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Novel beamforming with dual-layer array transducers for 3-D ultrasound imaging

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Novel beamforming with dual-layer array transducers for 3-D ultrasound imaging

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Content NOVEL BEAMFORMING WITH DUAL-LAYER ARRAY TRANSDUCERS FOR 3-D ULTRASOUND IMAGING by Yuling Chen 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) May 2013 Copyright 2013 Yuling Chen ii TABLE OF CONTENTS LIST OF TABLES ......................................................................................................................... vi LIST OF FIGURES ...................................................................................................................... vii ABSTRACT .....................................................................................................................................x Chapter 1 Introduction .....................................................................................................................1 1.1 Background ................................................................................................................... 1 1.2 2-D Array transducers for 3-D Ultrasound Imaging ..................................................... 2 1.3 Motivations and objectives ........................................................................................... 4 1.4 Outline ........................................................................................................................... 6 Chapter 2 A 7.5 MHz Planar Dual-Layer Transducer Array for 3-D Rectilinear Imaging .............8 2.1 Introduction ................................................................................................................... 8 2.2 Methods....................................................................................................................... 10 2.2.1 Simulated Beamplots ................................................................................... 10 2.2.2 Design and Fabrication ................................................................................ 11 2.2.3 Data Acquisition .......................................................................................... 15 2.2.4 Beamforming, Signal Processing, and Display ............................................ 18 2.3 Experimental Results .................................................................................................. 19 2.3.1 Impedance Measurements ............................................................................ 19 2.3.2 Pulse-echo Measurements ............................................................................ 20 2.3.3 3-D Imaging – Multiwire Phantom .............................................................. 21 2.3.4 3-D Imaging – Cyst Phantom ...................................................................... 23 2.4 Conclusions and Discussions ...................................................................................... 25 iii Chapter 3 A 5 MHz Cylindrical Dual-Layer Transducer Array for 3-D Transrectal Imaging ..........................................................................................................................................28 3.1 Introduction ................................................................................................................. 28 3.2 Method ........................................................................................................................ 31 3.2.1 Simulated Beamplots ................................................................................... 31 3.2.2 Design and Fabrication ................................................................................ 32 3.2.3 Data Acquisition .......................................................................................... 36 3.2.4 Beamforming, Signal Processing, and Display ............................................ 37 3.3 Experimental Results .................................................................................................. 38 3.3.1 Impedance Measurements ............................................................................ 38 3.3.2 Pulse-echo Measurements ............................................................................ 39 3.3.3 3-D Imaging – Single Nitinol Wire ............................................................. 40 3.3.4 3-D Imaging – Multiple Nylon Wires Embedded in a Speckle Source ....... 42 3.3.5 3-D Imaging – Cyst Phantom ...................................................................... 43 3.4 Conclusions and Discussions ...................................................................................... 43 Chapter 4 Beamforming by Spatial Matched Filtering with Plane Wave Transmissions .............45 4.1 Introduction ................................................................................................................. 45 4.2 Method ........................................................................................................................ 46 4.2.1 Rayleigh-Sommerfeld diffraction analysis .................................................. 46 4.2.2 Filter size considerations for SMF beamforming ........................................ 51 4.2.3 Computer simulations .................................................................................. 55 4.2.4 Experiments with tissue-mimicking phantoms ............................................ 56 4.3 Simulation and experimental results ........................................................................... 57 4.3.1 Beam patterns from the Rayleigh-Sommerfeld diffraction analysis ............ 57 4.3.2 Simulation results......................................................................................... 59 4.3.3 Experimental results ..................................................................................... 62 iv 4.3.4 Field II simulations with filters containing noise ........................................ 65 4.4 Conclusions and discussion ........................................................................................ 66 Chapter 5 Processing on SMF beamforming using dual apodization with cross-correlation for enhanced image contrast ..........................................................................................................68 5.1 Introduction ................................................................................................................. 68 5.2 Methods....................................................................................................................... 71 5.2.1 Beamforming by spatially matched filtering (SMF) .................................... 71 5.2.2 Dual apodization with cross-correlation (DAX) .......................................... 74 5.2.3 Application of DAX to SMF beamforming ................................................. 75 5.2.4 Computer simulations .................................................................................. 76 5.2.5 Experiments with phantoms ......................................................................... 77 5.2.6 Experiments with phantoms – electronic phase aberrators .......................... 78 5.3 Simulations and experimental results ......................................................................... 78 5.3.1 Computer simulations of anechoic cysts ...................................................... 78 5.3.2 Experiments of anechoic cysts – without phase aberrations ........................ 80 5.3.3 Experiments of anechoic cysts – with phase aberrations ............................. 82 5.4 Conclusions ................................................................................................................. 84 Chapter 6 Conclusions and Future work ........................................................................................85 6.1 Conclusions ................................................................................................................. 85 6.2 Future work ................................................................................................................. 86 Bibliography ..................................................................................................................................90 Appendix A: Program for data acquisition with VDAS in Matlab ................................................94 Appendix B: DAS beamforming with dual-layer transducers in Matlab ......................................95 Appendix C: Program for implementing Rayleigh-Sommerfeld analysis in Matlab ..................101 v Appendix D: SMF beamforming with PWT in Matlab ...............................................................104 Appendix E: SMF beamforming with DAX applied in Matlab ...................................................106 vi LIST OF TABLES Table 1: Comparison of CNR of volumes before and after GCF processing ............................... 24 Table 2: -6 dB beamwidth and off-axis energy of SMF beamforming with different filter sizes. 53 Table 3: CNR values for simulated images containing a 6 mm diameter anechoic cyst using DAS, PWT+rDAS and PWT+SMF. ............................................................................................. 62 Table 4: CNR values for experimental images containing anechoic cysts of 4 mm diameter and 6 mm diameter using DAS, PWT+rDAS and PWT+SMF. ............................................................ 64 Table 5: Comparison between real-time 3-D systems using fully sampled 2-D arrays and systems using dual-layer arrays with SMF beamforming implemented. ................................................... 89 vii LIST OF FIGURES Figure 1-1: Schematic of 2-D array transducers: (a) 2-D sectored phased array, (b) 2-D linear sequential array, and (c) 2-D curvilinear array. .............................................................................. 3 Figure 2-1: Simulated beamplots of the dual-layer transducer (Chen, Nguyen, & Yen, 2011) ... 12 Figure 2-2: Acoustic stack of the dual-layer transducer array ...................................................... 13 Figure 2-3: Photo of the prototype dual-layer transducer ............................................................. 15 Figure 2-4: Schematic of transmit and receive elements grouping ............................................... 17 Figure 2-5: Schematic of system configuration for data acquisition with VDAS ........................ 18 Figure 2-6: Simulated and experimental impedance measurements of PZT and P[VDF-TrFE] layers ............................................................................................................................................. 20 Figure 2-7: Simulated and experimental pulse and spectra of the dual-layer transducer ............. 21 Figure 2-8: Experimental images of multi-wire with a dynamic range of 25 dB ......................... 22 Figure 2-9: Azimuthal and elevational lateral wire target responses ............................................ 22 Figure 2-10: Experimental images of cyst phantom without GCF applied .................................. 24 Figure 2-11: Experimental images of cyst phantom with GCF applied ....................................... 25 Figure 3-1: 2-D cylindrical array for 3-D TRUS. ......................................................................... 31 Figure 3-2: Simulated beamplots of the cylindrical dual-layer transducer ................................... 32 Figure 3-3: Acoustic stack of the cylindrical dual-layer transducer array .................................... 34 Figure 3-4: Photo of the prototype cylindrical dual-layer transducer ........................................... 35 Figure 3-5: Simulated and experimental impedance measurements of PZT and P[VDF-TrFE] layers ............................................................................................................................................. 38 viii Figure 3-6: Simulated and experimental pulses and spectrum of the cylindrical dual-layer transducer ...................................................................................................................................... 39 Figure 3-7: Experimental images of single nitinol wire with a dynamic range of 25 dB ............. 41 Figure 3-8: Transverse and longitudinal lateral wire target responses ......................................... 41 Figure 3-9: Experimental images of multiple nylon wires with a dynamic range of 35 dB ......... 42 Figure 3-10: Experimental images of cyst phantom with GCF applied ....................................... 43 Figure 4-1: Geometry of a 1-D linear array transducer and the coordinate system used in the Rayleigh-Sommerfeld diffraction analysis. .................................................................................. 47 Figure 4-2: Comparisons of mainlobes between standard DAS beamforming and SMF beamforming using filters with (a) 90% of total energy, (b) 80% of total energy, (c) 70% of total energy, and (d) 60% of total energy. ............................................................................................. 52 Figure 4-3: Beam patterns of standard DAS beamforming and SMF beamforming using filters with (a) 90% of total energy, (b) 80% of total energy, (c) 70% of total energy, and (d) 60% of total energy. ................................................................................................................................... 54 Figure 4-4: Transmit-receive beam patterns of the Rayleigh-Sommerfeld analysis for DAS, PWT+rDAS and PWT+SMF at the depth of (a) 20 mm and (b) 40 mm. ..................................... 57 Figure 4-5: Simulation transmit-receive beam patterns of Field II for DAS, PWT+rDAS and PWT+SMF of a point reflector located at (a) 20 mm depth, and (b) 40 mm depth. .................... 59 Figure 4-6: Images with an anechoic cyst of 6 mm in diameter at different depths from Field II simulations of different beamforming methods: (a) cyst at 20 mm depth with DAS, (b) cyst at 20 mm depth with PWT+rDAS, (c) cyst at 20 mm depth of PWT+SMF, (d) cyst at 40 mm depth with DAS, (e) cyst at 40 mm depth with PWT+rDAS, (f) cyst at 40 mm depth with PWT+SMF. ....................................................................................................................................................... 60 Figure 4-7: Experimental transmit-receive beam patterns for DAS, PWT+rDAS and PWT+SMF of a point reflector located at (a) 20 mm depth and (b) 40 mm depth. ......................................... 62 Figure 4-8: Images with anechoic cysts of 4 mm diameter and 6 mm diameter at different depths from experiments of different beamforming methods: (a) cysts at 20 mm depth with DAS, (b) cysts at 20 mm depth with PWT+rDAS, (c) cysts at 20 mm depth of PWT+SMF, (d) cysts at 40 mm depth with DAS, (e) cysts at 40 mm depth with PWT+rDAS, (f) cysts at 40 mm depth with PWT+SMF. ................................................................................................................................... 63 Figure 4-9: Images with an anechoic cyst of 6 mm in diameter at 40 mm depth from Field II simulations of different beamforming methods: (a) DAS, (b) PWT+SMF with noise-free filters, and (c) PWT+SMF with filters containing noise (SNR = 40 dB). ............................................... 65 ix Figure 5-1: Images containing a 4 mm diameter anechoic cyst from Field II simulations. RF data is processed using standard DAS (“DAS” column), DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). Cysts are located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. The transmit focus for all cases is set to 30 mm depth. ............................ 