. Similar to the simulation results, the gated transmit beamforming
improved the image quality for Fresnel beamforming: Figure 5-8a vs. b and Figure 5-8c vs. d.
The wires at 50 mm depth became more visible with the implementation of gated transmit
beamforming for both 1-module and 4-module Fresnel beamforming. Increasing the number of
modules in Fresnel beamforming also improved the image quality. The wires at around 10, 20,
and 30 degree scan angles, which were unclear in the case of 1-module Fresnel beamforming,
became more distinctive in the case of 4-module Fresnel beamforming with gated transmit.
Figure 5-9 quantifies the experimental lateral beamwidths and pulse lengths at different
scan angles for different transmit and receive beamforming methods. These plots for the
experimental beamwidths are in strong agreement with those for the simulated beamwidths in
Figure 5-7. However, due to the decreasing sensitivity with large scan angles and the existing
focal errors, wires at 30 degree were not visible with 1- and 2-module Fresnel beamforming. The
combination of 4-module Fresnel receive beamforming and gated transmit beamforming was
confirmed to have spatial resolution most comparable to that of delay-and-sum beamforming.
Their differences in lateral beamwidth gradually increased from 3.6% at 0 degree scan angle to
10.4% at 30 degree scan angle. These differences in axial pulse length also increased from 2.5%
at 0 degree scan angle to 91% at 30 degree scan angle.

85

Figure 5-8: Experimental multi-wire images using different beamforming methods

Figure 5-9: Experimental spatial resolution at different scan angles for different beamforming methods
with gated transmit
86
5.4.3. Experimental results – contrast
Figure 5-10 shows the experimental cyst images with different beamforming methods:
with (left column) and without (right column) gated transmit beamforming combined with 1-
module Fresnel beamforming, 4-module Fresnel beamforming; and the gold standard delay-and-
sum beamforming (Figure 5-10e). In the case without gated transmit beamforming, only the
cysts at 0 degree scan angle were visible while the cysts at larger angles were smeared. On the
other hand, by using gated transmit, not only did the cysts at larger scan angles become visible
but also the amount of clutter inside the cysts at 0 degree scan angle was reduced. These visual
improvements were confirmed with CNR measurements shown in Figure 5-11. For 1-module
Fresnel beamforming, using gated transmit increased the CNR by 15% at 0 degree scan angle,
247% at 20 degree scan angle and 360% at 40 degree scan angle. These improvements for 4-
module Fresnel beamforming were 59%, 260%, and 300%, respectively.
Increasing the number of Fresnel beamforming modules also improved the image
contrast. For example, in the case without gated transmit beamforming, the CNR at 0 degree scan
angle improves from 2.7 with 1-module Fresnel beamforming to 2.8 with 4-module Fresnel
beamforming, or a 5% improvement. The improvement due to the increasing number of Fresnel
beamforming modules became more pronounced in the case with gated transmit beamforming,
where the CNR at 0 degree scan angle increased from 3.1 to 4.7, equivalent to a 54%
improvement. Here, 4-module Fresnel beamforming was shown to have image contrast
comparable to that of delay-and-sum beamforming. The CNRs were 4.73, 4.72, and 3.61 for 4-
module Fresnel beamforming with gated transmit at 0, 20 and 40 degree scan angle, respectively.
These CNRs for delay-and-sum beamforming were 5.03, 5.29, and 4.53.
87

Figure 5-10: Experimental cyst images using different beamforming methods

Figure 5-11: Comparison of contrast-to-noise ratios for experimental cysts at different scan angles
obtained with different beamforming methods
88
To further improve the image contrast, dual apodization with cross-correlation (DAX)
was applied on the beamformed RF data. Figure 5-12 shows the experimental cyst images using
4-module Fresnel beamforming with gated transmit beamforming and those using delay-and-sum
beamforming, without DAX (left column) and with DAX (right column). These images are
shown in 50 dB dynamic range. With DAX, the cysts appeared darker with less clutter for both
4-module Fresnel beamforming and delay-and-sum beamforming. Figure 5-13 summarizes the
CNRs for the cysts at different scan angles. For 4-module Fresnel beamforming, applying DAX
improved the CNRs from 4.73 to 11.57 at 0 degree scan angle, from 4.72 to 5.78 at 20 degree
scan angle and from 3.61 to 4.86 at 40 degree scan angle. The post-DAX CNRs for 4-module
Fresnel beamforming at 0, 20, and 40 degree scan angles were 129%, 9% and 7%, respectively,
higher than those of traditional delay-and-sum beamforming.

89

Figure 5-12: Experimental cyst images using 4-module Fresnel beamforming and delay-and-sum without
DAX (left column) and with DAX (right column)

Figure 5-13: Comparison of contrast-to-noise ratios for experimental cysts at different scan angles
obtained with 4-module Fresnel beamforming and DAS, with and without DAX.

90
5.5. Summary
This chapter introduced and evaluated two new ideas to improve the performance of
Fresnel beamforming: gated transmit beamforming and modular Fresnel receive beamforming.
Gated transmit beamforming allows the system to transmit focus with only 4 transmitters and a
set of single-pole/single-throw switches. This method can be used for any array transducer to
reduce the number of transmit channels from 64-128 down to 4. For a system using Fresnel
beamforming, implementation of this method only requires logic programming to turn the
existing set of switches on and off at the specified time. The modular Fresnel beamforming
technique helps to reduce the number of focal errors in Fresnel beamforming by dividing the
transducer elements into sub-apertures, each of which has one set of two receive channels. This
receive beamforming technique requires additional hardware implementation. For example,
while a 1-module Fresnel receive beamformer (the unmodified version) requires only 2 receive
channels, a 4-module Fresnel receive beamformer has a total of 8 receive channels. For a phased
array, the simulation and experimental results show that the performances of 4-module Fresnel
beamforming with gated transmit beamforming and of delay-and-sum beamforming are
comparable in terms of spatial resolution and image contrast.