79 Figure 5-2: Images containing an anechoic cyst of 4 mm diameter, along with their CNR values, from experiments with VDAS. Data is processed using standard DAS (“DAS” column), DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). Cysts are located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. The transmit focal depth is 30 mm for all cases. ...................................................................................................................... 81 Figure 5-3: Images containing an anechoic cyst of 4 mm diameter from experiments with VDAS. A 45 ns rms, 5 mm FWHM aberrator profile is added to the experimental data. Figures are constructed from processing the signals using standard DAS (“DAS” column), DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). Cysts are located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. The transmit focus is set to 30 mm for all cases. ............................................................................................................................................. 83 x ABSTRACT The difficulties associated with fabrication and interconnection have limited the development of 2-D ultrasound array transducers with a large number of elements (>9000). The dual-layer array design provides an alternative solution to the problem by substantially reducing the fabrication complexity as well as the channel count, making 3-D ultrasound imaging more realizable. This dissertation presents the design, fabrication, tests and imaging experiments of two dual-layer array transducers for different 3-D ultrasound applications. One is a planar transducer for 3-D rectilinear imaging, which has a -6 dB fractional bandwidth of 71% with a center frequency of 7.5 MHz. The measured lateral beamwidths are 0.521 mm and 0.482 mm in azimuth and elevation, respectively, compared with a simulated beamwidth of 0.43 mm. The other one is a cylindrical transducer for 3-D transrectal imaging, with a center frequency of 5.7 MHz and a -6 dB fractional bandwidth of 62%. The measured lateral beamwidths are 1.28 mm and 0.91 mm in transverse and longitudinal directions, whereas simulated beamwidths in these directions are 0.92 mm and 0.74 mm. For both transducers, 3-D synthetic aperture data sets were acquired by interfacing them with a Verasonics Data Acquisition System (VDAS). Offline beamforming was performed using the conventional delay-and-sum (DAS) beamforming method to obtain volumes of wire phantoms and cyst phantoms, which were used for spatial resolution and image contrast evaluation. Generalized coherence factor (GCF) was applied to the beamformed data to improve the contrast of cyst images. Preliminary real-time volumetric data acquisition was realized with the planar dual-layer array. xi The nature of the dual-layer design determines that there is only one-way focusing can be achieved in each of the azimuth and elevation directions, which indicate the directions of the transmit array and receive array respectively. For instance, in the elevation direction of the dual- layer design, transmit pulses emitted from the elongated elements are unfocused, plane wave pulses. Image quality is consequently worse compared to fully-sampled 2-D arrays, which are capable of two-way, or transmit-receive, focusing in both lateral directions. A novel beamforming method by spatially matched filtering (SMF) the echo signals was investigated in this dissertation to compensate for the degradation of image quality. With plane wave pulses used on transmit, the validity of SMF beamforming was demonstrated by analysis based on the Rayleigh-Sommerfeld diffraction theory. The performance of SMF beamforming was evaluated by spatial resolution and contrast of images beamformed from both computer simulations and experimentally acquired data with a one-dimension (1-D) linear array transducer. Simulation results showed a -6 dB beamwidth of 0.63 mm and an image contrast-to-noise ratio (CNR) of 5.34 with SMF beamforming, comparing to those of dynamic receive DAS beamforming, which were 0.74 mm and 2.00. In experiments, SMF beamforming gave a -6 dB beamwidth of 0.66 mm and an image CNR of 3.81. Experimental measurements of these values with dynamic receive DAS beamforming were 0.83 mm and 2.29 respectively. Furthermore, dual apodization with cross-correlation (DAX) was implemented on SMF beamforming to improve image contrast. The performance of the method was evaluated using both computer simulations and experiments. With a single transmit focus, DAX increased the CNR of anechoic cyst images of SMF beamforming at all depths without introducing any artifacts that might arise in the DAX- processed images using DAS beamforming. 1 Chapter 1 Introduction 1.1 Background The discovery of piezoelectricity by the Curie brothers in 1880 and the invention of the triode amplifier tube by Lee De Forest in 1907 set the stage for medical ultrasound imaging (Szabo, 2004). After decades of years of development, ultrasound imaging has become one of the most utilized imaging modalities. The widespread clinical use of ultrasound imaging is due to the unique characteristics of ultrasound and ultrasound imaging methods, including safety with non-ionizing radiation, non-invasive procedures, real-time scanning, good image qualities, portability and low cost. There are limitations of 2-D viewing of 3-D human anatomy using conventional ultrasound imaging, during which a 1-D ultrasound transducer is manipulated to acquire a series of 2-D ultrasound images (Fenster, Downey, & Cardinal, 2001). These 2-D images are translated mentally by the operators to form a subjective impression of the 3-D anatomy. Besides being time-consuming and inefficient, this procedure is also subjective and variable, thus leading to incorrect diagnoses. The success of diagnostic or interventional procedure using conventional ultrasound imaging is highly dependent on the skills and experience of the operators. In addition, some views or angles, such as the cross-sectional scans (C-scans) that are parallel to the transducer surface, are not available in conventional ultrasound imaging because 2 of restrictions imposed by the patient’s anatomy or position. Conventional 2-D ultrasound also provides low accuracy in estimating organ or tumor volumes, which are often required in some clinical decisions. In order to overcome these limitations, 3-D ultrasound was first demonstrated in the 1970s, and is rapidly achieving widespread use with numerous applications (Fenster et al., 2001). 3-D ultrasound is most commonly implemented in three ways: mechanical scanning, free-hand scanning, and scanning using 2-D array transducers. Both mechanical scanning and free-hand scanning use 1-D transducers to acquire series of 2-D images, and combine the images into a 3-D volume based on the predefined scanning protocol or the measurements of transducer movements. These two approaches are relatively slow, user-dependent and unreliable. A 2-D array transducer, for which the elements are distributed in two perpendicular directions, could remain stationary and sweep the ultrasound beams over the entire volume by electronic scanning during 3-D imaging. This approach is user-independent, reliable, and capable of real-time 3-D imaging. 1.2 2-D Array transducers for 3-D Ultrasound Imaging Real-time 3-D volumetric ultrasound was first developed by von Ramm and Smith specifically for cardiac imaging in the early 1990s at Duke University (Von Ramm & Smith, 1990). The system was capable of employing a 2-D sectored phased array to scan in both azimuth and elevation. A pyramidal volume of data was acquired without mechanical translation or reconstruction (Figure 1-1 (a)). Other types of 2-D array transducers were also developed at 3 Duke University. Analogous to 1-D linear sequential arrays, 2-D array transducers capable of 3- D rectilinear imaging, enabling visualization of structures close to the transducer surface, could be constructed by stepping sub-apertures of elements in two perpendicular directions as shown in Figure 1-1 (b) (Yen & Smith, 2002a). A spherical curvilinear array (Figure 1-1 (c)) and a cylindrical curvilinear array (Pua, Yen, & Smith, 2003) were also developed by extending 1-D curvilinear arrays into two dimensions. In addition, real-time 3-D ultrasound imaging has been extended to intracardiac applications by developing 2-D array transducers at the tip of a catheter at Duke University (Light, Idriss, Wolf, & Smith, 2001). Matrix array transducers within catheters in both forward viewing and side scanning configurations were developed to visualize cardiac structures of interest. Figure 1-1: Schematic of 2-D array transducers: (a) 2-D sectored phased array, (b) 2-D linear sequential array, and (c) 2-D curvilinear array. The techniques of capacitive micromachined ultrasonic transducers (CMUTs) are another option for building 2-D transducers for 3-D imaging. The low sensitivity issue due to the 4 mismatch between the impedance of the small-sized crystal elements and the characteristic impedance of connecting cables does not arise in CMUTs. In addition, since CMUTs can be fabricated into arrays with integrated electronics, they could be relatively inexpensive if manufactured in large quantities. Researchers at Stanford University have been investigating in this area (Oralkan et al., 2003), and produce a 16×16 array, flip-chip bonded to a custom driver integrated circuit (Wygant et al., 2008). Commercial 2-D array transducers are being investigated in parallel with academic research. Phillips is currently offering a range of phased-array probes, operating at frequencies from 1 MHz and 7 MHz, with up to 9,212 fully connected elements. Siemens has been working with University of Wisconsin-Madison to exploit the improved bandwidth of their prototype CMUT-based 3-D probe for tissue characterization (Liu et al., 2008). 1.3 Motivations and objectives There are three major challenges during the development of 2-D array transducers for real-time 3-D ultrasound imaging (Smith et al., 2002): the requirement of large amount of active transducer elements, the severe fabrication difficulties in electronic connections, and the low transducer sensitivity because of the impedance mismatch between elements and scanner systems. The dual-layer design provides an alternative solution regarding these challenges. Instead of N 2 active elements as in fully-sampled 2-D transducers (typical value for N is 128 or 256), only 2×N elements are needed to construct a dual-layer array transducer, assigning N for 5 transmit and N for receive. As a result, the fabrication complexity and channel count are remarkably reduced for dual-layer transducers, making 3-D ultrasound imaging more feasible. Additionally, the dual-layer configuration also enables optimization of materials separately for different layers and also isolate transmit and receive electronics. The nature of the dual-layer design determines that only one-way focusing can be achieved in the azimuth direction or elevation direction of 3-D imaging with conventional delay- and-sum (DAS) beamforming. For instance, in the elevation direction of the dual-layer design, transmit pulses emitted from the elongated elements are unfocused, plane wave pulses. This will lead to worse image quality compared to two-way (transmit-receive) focusing in terms of both degraded spatial resolution and image contrast. Different beamforming techniques, which can compensate for the degradation of image quality without significantly reducing frame-rate or signal-to-noise ratio (SNR) of the system, are needed. Beamforming by spatial matched filtering (SMF) is capable of achieving both transmit and receive focusing uniformly throughout field of view. Inspired by this, I present the first studies using SMF beamforming to achieve two-way focusing, consequently improving image resolution and contrast, with plane wave transmissions (PWT). Because the elevation direction of dual-layer 3-D imaging resembles the case of a 1-D linear array with plane wave transmissions, it is reasonable to test the feasibility of SMF beamforming using 1-D linear array as an initial step towards the final implementation of SMF to dual-layer array transducers. Therefore, the work with SMF beamforming presented in this dissertation was accomplished using 1-D linear arrays. The ultimate objective of this dissertation is to have a real-time 3-D imaging system with similar image quality compared to a system with 6 a fully-sampled 2-D array, using a more practical transducer design combined with novel beamforming techniques. 1.4 Outline The dissertation is outlined as follows: Chapter 1 gives introductory remarks of my research work. Chapter 2 describes the design, fabrication, tests and imaging experiments of a 7.5 MHz planar dual-layer array for 3-D rectilinear imaging. Experimental measurements and data acquisition were performed on a 4×4 cm 2 prototype. Off-line DAS beamforming was used to construct volumetric images of a multi-wire phantom and an anechoic cyst phantom. The generalized coherence factor (GCF) was applied to enhance image contrast. Preliminary real- time 3-D imaging was also realized with this planar dual-layer transducer. Chapter 3 presents the design and fabrication procedure of a 5 MHz cylindrical dual-layer array transducer for 3-D transrectal imaging. Similar measurements and imaging experiments as described in chapter 2 were performed with the cylindrical array transducer. GCF was used for contrast improvement as well. Chapter 4 proposes the application of the novel SMF beamforming with plane wave transmissions. This condition resembles the dual-layer array imaging in elevation during which plane wave pulses are emitted from the elongated transmit elements. Plane wave transmissions also enable high frame-rate imaging. The validity of SMF beamforming was predicted using the 7 Rayleigh-Sommerfeld diffraction theory and evaluated by spatial resolution and contrast of images constructed. The performance of SMF beamforming was compared to conventional DAS methods in both simulations and experiments. Chapter 5 further improves the performance of SMF beamforming by using dual apodization cross-correlation (DAX). With fixed transmit focusing as in conventional imaging systems, implementation of DAX with SMF beamforming was able to increase the contrast-to- noise ratio (CNR) of images containing anechoic cysts without introducing artifacts almost throughout field of view. The performance of this method was evaluated with both computer simulations and experimental data. Electronic phase aberrations were added in to the receive signals to test the robustness of SMF beamforming with DAX applied. Chapter 6 summarizes the work of this dissertation and discusses the future research. 8 Chapter 2 A 7.5 MHz Planar Dual-Layer Transducer Array for 3- D Rectilinear Imaging 2.1 Introduction A real-time rectilinear volumetric scan can provide a wide field of view close to the transducer surface. Therefore, it is useful for abdominal, breast and vascular imaging. There are several clinical applications of 3-D rectilinear ultrasound imaging at present. Chiu et al reported their analysis of carotid lumen surface morphology using 3-D ultrasound imaging (Chiu, Beletsky, Spence, Parraga, & Fenster, 2009). Krasinski et al evaluated 3-D ultrasound-derived vessel wall volume (VWV), which is a 3-D measurement of the carotid artery intima and media (Krasinski, Chiu, Spence, Fenster, & Parraga, 2009). Yagel et al reviewed 3-D/4-D ultrasound applications in fetal medicine (Yagel, Cohen, Messing, & Valsky, 2009). Compared to mechanical scanners and free-hand scanners, solid-state 2-D array transducers do not require the motion parts for 3-D scanning, making the imaging procedures fast, user independent and reliable. However, due to the difficulties in fabricating the high densely populated arrays and providing individual electrical connections to each element, most of the 2-D arrays have less than 10,000 elements and operate at frequencies lower than 6 MHz. Light et al. presented catheter-based 2-D transducer arrays operating at frequencies up to 10 9 MHz with small amount of elements for intravascular imaging (Light & Smith, 2003). In addition, there are also challenges in acquiring and processing data from a large number of channels. Sparse arrays were designed for 3-D rectilinear imaging focused on suppressing clutter (Yen & Smith, 2002a)(Yen & Smith, 2002b)(Yen & Smith, 2004). Other potential solutions include a crossed-electrode scheme using a hemispherically shaped array to scan a pyramidal volume (Morton & Lockwood, 2003) and a row-column addressing technique to simplify interconnections of a 4 × 4 cm 2 2-D transducer array (Seo & Yen, 2007). Dual-layer or multilayer transducers have been proposed for diagnostic applications. Merks et al measured the bladder volume on the basis of nonlinear ultrasound wave propagation using a multilayer transducer, which was constructed by bonding PVDF film onto a commercially available, single-elements PZT transducer (Merks et al., 2006). Saitoh et al simultaneously obtained a B-mode images and a Doppler mode image from a dual frequency probe using a multilayer ceramic (Saitoh, Izumi, & Mine, 1995). Hossack et al achieved high bandwidth at the fundamental transmitted frequency and simultaneously achieved high bandwidth at the harmonic frequency during the receive operation based on using a dual layer transducer system (Hossack, Mauchamps, & Ratsimandresys, 2000). Yen previously proposed a 5 MHz dual-layer transducer for 3-D imaging (Yen, Seo, Awad, & Jeong, 2009). This transducer contained one PZT layer for transmit and one separate P[VDF-TrFE] copolymer layer, closer to the targets, for receive. Each layer was a 1-D square-shaped array composed of 256 parallel elongated elements. The layers were oriented with transmit and receive elements perpendicular to each other. By moving the locations of selected transmit and receive sub- apertures in two perpendicular directions respectively, a rectilinear volume is scanned. This 10 design can be viewed as an array with multiple Mills cross arrays (Yen & Smith, 2002a). The dual-layer configuration also enabled optimization of materials separately for different layers and also isolate transmit and receive electronics. This chapter describes the design, fabrication, test, and imaging experiments of a 7.5 MHz dual-layer transducer with 256 PZT elements and 256 P[VDF-TrFE] copolymer elements, since higher frequencies (> 5 MHz) are more commonly used in clinical applications or imaging targets near transducers, such as the breast, carotid and musculoskeletal tissue. As another realization of the aforementioned dual-layer method, this transducer used a thinner layer of PZT, 125 µm, which required a re-design of the acoustic stack, and refinement of the fabrication process. A 4 × 4 cm 2 prototype was developed to demonstrate the feasibility of the transducer. The generalized coherence factor (GCF) (Li & Li, 2003) was also applied to improve the image quality furthermore. The ultimate goal is to have a system with image quality comparable to a system with a fully-sampled 2-D array, using a more practical transducer design combines with suitable signal processing algorithms. 2.2 Methods 2.2.1 Simulated Beamplots To evaluate the theoretical imaging performance, simulated beamplots were acquired using Field II (Jensen & Svendsen, 1992). The transmit aperture was a 1-D array with an azimuthal element pitch of 150 µm and an elevational height of 38.4 mm. The receive aperture 11 had an elevational element pitch of 150 µm and an azimuthal length of 38.4 mm. A Gaussian pulse with a center frequency of 7.5 MHz and 50% fractional bandwidth was used. For the beamplot, a 128-element sub-aperture was used in both transmit and receive and focused on-axis to (x,y,z) = (0,0,30) mm. Figure 2-1 shows the simulated beamplots of the dual-layer transducer. The lines in Figure 1B are at -10, -20, -30, -40, and -50 dB. The −6 dB beamwidth is 0.43 mm, and the highest clutter levels, around −30 to −40 dB, are seen along the azimuth and elevation axes. The clutter levels drop off dramatically in regions away from the principal azimuth and elevation axes. 2.2.2 Design and Fabrication Figure 2-2 shows the acoustic stack of the dual-layer transducer array schematically. A backing with acoustic impedance of 13 MRayls was used to minimize reverberation between different layers. This backing was produced using 85% tungsten powder (Atlantic Equipment Engineers, Bergenfield, NJ) and 15% Epo-Tek 301 epoxy (Epoxy Technology, Billerica, MA), by weight. 85% of the tungsten particles were of 10 µm diameter, while the remaining 15% were of 1 µm. The mixture was then centrifuged at 3000 revolutions per minute (rpm) in a Beckman- Coulter Allegra 6 centrifuge (Fullerton, CA). After lapping, one side of the backing was sputtered with 500 angstroms of chrome and 1000 angstroms of gold to provide a ground plane for all PZT elements. 12 Figure 2-1: Simulated beamplots of the dual-layer transducer (Chen, Nguyen, & Yen, 2011) A 40 x 40 mm 2 active area size was chosen by considering the typical field of view used in clinical settings. I also chose a pitch of 150 µm for the array to keep the elements spaced less than one wavelength to avoid grating lobes. As a result, each layer had 256 elements. A 40 x 40 mm 2 wafer of gold-plated 300 µm thick PZT-5H was bonded to the sputtered surface of the backing. A DAD321 automatic dicing saw (DISCO Corporation, Tokyo, Japan) with a 28 µm width diamond blade (DISCO Corporation, Tokyo, Japan) was first used to dice the PZT wafer into 256 elongated posts at a 150 µm pitch. These first cuts were filled with Epo-Tek 301 epoxy. 13 After curing at room temperature in a dry environment for 48 hours, PZT along with the excess epoxy was lapped down to the desired thickness of 125µm and sputtered with chrome/gold electrode on top. A second set of cuts was made by aligning the dicing saw to the center of the ceramic posts created by the first set. All cuts were made through the PZT piece and about 50 µm into the backing. After the second dicing process, I created the elements for a 2-2 composite array with a ceramic volume fraction around 70%. This sub-dicing strategy was used to reduce the width-to-height ratio of ceramic posts to around 0.32, which exceeded the requirement for low lateral coupling (McKeighen, 1998). Without sub-dicing, the determined transducer specifications would make the width-to-height ratio close to 1, which would translate to high lateral coupling. Figure 2-2: Acoustic stack of the dual-layer transducer array 14 A prototype 25 µm thick flexible circuit (Microconnex, Snoqualmie, WA, Flex 1 in Figure 2-2) was then bonded to one edge of the PZT array using nonconductive epoxy, with fine alignment between PZT elements and copper traces of the flex to create electrical connections. The flexible circuits were made of 25 µm thick polyimide with 4 µm thick copper traces printed on one side. A 40 x 40 mm 2 sheet of P[VDF-TrFE] copolymer, which had been poled and metalized with Cr/Au on the negative side by manufacturer, was bonded to the other flexible circuit (Flex 2 in Figure 2-2), identical to Flex 1, on the positive, un-metalized side. Both the Cr/Au layer and the copper traces on Flex 2 will serve as electrodes for the copolymer elements. A single P[VDF-TrFE] copolymer element was 75 µm wide and 40 mm long, defined by the copper traces. This copolymer/flex module was then bonded to the top of the PZT so that the PZT and copolymer elements were perpendicular to each other. A 3 µm thick parylene layer was sputtered on PZT to electrically isolate the elements of the two layers. The copolymer combines with the two flex circuits to serve as a simple matching layer for the PZT transmit layer, which possesses an acoustic impedance of around 4 MRayls and a total thickness of 75 µm. This matching layer was not diced, and could possibly reduce angular response of the PZT elements. However, since I was not doing steering during data acquisition at the present stage, the degradation of angular response would not affect the performance of the transducer significantly. In all bonding steps, the applied pressure was approximately 100 psi, which assured a thin enough bonding thickness to achieve electrical contact. The array was finally sealed with non- conductive epoxy to be protected from moisture and possible physical damage. 15 Samtec connectors (Samtec USA, New Albany, IN) were soldered onto both flexes to serve as the interface between the transducer and printed circuit boards. A photo of the finished prototype transducer is shown in Figure 2-3. Figure 2-3: Photo of the prototype dual-layer transducer 2.2.3 Data Acquisition After performing electrical impedance and pulse-echo measurements, the dual-layer transducer array was interfaced with a 4-board Verasonics data acquisition system, VDAS (Verasonics, Redmond, WA) using custom-printed circuit boards. This system allows users to control imaging parameters such as aperture size, transmit frequency, filtering, and time-gain 16 compensation. The VDAS provides 256 transmit channels and 128 receive channels, which reduces the time length of data collection, to less than 2 hours, and the complexity of operation significantly. Figure 2-4 and Figure 2-5 shows a schematic of transmit and receive elements grouping for synthetic data acquisition and a schematic of system configuration with VDAS, respectively. During acquisition, each of the TX1 elements were connected to 128 individual channels of the VDAS configured to operate in transmit mode, while RX1 elements were connected to the remaining 128 system channels in receive mode. Data from each receive channel was collected 100 times with a 36 MHz sampling frequency, and averaged to minimize the effects of random noise. Next, the RX2 group was connected manually to the same set of receive channels, completing collection from all 256 receive element. The above process was repeated for TX2 group, and all transmit/receive element combinations were acquired. Real-time data acquisition was realized through programming the event sequences with VDAS. A 64-element sub-aperture of PZT layer was used for transmit focusing at a desired depth in each event, and data from all receive channels was collected. 129 transmit events covered the whole aperture by moving the sub-aperture across the array, and created one image volume. This procedure was repeated for different data volumes with a volume rate set as 30 vol/sec. 17 Figure 2-4: Schematic of transmit and receive elements grouping I acquired 3-D volumetric data of a home-made 70 x 70 x 70 mm 3 gelatin phantom containing 5 pairs of 100 µm diameter nitinol wire targets with axial separation of 0.5, 1, 2, 3, and 4 mm, to evaluate the spatial resolution. The bottom wire in each pair was laterally shifted by 1 mm with respect to the top wire. This background material of the wire phantom consisted of 400 g deionized (DI) water, 36.79 g n-propanol, 0.238 g formaldehyde, and 24.02 g gelatin. These ingredients and quantities were based on published recipes (Hall, Bilgen, Insana, & Krouskop, 1997). The second phantom had an 8 mm diameter cylindrical anechoic cyst located 18 at a depth of 30 mm from the transducer face. The background of this cyst used the same ingredients as the wire target phantom plus 3.89 g of graphite powder to provide scattering. Figure 2-5: Schematic of system configuration for data acquisition with VDAS 2.2.4 Beamforming, Signal Processing, and Display The acquired data was imported into Matlab (Mathworks, Natick, MA) for offline 3-D delay-and-sum (DAS) beamforming, signal processing, and image display. RF data was filtered with a 64-tap FIR bandpass filter with frequency range of 4.8 - 10 MHz. Then beamforming with dynamic transmit and receive focusing of 1 mm increments was done with a constant sub- aperture size of 128 elements, or 19.2 mm. A 3-D volume was acquired by selecting the appropriate transmit sub-apertures in azimuth and receive sub-apertures in elevation to focus a 19 beam directly ahead. The dimensions of the acquired volume were 38.4 (azimuth) x 38.4 (elevation) x 44.5 (axial) mm 3 . The generalized coherence factor (GCF) was calculated and used as weighting factor for the reconstructed images of the cyst phantom to improve contrast of the images. After 3-D beamforming, envelope detection was done using Hilbert transform. Images were then log-compressed and displayed with proper dynamic ranges. Azimuth and elevation B- scans are displayed along with C-scans which are parallel to the transducer face. Movies were made out of real-time acquired data to show motions of phantoms. 2.3 Experimental Results 2.3.1 Impedance Measurements Experimental electrical impedance measurements of the transducer were taken using an Agilent 4294A impedance analyzer (Santa Clara, CA). Figure 2-6 shows the electrical impedance results of both layers by simulation using 1-D KLM modeling software (PiezoCAD, Sonic Concepts, Woodinville, WA) (Krimholtz, Leedom, & Matthaei, 1970), and by experiments. For PZT, the simulated impedance magnitude was 20 Ω at a series resonance frequency of 11.5 MHz while the experimental impedance curve showed a series resonance of 45 Ω at 11.4 MHz. The phase plots peak at 15.4 MHz for the KLM simulation and at 14.8 MHz in the experimental case. For P[VDF-TrFE] copolymer, the impedance magnitude was 806 Ω at 11.4 MHz in simulation, and the measured impedance magnitude was 1.11 kΩ. No resonance peaks are seen in the impedance magnitudes, and the phase remains near 83° to 86°. 20 Figure 2-6: Simulated and experimental impedance measurements of PZT and P[VDF-TrFE] layers 2.3.2 Pulse-echo Measurements Pulse-echo measurements of the transducer were made in a water tank using a Panametrics 5900PR pulser/receiver (Waltham, MA) with an aluminum plate reflector. To mimic imaging conditions, the excitation pulse was applied to a PZT element and a copolymer element was used as the receiver. Figure 2-7 shows the simulated and experimental time and frequency responses of the pulse-echo signals. In simulation, the center frequency was 8.8 MHz with a -6 dB fractional bandwidth of 53%, compared to a 7.5 MHz center frequency with a -6 dB 0 5 10 15 20 0 50 100 150 Frequency (MHz) Magnitude (Ohms) A. PZT Impedance Magnitude 0 5 10 15 20 -100 -50 0 50 B. PZT Impedance Phase Frequency (MHz) Phase (Degrees) 0 5 10 15 20 0 1 2 3 4 5 C. P[VDF-TrFE] Impedance Magnitude Frequency (MHz) Magnitude (kOhms) 0 5 10 15 20 -80 -60 -40 -20 0 D. P[VDF-TrFE] Impedance Phase Frequency (MHz) Phase (degrees) Experimental KLM Experimental KLM Experimental KLM Experimental KLM 21 fractional bandwidth of 71% in experiment. Low amplitude reverberations after the pulse peak are seen in both the simulation and experimental pulses in the time domain. Figure 2-7: Simulated and experimental pulse and spectra of the dual-layer transducer 2.3.3 3-D Imaging – Multiwire Phantom Figure 2-8 (a)-(c) show the azimuth B-scan, elevation B-scan, and C-scan respectively when the short axes of wire targets were in elevation. The azimuth B-scan (Figure 2-8 (a)) shows the pair of wires with 0.5 mm axial separation, and the two wires are discernible. The C- scan, taken at a depth of 35 mm, is parallel to the transducer face. Figure 2-8 (d)-(f) show images of the same phantom with short axis of wire targets in azimuth. The pair of wires with 0.5 mm axial separation is also discernible in the elevation B-scan shown in Figure 2-8 (e). Figure 2-8 (f) shows a C-scan which has been tilted to encompass the entire length of the wires, when the wires are not perfectly parallel to the transducer face because of mechanical 22 positioning. All images shown in Figure 2-8 are log-compressed and shown on a 25 dB dynamic range. Figure 2-8: Experimental images of multi-wire with a dynamic range of 25 dB Figure 2-9: Azimuthal and elevational lateral wire target responses 23 Solid curves in Figure 2-9 show the experimental radiation patterns in azimuth (Figure 2-9A) and in elevation (Figure 2-9B). In both cases, the wire closest to the transducer was used for measurement. The -6 dB beamwidth in azimuth was 0.521 mm and 0.482 mm in elevation compared to a simulated beamwidth of 0.43 mm in both directions represented by the dashed curves based on Field II. Sidelobes above -15 dB and some clutter around -20 dB were present in both figures, and more severe clutter was observed in azimuth than in elevation. 