91
Chapter 6. CONCLUSIONS AND FUTURE
WORK
6.1. Conclusions
The major purposes of this Ph.D. work were to introduce, to evaluate, and to refine a new
beamforming technique that can be a potential alternative beamforming method for low-cost,
portable ultrasound systems. An analogy of this ultrasonic beamforming method is the optical
Fresnel lens, which is most known for its use in light houses. Compared to a conventional optical
lens, a Fresnel lens is much thinner and yet possesses similar transmission ability. Similarly, with
Fresnel beamforming technique, an ultrasound system with a reduced number channel count, 4
transmit and 2 receive channels, can be used to focus an array with 64 to 128 elements. However,
reducing the number of channels in ultrasound systems comes with several benefits. First,
instead of using 64-128 channels with one analog-to-digital converter (ADC) for each channel,
the proposed Fresnel beamforming uses a total of two ADCs. Second, the number of time-gain-
compensation (TGC) circuits can also be reduced by placing the TGC circuits after the
inverting/non-inverting summing amplifiers. Third, the cost and size of connecting cable can also
be reduced due to the reduction of channel count.
The main trade-off of Fresnel beamforming is the presence of focal errors. These focal
errors result in larger beamwidths, higher clutter, and longer pulse lengths, leading to image
quality reduction. Several solutions to this limitation were proposed throughout my Ph.D. work.
The first solution is to use the novel clutter suppression method, called dual-apodization with
cross-correlation (DAX). This clutter suppression method was shown to effectively improve
92
image contrast, without compromising spatial resolution, for Fresnel beamforming. To explicate,
one weakness of Fresnel beamforming implementation is that it is difficult or impractical to
apply apodization, which is commonly used to reduce side-lobe levels. However, the two
apodizations inherent in the two receive channels of Fresnel beamforming allow DAX to be
integrated in Fresnel beamforming. Furthermore, these two apodization functions dynamically
change with different foci, resulting in a reduction of black artifacts (Nguyen and Yen 2013). In
Seo and Yen at al. (2009), these artifacts in conventional delay-and-sum beamforming were
suppressed using different pairs of apodization functions at different depths. The second solution
to the limitations of Fresnel is to utilize harmonic imaging in Fresnel beamforming to suppress
side lobes and aberration effects. This approach also effectively improves image quality in terms
of contrast and spatial resolution for Fresnel beamforming, especially in the presence of phase
aberration. Lastly, a modified version of Fresnel beamforming, modular Fresnel beamforming,
decreases the number of focal errors with the cost of increasing the number of receive channels.
Additionally, these solutions are not mutually exclusive and can all be used together to help
improve the performance of Fresnel beamforming. Also presented in this dissertation is the gated
transmit beamforming method which allows the use of 4 transmitters with a set of single-
pole/single-throw switches to achieve an ideal transmit focusing. The implementation of gated
transmit beamforming can be straightforwardly achieved in the Fresnel beamformer due to the
existing set of single-pole/single-throw switches.

93
6.2. Future Work
Figure 6-1 shows the overall schematic of the prototype for Fresnel beamforming. This
prototype will interface with the Verasonics Data Acquisition System (VDAS) to convert signals
from analog to digital and enable real-time display for the Fresnel beamformer. The printed
circuit board will contain a set of switches, connected to a complex programmable logic device
(CPLD), transmit/receive (T/R) switches, and amplifiers.

Figure 6-1: Overall design schematic for Fresnel beamforming

94
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Abstract (if available)

Abstract The contributions of this dissertation are proposing, evaluating, and refining a novel beamforming method that can reduce the size and cost of ultrasound imaging systems while providing image quality comparable to that of conventional systems. This method, called Fresnel beamforming, has a delay profile with a shape similar to a physical Fresnel lens (Figure 1-3). This method uses a unique combination of analog and digital beamforming methods. The advantage of Fresnel beamforming is that a system with 4 transmit and 2 receive channels with a network of single-pole/single-throw switches can be used to focus an array with 64 to 128 elements. The main trade-off of this method is the presence of focal errors, leading to image degradation. Several techniques are presented in this dissertation for overcoming the trade-off of Fresnel beamforming. These techniques include 1) integrating a novel side-lobe suppression method, called dual apodization with cross-correlation (DAX)

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Asset Metadata

Creator Nguyen, Man (author)

Core Title Fresnel beamforming for low-cost, portable ultrasound systems

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 08/01/2013

Defense Date 04/22/2013

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

Tag beamforming,DAX,harmonic,low-cost,OAI-PMH Harvest,phased array,ultrasound

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Yen, Jesse T. (committee chair), McNitt-Gray, Jill L. (committee member), Shung, Kirk (committee member), Zhou, Qifa (committee member)

Creator Email manmnguyen@gmail.com,mmnguyen@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-310745

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Legacy Identifier etd-NguyenMan-1926.pdf

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Document Type Dissertation

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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...

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