2.3.4 3-D Imaging – Cyst Phantom Figure 2-10, as control, contains volumetric images of a phantom with an 8 mm diameter cylindrical cyst at 30 mm depth without GCF processing. GCF was derived from the spatial spectrum of the properly delayed data and applied on a voxel by voxel basis. Figure 2-11 presents the same group of images as in Figure 2-10 with GCF applied. In both figures, (a)-(c) show the azimuth B-scan, elevation B-scan and C-scan with the short axis of the cyst in elevation, (d)-(f) show the two perpendicular B-scans and the C-scan with short axis of the cyst in azimuth, and(g)-(i) show the scan images with the cyst being positioned diagonally above the transducer surface. All images are log-compressed and shown with 50 dB dynamic range. Comparison of contrast-to-noise (CNR) ratio of volumes before and after GCF processing is listed in Table 1. Improved image contrast was achieved by applying GCF according to the CNR values. 24 Figure 2-10: Experimental images of cyst phantom without GCF applied Table 1: Comparison of CNR of volumes before and after GCF processing Cyst orientation CNR without GCF CNR with GCF Short axis in elevation 1.84 3.47 Short axis in azimuth 1.72 2.36 Diagonal 1.44 1.76 25 Figure 2-11: Experimental images of cyst phantom with GCF applied 2.4 Conclusions and Discussions In this chapter, I described the design, fabrication, test and imaging of a 7.5 MHz frequency dual-layer transducer array using PZT and P[VDF-TrFE] copolymer for transmit and receive, respectively. Compared to the initial 5 MHz transducer, fabrication of higher frequency 26 dual-layer transducers requires a new design and additional fabrication steps. Design constrains such as element aspect ratio and number of elements became more stringent as the frequency increases. I addressed these considerations in this work and described methods to design these types of transducers for 7.5 MHz. Experimental measurements of the transducer showed good agreement with simulation results. By imaging the multi-wire phantom, lateral resolution was improved due to a higher center frequency. In order to improve image quality further, I applied GCF on the cyst phantom images which contained speckles from scatterers in the background. The contrast of the images was enhanced after being GCF processed. By combining GCF with a higher center frequency dual-layer transducer, I achieved better image quality in terms of resolution and contrast. Figure 2-9 shows that clutter levels were higher in the azimuth direction than in the elevation direction. The difference in clutter levels between the two directions was also reflected in quality of images. In cyst phantom images, when the long-axis of the cyst was in the azimuth direction, clutter contribution from the azimuth sidelobes was minimized or not even present. This result is consistent with the cyst images which show the highest CNR when the long axis of the cyst was in the azimuth direction (Figure 2-11 (a)-(c)). When the long-axis of the cyst was in the elevation direction, clutter contributions from the azimuth sidelobes were greater resulting in a lower CNR. CNR values were lowest when the cyst lied along the diagonal (Figure 2-11 (g)- (i)). This is expected since clutter contributions from both principal axes were present. The unwanted clutter was likely due to variation of element-to-element performance from the difficulty of achieving uniform pressure over 4 × 4 cm 2 area while bonding. In addition, 27 because the dual-layer design allows only one-way focusing in each direction, the transducer will have lower image quality compared to fully-sampled 2-D transducer arrays which are capable of two-way focusing. As a result, signal processing algorithms are required to improve image quality. I took advantage of GCF to improve the contrast of the images in this chapter. Future work will focus on investigating other signal processing approaches to enhance image quality further. 28 Chapter 3 A 5 MHz Cylindrical Dual-Layer Transducer Array for 3-D Transrectal Imaging 3.1 Introduction Prostate cancer is the second most common cancer and the second leading cause of cancer death in American males, accounting for 29% (241,740) of newly diagnosed cancers expected in 2012 (Siegel, Naishadham et al. 2012). The primary tools to detect and diagnose prostate cancer include digital rectal examination (DRE), serum concentration of prostate specific antigen (PSA), and transrectal ultrasound (TRUS) guided biopsies, which are required for histopathological confirmation on the basis of the PSA level and/or a suspicious DRE (Heidenreich, Bellmunt et al. 2011). TRUS is also widely used for monitoring therapy procedures like brachytherapy and cryotherapy (Ritch and Katz 2009; Kao, Cesaretti et al. 2011), and transrectal HIFU treatment devices have already been available on the market since 2011 (Uchida, Nakano et al. 2012). In addition, by combining other TRUS capabilities, such as color and power Doppler, contrast-enhancement, harmonic and flash replenishment imaging, and elastography, prostate cancer detection could be further improved (Aigner, Mitterberger et al. 2010; Trabulsi, Sackett et al. 2010). Although conventional TRUS has been shown to have significant advantages, some major limitations exist. Since human anatomy is 3-D, the inherent 2-D character of conventional TRUS makes the imaging procedure highly operator-dependent. 29 Also, certain orientations, such as a C-scan, are unavailable with conventional 2-D TRUS. Furthermore, quantitative estimation of the prostate or tumor volumes can provide critical information (Park, Choi et al. 2004). However, the measurements based on selected conventional 2-D images are likely to be inaccurate, especially for tumors, whose geometry is highly variable (Tong, Downey et al. 1996). For these reasons, 3-D TRUS has been proposed for different clinical applications, including guiding prostate biopsies (Natarajan, Marks et al. 2011), detecting brachytherapy seeds (Wen, Salcudean et al. 2010), and prostate volume evaluation (Smith, Lewis et al. 2007). 3-D TRUS is also combined with other imaging modalities like MRI or PET/CT to better guide the diagnostic and therapeutic procedures of prostate cancer and image the prostate (Kadoury, Yan et al. 2010; Fei 2011). Ukimura et al recently proposed real- time 3-D TRUS guidance of prostate biopsy with MR/TRUS image fusion that can accomplish volumetric data acquisition in 3 seconds (Ukimura, Desai et al. 2012). Most of the 3-D TRUS systems manually or mechanically translate 1-D arrays to acquire multiple B-scans, and implement 3-D reconstruction by offline processing. The mechanical components of such systems can be slow, user-dependent and unreliable. Solutions to these issues can be provided by solid-state 2-D transducer arrays which do not require the moving parts for 3-D scanning. A fully sampled cylindrical 2-D array for 3-D transrectal imaging analogous to the 1-D curvilinear array, typically having 256 elements and using a sub-aperture of 128 elements per image line, would require up to 256 × 256 = 65,536 elements and a sub-aperture of 128 × 128 = 16,384 elements. Figure 3-1 shows a fully-sampled, side-firing, cylindrical 2-D ultrasound array which scans a volume consisting of many curvilinear scans stacked together along the long-axis of the probe. The issues associated with fabrication and interconnection have made it extremely 30 difficult to construct such transducers. The dual-layer array design provides an alternative solution to the problem by reducing the fabrication complexity and channel count of the transducer. The basic structure of these transducers contained one PZT layer for transmit and one separate P[VDF-TrFE] copolymer layer, closer to the target, for receive. Each layer was a 1- D square-shaped array composed of parallel elongated elements. The layers were oriented with transmit and receive elements perpendicular to each other. In this chapter, I describe the design, fabrication, test, and imaging experiments of a 5 MHz cylindrical 2-D transducer based on the dual-layer design for 3-D transrectal imaging, with 128 PZT elements and 128 P[VDF-TrFE] copolymer elements. This transducer took advantage of the flexible nature of the diced PZT and P[VDF-TrFE] copolymer to create a curved geometry. The transducer required a new design of the acoustic stack, and refinement of the fabrication process. A prototype, with a transverse diameter of 25 mm and a longitudinal height of 40 mm, was developed to demonstrate the feasibility of the transducer. The generalized coherence factor (GCF) was also applied to improve the image quality furthermore. The goal is to have a real-time transrectal system for prostate imaging with image quality comparable to a system with a fully-sampled 2-D array, using a more practical transducer design combines with suitable signal processing algorithms. 31 Figure 3-1: 2-D cylindrical array for 3-D TRUS. 3.2 Method 3.2.1 Simulated Beamplots To simulate imaging performance of the cylindrical dual-layer transducer array, simulated beamplots were acquired using Field II (Jensen and Svendsen 1992). The transmit aperture was a 1-D array with a transverse element pitch of 300 µm and a longitudinal height of 38.4 mm. The receive aperture had a longitudinal element pitch of 300 µm and a transverse length of 38.4 mm. A Gaussian pulse with a center frequency of 4.5 MHz and 50% fractional bandwidth was used. For the beamplot, a 64-element sub-aperture was used in both transmit and receive and focused on-axis to (x,y,z) = (0,0,30) mm. Figure 3-2 shows the simulated beamplots of the dual-layer transducer in transverse direction and longitudinal direction. The −6 dB 32 beamwidth is 0.92 mm in transverse and 0.74 mm in longitudinal, respectively. Sidelobe levels, around −15 to −20 dB, are seen along the transverse and longitudinal axes. Figure 3-2: Simulated beamplots of the cylindrical dual-layer transducer 3.2.2 Design and Fabrication Figure 3-3 shows a schematic of the acoustic stack of the dual-layer transducer array. A cylindrical backing with acoustic impedance of 8 MRayls was used to minimize reverberation between different layers. This backing was produced using 82% tungsten powder with particle diameter of 1 µm (Atlantic Equipment Engineers, Bergenfield, NJ) and 18% Epo-Tek 301 epoxy (Epoxy Technology, Billerica, MA), by weight. The mixture was then centrifuged at 2400 revolutions per minute (rpm) in a Beckman-Coulter Allegra 6 centrifuge (Fullerton, CA) for 10 minutes. After lapping off the excess epoxy, the curved surface of the backing was sputtered with 500 angstroms of chrome and 1000 angstroms of gold to provide a ground electrode for all PZT elements. 33 The diameter of the cylindrical backing was 25 mm, which, by combining a 40 x 40 mm 2 active area size, provided a transverse scan angle of around 180°. The dimensions were chosen based on typical settings in clinical applications. I also chose a pitch of 300 µm for the array to keep the elements spaced approximately one wavelength to avoid grating lobes. As a result, each layer had 128 elements. A 40 x 40 mm 2 wafer of gold-plated 300 µm thick PZT-5H was bonded to a prototype flexible circuit (Microconnex, Snoqualmie, WA, Flex 1 in Figure 3-3) using Epo-Tek 301 epoxy. The flexible circuit was made of 25 µm thick polyimide with 5 µm thick copper traces spaced at 150 µm printed on one side. A DAD321 automatic dicing saw (DISCO Corporation, Tokyo, Japan) with a 30 µm width diamond blade (DISCO Corporation, Tokyo, Japan) was used to dice the PZT wafer into 256 elongated pillars. The dicing saw was carefully calibrated to position each cut at the middle between two adjacent copper traces, and all cuts were made through the PZT piece and Flex1. Each pillar serves as a sub-element, and two adjacent sub-elements were combined electrically in parallel to perform as one transmit element. The sub-element strategy was used to reduce the aspect ratio of ceramic pillars to around 0.4. Without the sub-element dicing, the determined transducer specifications would make the aspect ratio close to 1, which would translate to high lateral coupling. Then the diced PZT, together with Flex 1, was bonded to the sputtered curved surface of the backing with PZT elements ran parallel to long-axis. 34 Figure 3-3: Acoustic stack of the cylindrical dual-layer transducer array A 40 x 40 mm 2 sheet of P[VDF-TrFE] copolymer, which had been poled and metalized with Cr/Au on the negative side by manufacturer (Precision Acoustics, Dorset, UK), was bonded to another flexible circuit (Flex 2 in Figure 3-3), identical to Flex 1, on the positive, unmetalized side. Both the Cr/Au layer and the copper traces on Flex 2 will serve as electrodes for the copolymer elements. A single P[VDF-TrFE] copolymer element was 75 µm wide and 40 mm long, defined by the width of copper traces on the flexible circuit. This copolymer/flex module was then bonded to the top of Flex 1 so that the PZT and copolymer elements were perpendicular to each other. The polyimide layer of Flex 1 would electrically isolate the elements of the two 35 layers. The copolymer combined with the two flexible circuits to serve as a simple matching layer for the PZT transmit layer, which possesses an acoustic impedance of around 4 MRayls and a total thickness of 75 µm. The applied pressure was approximately 100 psi when bonding materials to the flexible circuits, which assured a thin enough bonding thickness to achieve electrical contact. The array was finally sealed with non-conductive epoxy and RTV silicone to protect from moisture and possible physical damage. Samtec connectors (Samtec USA, New Albany, IN) were soldered onto both flexes to serve as the interface between the transducer and printed circuit boards. A photo of the finished prototype transducer is shown in Figure 3-4. Figure 3-4: Photo of the prototype cylindrical dual-layer transducer 36 3.2.3 Data Acquisition After performing electrical impedance and pulse-echo measurements, the cylindrical dual-layer transducer array was interfaced with a 4-board Verasonics Data Acquisition System, VDAS (Verasonics, Redmond, WA). VDAS is an ultrasound research platform that allows acquiring, storing, displaying and analyzing ultrasonic data. Users are able to control imaging parameters such as aperture size, transmit frequency, filtering, and time-gain compensation on the system. The VDAS can provide 256 transmit channels and 128 receive channels simultaneously, which reduces the time of data collection and the complexity of operation. During data acquisition, the transducer was interfaced with VDAS by two sets of 128- channel coaxial cable bundles (Prosonic, Gyeongbuk, Korea), which were plugged into the two scanhead connectors (SHCs) on the front panel of VDAS at the other end. Each of the PZT elements were connected to the 128 individual channels of one SHC configured to operate in transmit mode, while the PVDF copolymer elements were connected to the remaining 128 system channels of the other SHC in receive mode. Data from each receive channel was collected 300 times with a 36 MHz sampling frequency, and averaged to minimize the effects of random noise for synthetic aperture acquisition. I performed the data acquisition process with the transducer immersed in an oil bath. 3-D volumetric data was acquired of different targets. A single nitinol wire target, with a diameter of 100 µm, was scanned to evaluate the spatial resolution. Multiple nylon wires were placed inside a sponge to mimic the seeds implanted during a brachytherapy procedure. Another target 37 scanned was a cyst target formed by cutting a cylindrical core, whose diameter was 8 mm, into the sponge. 3.2.4 Beamforming, Signal Processing, and Display The acquired synthetic data was imported into Matlab (Mathworks, Natick, MA) for offline 3-D delay-and-sum (DAS) beamforming, signal processing, and image display. RF data was filtered with a 64-tap FIR bandpass filter with frequency range of 3.5-6.5 MHz. Beamforming with dynamic transmit and receive focusing of 1 mm increments was then done with a constant sub-aperture size of 64 elements. A 3-D cylindrical volume was acquired by selecting the appropriate transmit sub-apertures in transverse and receive sub-apertures in longitudinal to focus a beam directly ahead. Scan conversion was performed in the transverse direction to provide a curvilinear scan format. The generalized coherence factors (GCF) were calculated and used as weighting factors for the reconstructed images of the cyst phantom to improve contrast of the images (Li and Li 2003). After 3-D beamforming and signal processing, envelope detection was done using the Hilbert transform followed by log-compression. Transverse and longitudinal B-scans are displayed along with C-scans which are parallel to the transducer face. The above processing was performed on iMac OS X 10.6.7, and took about 1 hour for computation. 38 3.3 Experimental Results 3.3.1 Impedance Measurements Figure 3-5: Simulated and experimental impedance measurements of PZT and P[VDF-TrFE] layers Experimental electrical impedance measurements of the transducer were taken using an Agilent 4294A impedance analyzer (Santa Clara, CA). Figure 3-5 shows the electrical impedance results of both layers by simulation using 1-D KLM modeling software (PiezoCAD, Sonic Concepts, Woodinville, WA)(Krimholt.R, Leedom et al. 1970), and by experiments. For PZT, the simulated impedance magnitude was 87 Ω at a series resonance frequency of 4.0 MHz 39 while the experimental impedance curve showed a series resonance of 74 Ω at 5.1 MHz. The phase plots peak at 5.4 MHz for the KLM simulation and at 6.0 MHz in the experimental case. For P[VDF-TrFE] copolymer, the impedance magnitude was 2.3 kΩ at 4.0 MHz in simulation, and the measured impedance magnitude was 1.8 kΩ at 5.1 MHz. No resonance peaks are seen in the impedance magnitudes, and the phase remains near 84° to 87°. 3.3.2 Pulse-echo Measurements Figure 3-6: Simulated and experimental pulses and spectrum of the cylindrical dual-layer transducer Pulse-echo measurements of the transducer were made in a water tank using a Panametrics 5900PR pulser/receiver (Waltham, MA) with an aluminum plate reflector. To mimic imaging conditions, the excitation pulse was applied to a PZT element and a copolymer element was used as the receiver. Figure 3-6 shows the simulated and experimental time and frequency responses of the pulse-echo signals. In simulation, the center frequency was 5.48 40 MHz with a -6 dB fractional bandwidth of 80.33%, compared to a 5.66 MHz center frequency with a -6 dB fractional bandwidth of 62.06% in experiment. Low amplitude reverberations after the pulse peak in the time domain and an in-band notch in the frequency domain are seen in both the simulation and experimental results. Compared to simulation, experimental pulse-echo test shows good agreement in terms of center frequency, with a moderately narrower bandwidth. 3.3.3 3-D Imaging – Single Nitinol Wire Figure 3-7 (a)-(c) show the transverse B-scan, longitudinal B-scan and C-scan respectively when the long axis of the wire target was in longitudinal direction. The transverse B-scan (Figure 3-7 (a)) was scan converted for sector display. The C-scan plane was selected after scan conversion in transverse direction, and parallel to the long axis of the transducer. Figure 3-7 (d)-(f) show images of the same nitinol wire target with long axis of the wire in transverse direction. Figure 3-7 (d) and (f) only show a portion of the wire, because of the specular reflection of the nitinol wire. Figure 3-7 (f) shows a C-scan whose slice has been thickened in the axial dimension to encompass as much of the wire target as possible, when the wires are not perfectly parallel to the transducer face because of mechanical positioning. All images are log-compressed and shown on a 25 dB dynamic range. Figure 3-8 shows the lateral wire target responses in transverse (left) and in longitudinal (right) directions. The -6 dB beamwidth was 1.28 mm in transverse and 0.91 mm in longitudinal compared to a simulated beamwidth of 0.92 mm and 0.74 mm respectively. Sidelobes above -20 dB and some clutter around -25 dB were present in both figures. 41 Figure 3-7: Experimental images of single nitinol wire with a dynamic range of 25 dB Figure 3-8: Transverse and longitudinal lateral wire target responses 42 3.3.4 3-D Imaging – Multiple Nylon Wires Embedded in a Speckle Source Figure 3-9: Experimental images of multiple nylon wires with a dynamic range of 35 dB Figure 3-9 contains volumetric images of 3 parallel nylon wires embedded in a sponge which provides scattering. This experiment mimicked a brachytherapy procedure with multiple seeds implanted in the prostate. In the above figure, (a)-(c) show the transverse B-scan, longitudinal B-scan and C-scan with the long axes of the nylon wires in longitudinal, and (d)-(f) show the two perpendicular B-scans and the C-scan with long axes of the wires in transverse. Again, only a portion of the wires were seen in (d) and (f) because of the specular reflection of the nylon wires. However, the sponge that would basically provide diffuse reflection could be seen all across the field-of-view. Figure 10(f) was also averaged in depth dimension to encompass the target as much as possible. All images are log-compressed and shown with 35 dB dynamic range. 43 3.3.5 3-D Imaging – Cyst Phantom Figure 3-10: Experimental images of cyst phantom with GCF applied Figure 3-10 shows volumetric images of a sponge with an 8 mm diameter cylindrical hole, which served as a cyst target phantom, with GCF applied on a voxel by voxel basis. Figures (a)-(c) show the transverse B-scan, longitudinal B-scan and C-scan with the long axis of the cyst in longitudinal, and (d)-(f) show the two perpendicular B-scans and the C-scan with the phantom rotated 90°. All images are log-compressed and shown with 55 dB dynamic range. 3.4 Conclusions and Discussions In this chapter, I described the design, fabrication, test and imaging of a proof-of-concept 5 MHz frequency cylindrical dual-layer transducer array for transrectal 3-D imaging. The 44 transducer uses PZT and P[VDF-TrFE] copolymer for transmit and receive, respectively. Experimental impedance measurements and pulse-echo tests of the transducer showed good agreement with simulation results. By imaging the single nitinol wire target, lateral resolution was evaluated for the transducer. In order to improve image quality further, GCF was applied on the cyst phantom images which contained speckles from scatterers in the background. Figure 3-6 shows that the measured bandwidth of the transducer was narrower than that was predicted by KLM model. One reason for this is the bond lines between layers could be thicker than expected, and the reverberation would prolong the pulse in time domain, narrowing down the frequency bandwidth as a result. Unwanted clutter could be observed in Figure 3-8, which would degrade quality of images. The clutters were likely due to variation of element-to-element performance from the difficulty of achieving uniform pressure over the transducer surface while bonding. In addition, because the dual-layer design allows only one-way focusing in each direction, the transducer will have lower image quality compared to fully-sampled 2-D transducer arrays which are capable of two-way focusing. As a result, signal processing algorithms are required to improve image quality. GCF was applied to improve the contrast of the cyst images in this chapter. 45 Chapter 4 Beamforming by Spatial Matched Filtering with Plane Wave Transmissions 4.1 Introduction During 3-D imaging with dual-layer array transducers, receive elements in the elevation direction composed a 1-D array, and beamforming can be performed using receive sub-apertures in this direction. However, transmit pulses are essentially plane wave pulses in the elevation direction. Similarly, in the azimuth direction, beamforming can be achieved using transmit sub- apertures. But receive focusing is not available in the azimuth direction. One-way focusing determined by the nature of the dual-layer design results in worse image quality compared to two-way, or transmit-receive, focusing. Kim et al proposed a novel beamforming method by spatial matched filtering (SMF) the echo radio frequency (RF) signals (Kim, Liu, & Insana, 2006). In this method, ultrasonic waves are transmitted from sub-apertures with fixed transmit focus as in conventional linear array systems. On receive, RF signals are spatially matched filtered by 2-D filters constructed from the system transmit-receive spatial impulse response. Through comparing with delay-and-sum (DAS) beamforming, in which dynamic focusing is applied in receive, their results show that SMF beamforming is able to perform effective transmit-receive focusing at all depths, and provide comparable lateral resolution and image contrast to DAS beamforming at transmit focus. 46 This inspired me to investigate SMF beamforming to compensate for the degradation of image quality in the elevation direction for dual-layer 3-D imaging. According to the dual-layer design, receive elements compose a 1-D array in the elevation direction, and transmit pulses from the elongated transmit are essentially plane wave pulses in this direction. Therefore, it is reasonable to test the performance of SMF beamforming using a 1-D array with plane wave transmissions as an initial step towards the goal of implementing SMF beamforming to dual- layer transducers. In this chapter, 1-D array transducers were used to demonstrate the feasibility of SMF beamforming with plane wave transmissions (PWT). The evaluation of the performance of SMF beamforming with PWT was carried out through comparing with conventional methods using beam pattern analysis based on the Rayleigh-Sommerfeld diffraction theory (Goodman, 1996). Furthermore, simulation data generated by Field II (Jensen & Svendsen, 1992) and experimental data acquired from a four-board Verasonics data acquisition system, VDAS (Verasonics, Redmond, WA), were beamformed using with different beamforming methods. Images were compared between the methods to verify the predicted advantages brought by SMF beamforming with PWT. 4.2 Method 4.2.1 Rayleigh-Sommerfeld diffraction analysis Figure 4-1 illustrates the geometry of a 1-D linear array transducer and the coordinate system used during analysis. 𝑥 and 𝑧 coordinates are in the azimuthal and axial directions of the 47 imaging plane respectively. According to the Rayleigh-Sommerfeld diffraction theory (Goodman, 1996), the complex field transmitted at frequency 𝜔 at field point (𝑥 ,𝑧 ) near the 𝑧 axis can be simplified as 𝜑 𝜔 𝑥 ,𝑧 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! (1) with wavelength 𝜆 and wave number 𝑘 = !𝜋 𝜆 . 𝑎 𝑡 𝑥 ! is the transmit aperture function of coordinate 𝑥 ! which is on the transducer surface. Figure 4-1: Geometry of a 1-D linear array transducer and the coordinate system used in the Rayleigh-Sommerfeld diffraction analysis. Beamforming, or focusing, is mathematically equivalent to eliminating the quadratic phase factor 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 in equation (1). The field pattern then becomes the spatial Fourier transform of 48 the transmit aperture function 𝑎 𝑡 𝑥 ! , and diffraction-limited lateral resolution can be attained (Goodman, 1996). The transmit field after beamforming is written as 𝜑 𝜔 𝑥 ,𝑧 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 ! !! 𝑑 𝑥 ! = 𝑒 𝑗𝑘 𝑧 𝑗𝜆𝑧 𝐴 ! 𝑢 𝑥 (2) where 𝐴 ! 𝑢 𝑥 =ℑ[𝑎 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 is the spatial Fourier transform of 𝑎 𝑡 𝑥 ! . DAS beamforming calculates the time delays to focus the field. It is equivalent multiplying the integrand with 𝑒 ! 𝑗𝑘 𝑥 ! ! !𝑧 𝐹 , where 𝑧 𝐹 is the transmit focal depth. Consequently, the complex field becomes 𝜑 𝜔 𝑥 ,𝑧 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 !𝑘 𝑥 ! ! ( ! !! ! ! !! ! ) ! !! 𝑑 𝑥 ! (3) When 𝑧 = 𝑧 𝐹 , the quadratic phase factor in equation (3) is cancelled out by 𝑒 ! 𝑗𝑘 𝑥 ! ! !𝑧 𝐹 . The transmit field comes to be the spatial Fourier transform of 𝑎 𝑡 𝑥 ! , suggesting a compact point spread function at the transmit focus. However, at depths away from the focus, the quadratic phase factor remains, resulting in broader point spread functions compared to focal depth. With 𝑎 𝑡 𝑥 ! being replaced by the receive aperture function 𝑎 𝑟 𝑥 ! , a similar expression as equation (1) can be written for receive field due to reciprocity (Pierce, 1981). Therefore, the pulse-echo field, which is the product of the transmit and receive fields, using DAS beamforming is 49 𝜓 !,!"# (𝑥,𝑧)= 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! 𝑢 𝑥 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 !𝑘 𝑥 ! ! ( ! !! ! ! !! ! ) ! !! 𝑑 𝑥 ! (4) where 𝐴 ! 𝑢 𝑥 =ℑ[𝑎 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆 𝑧 is the spatial Fourier transform of 𝑎 ! 𝑥 ! . The quadratic phase factor does not show up in the receive term because it is removed at every depth since receive focusing is implemented dynamically. Equation (4) indicates the best pulse-echo lateral resolution is obtained at the transmit focal depth 𝑧 = 𝑧 𝐹 , where the pulse-echo field is the product of the spatial Fourier transforms of transmit and receive aperture functions, that is 𝜓 !,!"# 𝑥,𝑧 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! 𝑢 𝑥 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 ! !! 𝑑 𝑥 ! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! 𝑢 𝑥 𝐴 ! 𝑢 𝑥 (5) The goal of SMF beamforming is to achieve the field expressed in equation (5) at all depths. With SMF beamforming, the cancellation of the quadratic phase factor is accomplished by convolving the complex pulse-echo field with spatial matched filters that are constructed from the spatial impulse response of the system. I filtered the receive signals of each individual element and then summed the filtered signals up along the receive aperture. For an individual element located at 𝑥 ! = 𝑥 𝑟 , the receive aperture function can be approximated by 𝑎 𝑟 𝑥 ! = 𝛿 (𝑥 ! −𝑥 𝑟 ) if the element width is smaller than the wavelength. The receive field 𝜑 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 at field point (𝑥 ,𝑧 ) from element at 𝑥 𝑟 is expressed as 𝜑 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑎 ! 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝛿 (𝑥 ! −𝑥 𝑟 )𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑒 𝑗𝑘 ! ! ! !𝑧 (6) 50 The pulse-echo field of SMF beamforming with PWT is given by 𝜓 𝜔 𝑥 ,𝑧 ;𝑥 𝑟 =𝜑 𝜔 𝑥 ,𝑧 𝜑 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑒 𝑗𝑘 ! ! ! !𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! (7) Spatially matched filtering the pulse-echo field gives 𝜓 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 =𝜓 𝜔 𝑥 ,𝑧 ;𝑥 𝑟 ∗𝜓 𝜔 ∗ −𝑥 ,𝑧 ;𝑥 𝑟 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝜏 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘 𝑥 !𝜏 𝑥 ! 𝑧 𝑒 ! !"! ! ! !! ! !! 𝑑 𝑥 ! 𝑑𝜏 ! !! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 𝑥 ! 𝑎 𝑡 𝑥 ! 𝑒 !𝑘 (𝑥 ! ! !𝑥 ! ! ) !! 𝑒 ! 𝑗𝑘𝜏 𝑥 ! !𝑥 ! 𝑧 𝑑𝜏 ! !! 𝑑 𝑥 ! ! !! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑑 𝑥 ! ! !! = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 𝑥 ! 𝑎 𝑡 𝑥 ! 𝑒 !𝑘 (𝑥 ! ! !𝑥 ! ! ) !! 𝛿 𝑥 ! −𝑥 ! 𝑑 𝑥 ! ! !! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑑 𝑥 ! ! !! = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 ! 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑑 𝑥 ! ! !! = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝐴 ! ,𝑡 𝑢 𝑥 (8) where 𝐴 ! ,𝑡 𝑢 𝑥 =ℑ[𝑎 𝑡 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 is the spatial Fourier transform of the square of the transmit aperture function 𝑎 𝑡 (𝑥 ! ). Equation (8) shows that the quadratic phase factor is eliminated after the field is spatially matched filtered. It suggests that SMF beamforming can achieve both transmit and receive focusing at every depth with PWT. At last, the filtered fields are summed with weighting by the square of the receive aperture function 𝑎 𝑟 (𝑥 ! ). 51 𝜓 𝜔 ,𝑆𝑀𝐹 𝑥 ,𝑧 = 𝑎 𝑟 ! (𝑥 𝑟 ) ! !! 𝜓 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 𝑑 𝑥 𝑟 = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! ,𝑡 𝑢 𝑥 𝑎 𝑟 ! 𝑥 𝑟 ! !! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑑 𝑥 𝑟 = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! ,𝑡 𝑢 𝑥 𝐴 ! ,𝑟 𝑢 𝑥 (9) where 𝐴 ! ,𝑟 𝑢 𝑥 =ℑ[𝑎 𝑟 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 is the spatial Fourier transform of the square of the receive aperture function 𝑎 𝑟 (𝑥 ! ). I examined the performance of DAS beamforming and SMF beamforming by comparing equation (4) and (9). The quadratic phase factor is present with transmit in equation (4) except at the focal depth, whereas it is eliminated for both transmit and receive terms in equation (9) at all depths. As a result, equation (9) predicts the effectiveness of SMF beamforming with PWT is equivalent to DAS beamforming at the transmit focus, as expressed in equation (5). Geometric time delay profiles for focusing are not required in SMF beamforming. Spatial matched filters constructed from the system transmit-receive spatial impulse response must be known. They can be obtained by scanning a point target at different locations in field. 4.2.2 Filter size considerations for SMF beamforming The above equations used infinite limits of integration to perform filtering. In practice, finite 2-D discrete matched filters are required. To determine an appropriate filter size for SMF beamforming, transmit-receive beam patterns generated from using filters with different sizes were compared to the standard DAS beamforming with both transmit and receive focusing. I based the filter size on the percent of total energy preserved in the finite matched filter. The 52 simulation was done by implementing discrete forms of equation (5) and (9). A rectangular aperture function with 20 mm width was used at a frequency of 5 MHz. The beam patterns were acquired at 40 mm depth. Figure 4-2: Comparisons of mainlobes between standard DAS beamforming and SMF beamforming using filters with (a) 90% of total energy, (b) 80% of total energy, (c) 70% of total energy, and (d) 60% of total energy. 53 By comparing to DAS beamforming with transmit and receive apertures both focused at 40 mm depth, the mainlobes for SMF beamforming with different filter sizes are shown in Figure 4-2. Measured -6 dB beamwidths of SMF beamforming using filters preserving 90% (Figure 4-2(a)), 80% (Figure 4-2(b)), 70% (Figure 4-2(c)), and 60% (Figure 4-2(d)) of total energy were 0.57 mm, 0.60 mm, 0.63 mm and 0.66 mm. These beamwidths are 5.5%, 11.1%, 16.7% and 22.2%, respectively, wider than the mainlobe of the standard, which is 0.54 mm at -6 dB. The results indicate that the mainlobe width with SMF beamforming increases as the filter size decreases. Table 2: -6 dB beamwidth and off-axis energy of SMF beamforming with different filter sizes. Standard 90% 80% 70% 60% -6 dB beamwidth (mm) 0.54 0.57 0.60 0.63 0.66 Off-axis energy fraction (%) 0.29 0.20 0.12 0.14 0.32 Complete beam patterns with both mainlobes and sidelobes using SMF beamforming with different filter sizes are compared to DAS beamforming in Figure 4-3. In order to assess the sidelobe levels, the off-axis energy fraction, defined as the ratio of energy in the sidelobes to the total energy, was calculated for each case. Table 2 summarizes the off-axis energy fractions, as well as the -6 dB beamwidths, of SMF beamforming using different filter sizes. As the filter size becomes smaller, the off-axis energy fraction decreases until it reaches 80% energy, and then goes up again. The reason for the drop in sidelobe levels is because the truncation of the 54 matched filters, for finite sizes, is essentially applying a weighting window function to them, and making the filters mismatched. Mismatched filtering can help reduce sidelobe levels, at the expense of widened mainlobe width (Misaridis & Jensen, 2005). However, when the filter contains too little energy, such as 60% in our simulation, SMF beamforming is less effective in terms of both wide mainlobe and high sidelobe levels. Figure 4-3: Beam patterns of standard DAS beamforming and SMF beamforming using filters with (a) 90% of total energy, (b) 80% of total energy, (c) 70% of total energy, and (d) 60% of total energy. 55 In summary, filter size with more than 90% energy preserved is preferred for applications in which lateral resolution is crucial. Smaller filters, such as 80% energy in our situation, could be used for achieving higher image contrast when some compromise of lateral resolution can be tolerated. In general, my results suggest that a filter which preserves an 80% energy level is a minimum criterion for SMF beamforming. 4.2.3 Computer simulations Computer simulations with Field II (Jensen & Svendsen, 1992) were performed to evaluate the performance of SMF beamforming in broadband systems. Echo RF data was generated for a 1-D linear array transducer, which is composed of 128 elements with an element pitch of 298 µm and an element height of 5 mm. A 5 MHz, 2-cycle sinusoidal pulse was used to excite the transducer elements. The generated RF data was imported to Matlab (Mathworks, Natick, MA) for beamforming, envelope detection, log compression, and image display. Point reflectors positioned at 20 mm depth and 40 mm depth were scanned to acquire transmit-receive beam patterns for DAS beamforming and SMF beamforming. Lateral beamwidths and sidelobe levels were measured from the beamplots. The point reflectors were also used to construct spatial matched filters for SMF beamforming. To complete the evaluation, scattering fields that contain speckle and anechoic targets must be included in simulations. 6 mm diameter anechoic cysts, located at 20 mm depth and 40 mm depth, embedded in scatterers were imaged. Contrast to noise ratio (CNR) was calculated to quantify image contrast. The definition of CNR used in this context was the difference between the mean value of a target, or a cyst, 56 region and the mean value of the background, in dB, divided by the standard deviation of the background, in dB (Krishnan, Rigby, & O’Donnell, 1997). 4.2.4 Experiments with tissue-mimicking phantoms During our experiments, RF signals from individual receive channel were collected using a four-board Verasonics data acquisition system, or VDAS. This system has great flexibility and allows users to control imaging parameters such as aperture size, transmit frequency, and time- gain compensation. A L7-4 1-D linear array transducer with 128 elements, spacing at 298 μm, was used in the experiments, and the transducer was excited by 5 MHz, 2-cycle sinusoidal pulses. Offline beamforming of the acquired data was performed using Matlab. Transmit-receive beam patterns were obtained by imaging a human hair, serving as a point reflector, placed at 20 mm depth and 40 mm depth in a peanut oil bath. Spatial matched filters for SMF beamforming were also constructed from scanning the human hair. Anechoic cysts, with diameters of 4 mm and 6 mm, from an ATS tissue-mimicking phantom (Model 549, ATS Laboratories, Bridgeport, CT) were imaged during the experiments. CNRs were calculated for image contrast evaluation and were compared between different beamforming methods. 57 4.3 Simulation and experimental results 4.3.1 Beam patterns from the Rayleigh-Sommerfeld diffraction analysis In all results presented in Section III, “DAS” described results from conventional DAS beamforming with fixed transmit focusing and dynamic receive focusing. The transmit focal depth of “DAS” was always at 40 mm depth. With plane wave pulses used on transmit, “PWT+rDAS” and “PWT+SMF” indicated dynamic DAS beamforming and SMF beamforming on receive respectively. (a) (b) Figure 4-4: Transmit-receive beam patterns of the Rayleigh-Sommerfeld analysis for DAS, PWT+rDAS and PWT+SMF at the depth of (a) 20 mm and (b) 40 mm. The beam patterns shown in Figure 4-4 were calculated based on the Rayleigh- Sommerfeld diffraction analysis described in Section II. The calculation was done at a 58 frequency of 5 MHz using a rectangular aperture function with 20 mm width. In Figure 4-4 (a), where the depth was at 20 mm, the -6 dB beamwidth and the first sidelobe level of DAS were 0.38 mm and -12.9 dB. The values for PWT+rDAS were 0.37 mm and -13.4 dB respectively. SMF beamforming with PWT gave a narrower mainlobe width and lower sidelobe levels than both delay-and-sum methods. The -6 dB beamwidth and the first sidelobe amplitude of PWT+SMF were 0.27 mm and -26.6 dB. Figure 4-4 (b) exhibited the beam patterns of the three beamforming methods at 40 mm depth, where transmit beams were focused at for DAS. There was no visible difference between the beamplots of DAS and PWT+SMF, both having a -6 dB beamwidth of 0.54 mm and a first sidelobe level of -26.5 dB. However, PWT+rDAS showed wider mainlobe width (0.76 mm) and higher sidelobe levels (-12.8 dB) than the others, since there was no transmit focusing for this method. The beamplots in Figure 4-4 demonstrated that PWT+SMF was able to provide improved beam patterns, in terms of narrower mainlobe and lower sidelobe levels, compared to DAS at depths away from the transmit focus. However, at the transmit focus, beam patterns of the two beamforming methods are similar. In high frame-rate imaging systems, PWT+SMF consistently showed narrower mainlobe and lower sidelobes than PWT+rDAS. The beam patterns were calculated by directly implementing equation (4) and (9) derived during the analysis of the Rayleigh-Sommerfeld diffraction theory, which involved certain mathematical approximations, such as the paraxial approximation assuming the observed field points are near the z-axis in Figure 4-1. In addition, the above equations based on narrowband analysis cannot accurately predict the broadband results. Further evaluation of the performance 59 of SMF beamforming with field simulations and experimentally acquired data is needed for more realistic conditions. 4.3.2 Simulation results (a) (b) Figure 4-5: Simulation transmit-receive beam patterns of Field II for DAS, PWT+rDAS and PWT+SMF of a point reflector located at (a) 20 mm depth, and (b) 40 mm depth. Figure 4-5 shows the lateral transmit-receive beam patterns of the methods of DAS, PWT+rDAS and PWT+SMF from Field II simulations when a point reflector was placed at 20 mm depth (Figure 4-5 (a)) and 40 mm depth (Figure 4-5 (b)). In Figure 4-5 (a), the beamplots of DAS and PWT+rDAS are similar. The -6 dB beamwidths of DAS and PWT+rDAS are 0.58 mm and 0.50 mm, and they both possess a first sidelobe amplitude of around -10 dB. For PWT+SMF, a -6 dB beamwidth of 0.28 mm and a first side lobe level below -30 dB are measured from the beamplot. In Figure 4-5 (b), the location of the point reflector was at the 60 transmit focal depth of DAS. The -6 dB beamwidths of DAS, PWT+rDAS and PWT+SMF are 0.60 mm, 0.74 mm and 0.63 mm respectively. The first sidelobe levels for DAS and PWT+SMF are both below -30 dB, whereas this level of PWT+rDAS is as high as -15 dB. Figure 4-6: Images with an anechoic cyst of 6 mm in diameter at different depths from Field II simulations of different beamforming methods: (a) cyst at 20 mm depth with DAS, (b) cyst at 20 mm depth with PWT+rDAS, (c) cyst at 20 mm depth of PWT+SMF, (d) cyst at 40 mm depth with DAS, (e) cyst at 40 mm depth with PWT+rDAS, (f) cyst at 40 mm depth with PWT+SMF. (a) DAS (b) PWT+rDAS (c) PWT+SMF (d) DAS (e) PWT+rDAS (f) PWT+SMF 61 Figure 4-5 indicates that PWT+SMF is able to provide lateral beam patterns comparable to DAS at the transmit focal depth. It also has a narrower mainlobe and lower sidelobe levels than PWT+rDAS, consequently leading to enhanced image quality in high frame-rate imaging systems. These results agree with the beam patterns of the Rayleigh-Sommerfeld diffraction analysis. Figure 4-6 shows the images of a 6 mm diameter anechoic cyst at different depths using DAS, PWT+rDAS and PWT+SMF with RF data generated from Field II simulations. All images are displayed with a dynamic range of 40 dB. CNR was calculated for each image and summarized in Table 3. At 40 mm depth, DAS provides an image CNR value of 5.14 (Figure 4-6 (d)), which is the standard for comparisons. At 20 mm depth, the image beamfromed from DAS has a lower CNR value of 2.54 (Figure 4-6 (a)) because the position of the cyst was away from the transmit focus. In Figure 4-6 (b) and (e), where PWT+rDAS is implemented, CNR values of the images are 1.12 and 2.00 respectively. Both are lower than the standard due to the lack of transmit focusing. PWT+SMF provides CNR values of 4.49 and 5.34 for images when the cyst was at 20 mm depth (Figure 4-6 (c)) and 40 mm depth (Figure 4-6 (f)). The SMF results are comparable to the standard DAS beamforming at transmit focal depth. Furthermore, the SMF contrast is superior to PWT+rDAS throughout imaging depth. 62 Table 3: CNR values for simulated images containing a 6 mm diameter anechoic cyst using DAS, PWT+rDAS and PWT+SMF. DAS PWT+rDAS PWT+SMF Cyst located at 20 mm 2.54 1.12 4.49 Cyst located at 40 mm 5.14 2.00 5.34 4.3.3 Experimental results (a) (b) Figure 4-7: Experimental transmit-receive beam patterns for DAS, PWT+rDAS and PWT+SMF of a point reflector located at (a) 20 mm depth and (b) 40 mm depth. 63 (a) DAS (b) PWT+rDAS (c) PWT+SMF (d) DAS (e) PWT+rDAS (f) PWT+SMF Figure 4-8: Images with anechoic cysts of 4 mm diameter and 6 mm diameter at different depths from experiments of different beamforming methods: (a) cysts at 20 mm depth with DAS, (b) cysts at 20 mm depth with PWT+rDAS, (c) cysts at 20 mm depth of PWT+SMF, (d) cysts at 40 mm depth with DAS, (e) cysts at 40 mm depth with PWT+rDAS, (f) cysts at 40 mm depth with PWT+SMF. Figure 4-7 shows the lateral transmit-receive beam patterns acquired from experiments with VDAS for DAS, PWT+rDAS and PWT +SMF when a human hair, serving as a point reflector, was positioned at the depth of 20 mm (Figure 4-7 (a)) and 40 mm (Figure 4-7 (b)). With the point reflector at 20 mm depth, -6 dB beamwidths are 0.51 mm, 0.68 mm and 0.39 mm for DAS, PWT+rDAS and PWT+SMF respectively. PWT+SMF gives a first sidelobe level of - 28 dB, whereas this level for both DAS and PWT+rDAS is higher than -10 dB. At 40 mm depth, 64 -6 dB beamwidths for PWT+SMF and DAS are 0.66 mm and 0.59 mm. PWT+rDAS has a -6 dB beamwidth as wide as 0.83 mm. Both DAS and PWT+SMF have a similar first sidelobe level of around -30 dB. However, DAS has a lower overall sidelobe levels than PWT+SMF. The first sidelobe amplitude of PWT+rDAS is up to -16 dB. Figure 4-8 shows the experimental cyst images beamformed using DAS, PWT+rDAS and PWT+SMF. All images are displayed with a dynamic range of 40 dB. Table 4 summarizes the CNR values of cyst images in different cases that quantified the contrast of the images. At 20 mm depth, PWT+SMF has a CNR value of 3.54. This is higher than CNRs of DAS and PWT+rDAS, which are 2.68 and 2.04 respectively. At 40 mm depth, CNRs for PWT+rDAS and PWT+SMF are 2.29 and 3.81, whereas DAS provides an image CNR of 4.74, which is the highest among the three methods. Table 4: CNR values for experimental images containing anechoic cysts of 4 mm diameter and 6 mm diameter using DAS, PWT+rDAS and PWT+SMF. DAS PWT+rDAS PWT+SMF Cysts located at 20 mm 2.68 2.04 3.54 Cysts located at 40 mm 4.74 2.29 3.81 In the experimental results, PWT+SMF shows a CNR value that is 19.6% lower than DAS at 40 mm depth. This drop in CNR is not seen in the Field II simulations. One reason for this disparity could be the different noise levels of spatial matched filters in experiments and in simulations. Further investigation was performed with Field II simulations. 65 4.3.4 Field II simulations with filters containing noise The ideal spatial matched filter should be acquired from a point target placed at a specific position in field without noise. This goal can easily be achieved with computer simulations. However, for experimental acquisition, some noise is unavoidable. Experimentally acquired filters with VDAS had a signal-to-noise ratio (SNR) of 40 dB. To test the influence of filters with noise on image contrast for SMF beamforming, the same amount of noise was deliberately added in when generating spatial matched filters in Field II simulations. (a) DAS (b)PWT+SMF,noise-free filters (c) PWT+SMF, filters with noise CNR = 5.14 CNR = 5.34 CNR = 4.51 Figure 4-9: Images with an anechoic cyst of 6 mm in diameter at 40 mm depth from Field II simulations of different beamforming methods: (a) DAS, (b) PWT+SMF with noise-free filters, and (c) PWT+SMF with filters containing noise (SNR = 40 dB). Figure 4-9 shows images of a 6 mm diameter anechoic cyst, positioned at the depth of 40 mm, with DAS, PWT+SMF with noise-free filters, and PWT+SMF with filters containing noise. All images are displayed with a dynamic range of 40 dB. As shown in Figure 4-9 (a) and (b), CNRs for DAS and PWT+SMF with noise-free filters are 5.14 and 5.34 respectively. In Figure 4-9 (c), where the filters have an SNR of 40 dB, a CNR of 4.51 is seen with PWT+SMF, which 66 is 16.6% lower than that of DAS. The CNR values indicate that the image contrast of SMF beamforming is diminished if the filters have noise. 4.4 Conclusions and discussion In this chapter, I demonstrated the feasibility of beamforming by spatial matched filtering (SMF) with plane wave transmissions (PWT) for high frame-rate ultrasound imaging. I showed the capability of SMF beamforming with PWT to effectively focus both transmit and receive beams at every depth using mathematical analysis based on the Rayleigh-Sommerfeld diffraction theory. Both simulation data generated by Field II and experimental data acquired by the VDAS system were processed using DAS, PWT+rDAS and PWT+SMF beamforming methods. Results indicated that PWT+SMF was able to perform transmit-receive focusing throughout the field of view, and provided comparable lateral resolution and image contrast to DAS at the transmit focal depth. Current limitations, such as inevitable filter noise during experimental acquisition, lead to moderate degradation of image quality with SMF beamforming. Nevertheless, PWT+SMF showed better lateral resolution and image contrast compared to PWT+rDAS at every depth in our experiments. When experimentally acquiring filters, the relative position of the wire target to the transducer array could also have some influence on the quality of the filters. A human hair, used for the experiments described in this work, was assumed to be perpendicular to the image plane. Because the human hair was aligned manually, imperfect positioning could result in a filter with limited performance. Future work will focus on acquiring filters with better performance 67 through aligning the wire targets mechanically during experiments, and improving the SNR of the filters. Future work also involves enhancing image quality by applying other signal processing algorithms to SMF beamformers, such as adaptive imaging by dual apodization with cross- correlation (DAX) (Seo & Yen, 2008) or generalized coherence factors (GCF) (Li & Li, 2003). These methods have been demonstrated to be capable of improving image contrast with conventional delay-and-sum beamforming. I will investigate their capability of contrast improvement with SMF beamforming. Additionally, I plan to implement SMF beamforming to array transducers with the dual-layer design for 3-D imaging (Chen et al., 2011)(Chen, Nguyen, & Yen, 2012), where transmitters are elongated array elements emitting plane-wave pulses during imaging, to achieve both transmit and receive focusing. 68 Chapter 5 Processing on SMF beamforming using dual apodization with cross-correlation for enhanced image contrast 5.1 Introduction In conventional linear array imaging, separate focusing strategies are applied during pulse transmission and echo reception. To meet real-time imaging requirements, transmit focusing is usually performed at a single depth, or a few discrete depths. On receive, conversely, beams are dynamically focused at every depth to achieve uniform beamforming using the delay-and-sum (DAS) method. Therefore, the best lateral resolution, which is determined by the product of transmit and receive beamwidths, only happens at the transmit focal depth. Improvements of beamforming involve methods that can uniformly focus both transmit and receive beams throughout the field of view, without decreasing frame-rate or signal-to-noise ratio (SNR) of the imaging system. Kim et al proposed a novel beamforming method by spatially matched filtering (SMF) the received radio frequency (RF) signals (Kim et al., 2006). In this method, fixed transmit focusing was applied as in conventional array imaging systems. On receive, instead of being processed by dynamic DAS beamforming, RF signals from each receive element are passed through spatial matched filters constructed from the transmit-receive impulse response of the system, and the filtered signals are then summed up along the receive aperture. Their results showed that with transmit beams focused at a single depth, SMF beamforming was able to 69 perform both transmit and receive focusing effectively at all depths. It provided comparable lateral resolution and image contrast throughout field of view to DAS beamforming at transmit focus. The goal of ultrasonic beamforming is to focus all available acoustic energy to one location in the imaging field (Macovski, 1983). The same as DAS beamforming, there are also sidelobes and clutter inherent in ultrasound imaging with SMF beamforming, where spatial matched filters are used for concentrating and spatially registering echo energy from each receive element. The side effects of sidelobes and clutter are undesirable because they degrade the image quality by lowering contrast-to-noise ratio (CNR) of the system. Different techniques, such as apodization shading, spatial compounding, and frequency compounding, were utilized to suppress sidelobe and clutter levels, but at the expense of worsened spatial resolution, increased computation load, or reduced imaging frame-rate (Shankar, 1986)(Forsberg, Healey, Leeman, & Jensen, 1991). Seo and Yen proposed a sidelobe suppression technique known as dual-apodization with cross correlation, or DAX (Seo & Yen, 2008). In this method, two distinct receive apodization functions were used to create two point spread functions that were similar in mainlobe signals but obviously different with clutter patterns. Cross-correlation coefficients of the beamformed RF signals from the two receive apodizations were then calculated and used to generate a weighting matrix. This matrix was finally multiplied to the combined beamformed RF data acquired from the two apodizations. Results indicated that DAX was capable of improving image contrast remarkably by suppressing sidelobe and clutter levels without worsening lateral 70 or resolution, or increasing computational complexity significantly. The apodization strategy of alternating patterns, in which two complementary apodization functions with alternating elements enabled on one but disabled on the other, was reported to have the greatest CNR improvement. A follow-up study showed that due to the random nature of speckle, artifactual black spots may arise at regions away from the transmit focus in DAX-processed images. A dynamic DAX algorithm, in which different alternating patterns were used at different imaging depths, was proposed to remove the artifacts. However, the decision about which alternating pattern to use need to be specified for optimal results with this method (Seo & Yen, 2009). In this chapter, I applied the DAX technique to SMF beamforming for enhanced image contrast by suppressing sidelobe levels. The goal is to achieve improved CNR of images throughout field of view without introducing the artifactual black spots. I evaluated the performance of SMF beamforming with DAX using both computer simulations using Field II (Jensen & Svendsen, 1992) and experimental data from a four-board Verasonics data acquisition system, VDAS (Verasonics, Redmond, WA), and compared the results with DAS beamforming. In addition, electronic aberrators were added to the experimental data sets to test the robustness of the proposed method. 71 5.2 Methods 5.2.1 Beamforming by spatially matched filtering (SMF) According to the Rayleigh-Sommerfeld diffraction theory (Goodman, 1996), the expression of complex pulse-echo field at field point (𝑥,𝑧) with frequency 𝜔 can be written as 𝜓 ! (𝑥,𝑧)= 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! 𝑎 ! 𝑥 ! ′ 𝑒 ! 𝑗𝑘𝑥 𝑥 ! ! 𝑧 𝑒 𝑗𝑘 𝑥 ! !" !𝑧 ! !! 𝑑 𝑥 ! ′ (10) with wavelength 𝜆 and wave number 𝑘= !! ! . 𝑎 𝑡 𝑥 ! and 𝑎 𝑟 𝑥 ! are the transmit aperture function and the receive aperture function of assuming coordinate 𝑥 ! on the array surface (𝑥 ! ′ is a dummy variable for integration.). Beamforming, or focusing, is mathematically equivalent to eliminating the quadratic phase factors in equation (10). Conventional delay-and-sum (DAS) beamforming achieves this goal by multiplying 𝑒 !!"! ! ! !! ! and 𝑒 !!"! ! ! !! ! ! to the integrands of the transmit term and the receive term respectively, where 𝑧 ! and 𝑧 ! ′ are transmit focus and receive focus. The pulse-echo field with DAS beamforming is 𝜓 !,!"# (𝑥,𝑧) = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 !𝑘 𝑥 ! ! ( ! !! ! ! !! ! ) ! !! 𝑑 𝑥 ! 𝑎 ! 𝑥 ! ′ 𝑒 ! 𝑗𝑘𝑥 𝑥 ! ! 𝑧 ! !! 𝑒 !𝑘 𝑥 ! ! ! ( ! !! ! ! !! ! ! ) 𝑑 𝑥 ! ′ (11) At position 𝑧= 𝑧 ! = 𝑧 ! ′, where both transmit and receive beams are focused at, the quadratic phase factors are cancelled out, and the pulse-echo field pattern then turns into 72 𝜓 !,!"# 𝑥,𝑧 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 ! !! 𝑑 𝑥 ! 𝑎 ! 𝑥 ! ′ 𝑒 ! 𝑗𝑘𝑥 𝑥 ! ! 𝑧 ! !! 𝑑 𝑥 ! ! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! 𝑢 𝑥 𝐴 ! 𝑢 𝑥 (12) Equation (12) indicates that the field pattern is the product of 𝐴 ! 𝑢 𝑥 =ℑ[𝑎 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 and 𝐴 ! 𝑢 𝑥 =ℑ[𝑎 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 , which are spatial Fourier transforms of the transmit aperture function 𝑎 𝑡 𝑥 ! and the receive aperture function 𝑎 𝑟 𝑥 ! . Therefore, diffraction-limited lateral resolution can be attained at the transmit-receive focus (Goodman, 1996). For conventional array imaging systems, where dynamic focusing is performed on receive, the best pulse-echo resolution happens at the transmit focus. The goal of SMF beamforming is to achieve the field pattern expressed as in equation (12) at every depth. With SMF beamforming, cancellation of the quadratic phase factors is accomplished by convolving pulse-echo complex field with the spatial matched filters, which are constructed from the transmit-receive spatial impulse response of the imaging system (Kim et al., 2006). In this method, signals from each individual receive element are passed through the 2-D spatial matched filters first, and then the filtered signals are summed up for different elements. For a receive element located at 𝑥 ! = 𝑥 𝑟 , the receive aperture function can be approximated as 𝑎 𝑟 𝑥 ! = 𝛿 (𝑥 ! −𝑥 𝑟 ) if the element width is smaller than wavelength 𝜆. Thus, receive field 𝜑 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 at field point (𝑥 ,𝑧 ) from element at 𝑥 𝑟 is expressed as 73 𝜑 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑎 ! 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝛿 (𝑥 ! −𝑥 𝑟 )𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 𝑗𝑘 𝑥 ! ! !𝑧 ! !! 𝑑 𝑥 ! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑒 𝑗𝑘 ! ! ! !𝑧 (13) Pulse-echo field pattern from the receive element located at 𝑥 𝑟 of SMF beamforming with transmit focus of 𝑧 ! becomes 𝜓 𝜔 𝑥 ,𝑧 ;𝑥 𝑟 =𝜑 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 𝜑 𝜔 𝑥 ,𝑧 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑒 𝑗𝑘 ! ! ! !𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑒 !𝑘 𝑥 ! ! ( ! !! ! ! !! ! ) ! !! 𝑑 𝑥 ! (14) Therefore, the pulse-echo point spread function for SMF beamforming is 𝜓 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 =𝜓 𝜔 𝑥 ,𝑧 ;𝑥 𝑟 ∗𝜓 𝜔 ∗ −𝑥 ,𝑧 ;𝑥 𝑟 = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘𝜏 𝑥 ! 𝑧 𝑒 !𝑘 𝑥 ! ! ! !! ! ! !! ! ! !! 𝑑 𝑥 ! 𝑎 𝑡 𝑥 ! 𝑒 ! 𝑗𝑘 𝑥 !𝜏 𝑥 ! 𝑧 𝑒 !!𝑘 ! ! ! ! !! ! ! !! ! ! !! 𝑑 𝑥 ! 𝑑𝜏 ! !! = 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 𝑥 ! 𝑎 𝑡 𝑥 ! 𝑒 !𝑘 (𝑥 ! ! !𝑥 ! ! )( ! !! ! ! !! ! ) 𝑒 ! 𝑗𝑘𝜏 𝑥 ! !𝑥 ! 𝑧 𝑑𝜏 ! !! 𝑑 𝑥 ! ! !! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑑 𝑥 ! ! !! = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 𝑥 ! 𝑎 𝑡 𝑥 ! 𝑒 !𝑘 (𝑥 ! ! !𝑥 ! ! )( ! !! ! ! !! ! ) 𝛿 𝑥 ! −𝑥 ! 𝑑 𝑥 ! ! !! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑑 𝑥 ! ! !! = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑎 𝑡 ! 𝑥 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 ! 𝑧 𝑑 𝑥 ! ! !! = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝐴 ! ,𝑡 𝑢 𝑥 (15) where 𝐴 ! ,𝑡 𝑢 𝑥 =ℑ[𝑎 𝑡 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 is the spatial Fourier transform of the square of the transmit aperture function 𝑎 𝑡 (𝑥 ! ). 74 Finally, the filtered fields are summed up along the receive aperture with weighting by the square of the receive aperture function 𝑎 𝑟 𝑥 ! . 𝜓 𝜔 ,𝑆𝑀𝐹 𝑥 ,𝑧 = 𝑎 𝑟 ! (𝑥 𝑟 ) ! !! 𝜓 𝜔 ! 𝑥 ,𝑧 ;𝑥 𝑟 𝑑 𝑥 𝑟 = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! ,𝑡 𝑢 𝑥 𝑎 𝑟 ! 𝑥 𝑟 ! !! 𝑒 ! 𝑗𝑘𝑥 𝑥 𝑟 𝑧 𝑑 𝑥 𝑟 = 2𝜋𝑧 𝑘 𝑒 𝑗𝑘𝑧 𝑗𝜆𝑧 ! 𝐴 ! ,𝑡 𝑢 𝑥 𝐴 ! ,𝑟 𝑢 𝑥 (16) where 𝐴 ! ,𝑟 𝑢 𝑥 =ℑ[𝑎 𝑟 ! (𝑥 ! )] 𝑢 𝑥 ! 𝑥 𝜆𝑧 is the spatial Fourier transform of the square of the receive aperture function 𝑎 𝑟 (𝑥 ! ). Equation (16) shows that the quadratic phase factors for both transmit and receive field patterns are removed at any depth 𝑧 after receive fields are spatially matched filtered. Therefore, two-way focusing is achieved throughout field of view by SMF beamforming, though only a single transmit focus was implemented. 5.2.2 Dual apodization with cross-correlation (DAX) The technique of dual apodization with cross-correlation (DAX) can suppress sidelobe and clutter levels without widening the mainlobe, thus improve the spatial contrast within ultrasound imaging systems (Seo & Yen, 2008). The approach is based on the fact that if two different receive apodization functions are applied during imaging, they will generate two point spread functions that have similar mainlobe signals, but quite different clutter patterns. Therefore, echoes from targets that are dominated by the mainlobe components, such as speckle, 75 will be similar, whereas echo signals from targets dominated mainly by clutter, such as anechoic cysts, will appear notably different. In the DAX method, two beamformed RF data sets are created by the two distinct apodization functions. Normalized cross-correlation (NCC) coefficients are calculated to quantify the degree of similarity between the two data sets, and used to form a weighting matrix. The weighting matrix is then multiplied to the summation of the two data sets. There are different apodization schemes to realize DAX during ultrasound imaging. In this chapter, all results presented used a 6-6 alternating apodization scheme to implement DAX, in which the first aperture enables and disables 6 consecutive elements alternately, and the second aperture only enables the elements that are not used in the first aperture. In conventional DAS beamforming with dynamic receive focusing, it has been shown that the 6-6 alternating apodization is able to achieve high CNRs (Seo & Yen, 2008). However, artificial black spots arise in the regions away from transmit focus prevalently. According to the hypothesis presented in reference (Seo & Yen, 2009), the artifacts appear when the grating lobes, introduced by the alternating apodization of aperture, dominate the signals. Since the levels of grating lobes and clutter are higher at depths away from transmit focus, the artifacts become more visible at these depths. 5.2.3 Application of DAX to SMF beamforming With fixed transmit focusing, receive echo signals from each individual element were processed by 2-D spatial matched filters. These filters were acquired by scanning a point target 76 placed at the lateral center of the field at desired depth. After filtering the pulse-echo field using the pre-acquired filters and before the final summation along receive aperture, DAX was applied to the beamformed data to suppress the sidelobes and clutter. DAX was performed using a 6-6 alternating apodization scheme. The NCC coefficients were calculated using segments of beamformed data along axial direction at zero lag, and the length of the segments was typically chosen as 2 to 3 wavelengths empirically. The beamformed data was then multiplied by the weighting matrix, which was composed of NCC coefficients ranging from 0.001 to 1 after thresholding, and median filtered to minimize the any artifacts. 5.2.4 Computer simulations Computer simulations with Field II (Jensen & Svendsen, 1992) were performed to evaluate the contrast improvements of SMF beamforming after being DAX processed. RF data was generated for a broadband 1-D linear array transducer, which is composed of 128 elements with an element pitch of 298 µm and an element height of 5 mm. The elements were exited by 5 MHz, 2-cycle sinusoidal pulses. An f-number of 2 was used throughout field of view. The transmit focus was set to 30 mm depth for both DAS and SMF beamforming. The generated RF data was imported to Matlab (Mathworks, Natick, MA) for beamforming, envelope detection, log compression, and image display. Point reflectors positioned at the depths of 20 mm, 30 mm, and 40 mm were used to construct spatial matched filters for SMF beamforming. 4 mm diameter anechoic cysts, also located at 20 mm depth, 30 mm depth, and 40 mm depth, embedded in scatterers were imaged 77 for contrast evaluation. Contrast to noise ratio (CNR) was calculated and compared to indicate contrast improvements before and after DAX processing for both DAS beamforming and SMF beamforming. 5.2.5 Experiments with phantoms During experiments, RF signals from individual receive channel were collected using a four-board Verasonics data acquisition system, or VDAS. A L7-4 1-D linear array transducer with 128 elements, spacing at 298 μm, was used in the experiments, and the transducer was excited by a 5 MHz, 2-cycle sinusoidal transmit pulse. A fixed f-number of 2 was used for all depths. The transmit focal depth of both DAS beamforming and SMF beamforming was at 30 mm. Offline beamforming of the acquired data was performed using Matlab. A human hair, serving as a point reflector, was placed at 20 mm depth, 30 mm depth, and 40 mm depth in a peanut oil bath. Spatial matched filters for SMF beamforming were constructed from scanning the human hair. Anechoic cysts, with a diameter of 4 mm, from an ATS tissue-mimicking phantom (Model 549, ATS Laboratories, Bridgeport, CT) were scanned for contrast assessment. CNRs were calculated and compared before and after being DAX processed for both DAS beamforming and SMF beamforming. 78 5.2.6 Experiments with phantoms – electronic phase aberrators To test the robustness of SMF beamforming when DAX is applied, phase aberrations were added in to the experimentally acquired data. Assuming the aberration is a near-field, random phase screen modeled by a Gaussian process, phase aberration could be generated by convolving Gaussian random numbers with a Gaussian function as described in (Dahl, Guenther, & Trahey, 2005). A 45 ns root-mean-square (rms), 5 mm full-width at half-maximum (FWHM) aberrator profile was created and applied on both transmit and receive for the experimental data. 5.3 Simulations and experimental results 5.3.1 Computer simulations of anechoic cysts Figure 5-1 shows the images of a 4 mm diameter anechoic cyst embedded in a phantom of scatterers. RF echo signals were generated by Field II program and processed using standard DAS (“DAS” column), DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). The centers of the cysts were placed at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. All images are displayed with a dynamic range of 50 dB. CNR values are presented along with the images for all cases. Before DAX is applied, SMF beamforming consistently shows a higher CNR than DAS beamforming at all depths. For DAS, at the transmit focal depth of 30 mm, DAX processing is not introducing any artifacts. However, at both 20 mm depth and 40 mm depth, artifactual black spots arise in the images after applying DAX. There are not any 79 artifacts shown up in the 3 image with SMF beamfroming after DAX processing, since SMF beamforming is able to perform effective transmit-receive at all depths with single transmit focusing. DAS DAS+DAX SMF SMF+DAX (a) 20 mm 3.29 6.31 5.00 8.11 (b) 30 mm 4.48 9.19 4.71 9.52 (c) 40 mm 2.46 4.74 6.94 11.37 Figure 5-1: Images containing a 4 mm diameter anechoic cyst from Field II simulations. RF data is processed using standard DAS (“DAS” column), DAS+DAX with 6-6 alternating 80 apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). Cysts are located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. The transmit focus for all cases is set to 30 mm depth. 5.3.2Experiments of anechoic cysts – without phase aberrations Through acquiring experimental signal using VDAS, images containing a 4 mm diameter anechoic cyst located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth, are generated and shown in Figure 5-2. CNR is calculated and presented in the figure for each case. The RF data is processed by standard DAS (“DAS” column), DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). All images are displayed with a dynamic range of 50 dB. CNRs indicate DAX improves image contrast for both DAS beamforming and SMF beamforming. Before DAX processing, SMF beamforming provides higher contrast than DAS at all depths. For DAS beamforming, artifacts appeare in the DAX processed images except for the one near the transmit focus of 30 mm. DAX is not bringing artifacts to SMF beamforming in any of the images shown in the figure. The experimental results agree with the Field II simulation results. 81 DAS DAS+DAX SMF SMF+DAX (a) 20 mm 3.34 5.44 5.62 9.46 (b) 30 mm 5.14 10.62 6.00 10.72 (c) 40 mm 3.02 7.32 6.18 9.89 Figure 5-2: Images containing an anechoic cyst of 4 mm diameter, along with their CNR values, from experiments with VDAS. Data is processed using standard DAS (“DAS” column), DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). Cysts are 82 located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. The transmit focal depth is 30 mm for all cases. 5.3.3 Experiments of anechoic cysts – with phase aberrations To test the robustness of SMF beamforming with 6-6 alternating apodization DAX, electronic phase aberrations are generated and applied to the experimental data acquired from VDAS. RF signals with presence of 45 ns rms, 5 mm FWHM aberrator are beamformed and compared using DAX beamforming and SMF beamforming when DAX is applied. Figure 5-3 shows the figures constructed from experimental data with the presence of electronic phase aberrations. The centers of the cyst are placed at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. CNRs are increased after DAX processing, expect for the image created by DAS at 20 mm depth, in which artifacts are extremely severe. With 6-6 alternating apodization DAX, SMF beamforming indicates superior performance to DAS beamforming in terms of both higher image contrast and less artifacts. Nevertheless, deformation of the cyst due to the added phase aberrations is seen in both beamforming methods. 83 DAS DAS+DAX SMF SMF+DAX (a) 20 mm 2.71 2.59 4.05 7.76 (b) 30 mm 4.43 9.04 4.89 9.77 (c) 40 mm 2.77 5.46 4.15 6.65 Figure 5-3: Images containing an anechoic cyst of 4 mm diameter from experiments with VDAS. A 45 ns rms, 5 mm FWHM aberrator profile is added to the experimental data. Figures are constructed from processing the signals using standard DAS (“DAS” column), 84 DAS+DAX with 6-6 alternating apodization (“DAS+DAX” column), standard SMF (“SMF” column), and SMF+DAX with 6-6 alternating apodization (“SMF+DAX” column). Cysts are located at (a) 20 mm depth, (b) 30 mm depth, and (c) 40 mm depth. The transmit focus is set to 30 mm for all cases. 5.4 Conclusions In this chapter, I demonstrated the validity of application of DAX, with 6-6 alternating apodization, to SMF beamforming to improve image contrast. The analysis based on the Rayleigh-Sommerfeld diffraction theory indicated that SMF beamforming is able to uniformly focus both transmit and receive beams at all imaging depths with a single transmit focal depth. Therefore, uniform image quality can be achieved throughout the field of view by using SMF beamforming. The performance of SMF beamforming before and after being DAX processed was evaluated using both Field II simulations and experimental data acquired from VDAS, and compared to DAS beamforming. SMF+DAX created uniform cyst images with improved spatial contrast throughout the field of view, and consistently showed superior results, especially at regions away from the transmit focus, to DAS+DAX. No artifactual black spots, as shown in images of DAS+DAX, were seen in the SMF+DAX images. In addition, the robustness of the proposed method was tested by experimental data with presence of electronic phase aberrations. CNRs were improved with SMF+DAX at all the imaging depth without introducing any artifacts. The deformation of the cysts was seen with both beamforming methods, because of the electronic phase aberrations added in. 85 Chapter 6 Conclusions and Future work 6.1 Conclusions In summary, this dissertation has presented the design, fabrication, and imaging experiments of two dual-layer array transducers. The idea behind the dual-layer design is to perform transmit beamforming and receive beamforming separately in two perpendicular directions and form a 3-D scanning volume. Prototypes were built for a planar dual-layer array for 3-D rectilinear imaging that has a center frequency of 7.5 MHz with a -6 dB bandwidth of 71%, and a cylindrical dual-layer array for 3-D transrectal imaging whose center frequency and - 6 dB bandwidth are 5.7 MHz and 62%. Synthetic aperture data sets were acquired from both arrays and beamformed offline. Real-time volumetric data acquisition was realized with the planar array. Wire phantoms and anechoic cyst phantoms were scanned to evaluate the spatial resolution and contrast of the dual-layer arrays. Generalized coherence factor (GCF) was used to enhance image contrast. There is only one-way focusing in each of the transmit and receive directions during dual-layer array imaging, which results in degraded image quality compared to two-way focusing using a 2-D array. Beamforming by spatial matched filtering was investigated to compensate for the image quality degradation. I have demonstrated the ability of SMF beamforming to focus both transmit and receive beams throughout field of view with plane wave 86 transmissions, which resembles the conditions during dual-layer array imaging. The performance of SMF beamforming with PWT was predicted by the Rayleigh-Sommerfeld diffraction analysis, and evaluated using spatial resolution and contrast with both computer simulations and experimental data. The processing of dual apodization cross-correlation (DAX) was applied to SMF beamforming to further enhance image contrast. With fixed transmit focusing, anechoic cyst images showed that the improvements brought by DAX is comparable for DAS beamforming and SMF beamforming at the transmit focus. However, no artifacts were introduced with SMF beamforming than DAS beamforming after DAX processing. 6.2 Future work Though the Rayleigh-Sommerfeld diffraction analysis showed that two-way focusing can be achieved by SMF beamforming at all depths, the practical performance can behave quite differently from what has been predicted. One of the reasons is that during the Rayleigh- Sommerfeld analysis, certain mathematical approximations, such as the paraxial approximation, were used. These approximations may not be always valid in the near field. In addition, broadband results cannot be accurately predicted by the narrowband equations. Deeper insights into the actual behaviors of SMF beamforming under different conditions, especially when the approximations involved in the field analysis are likely to be invalid, are needed for broadband systems. Having demonstrated the performance of SMF beamforming with 1-D arrays, the next step is to implement SMF to dual-layer arrays for 3-D imaging. Field II simulation would be 87 performed to predict the performance of SMF beamforming with dual-layer arrays. During experimental implementation, some practical issues must be considered. The transmit-receive impulse response of the system, which is used to construct the spatial matched filter, should be acquiring by scanning a point target in a 3-D volume. A human hair, which is actually a wire target, cannot be used for creating filters in 3-D imaging. A gelatin phantom with a single point target suspended inside might be needed. Nevertheless, a dual-layer transducer with more uniform element-to-element performance is always preferred for 3-D imaging regardless which beamforming method is used. Throughout my work with SMF beamforming, I emphasized its feasibility in improving focusing in the elevation direction, in which receive elements compose a 1-D array, of the dual- layer 3-D imaging. The reason is that the spatially matched filtering happens at each individual receive and then the filtered signals are summed up. This mode is called a “filtering before summing” approach. In the azimuth direction of a dual-layer array, individual elongated receive elements are used to detect echoes, and signals collected at each receive channel have already been summed. Therefore, the “filtering before summing” approach is not applicable in the azimuth direction of the dual-layer arrays. There is also a “filtering after summing” approach to implement SMF beamforming. This is a much simpler procedure because only one-time filtering is needed for the beamforming. Theoretical field analysis (Kim et al., 2006) shows the “filtering after summing” approach has a narrower beamwidth compared to one-way DAS beamforming. However, the clutter levels of this approach are as high as those of one-way DAS beamforming. Though the “filtering after summing” approach will not work as well as “filter before summing”, 88 it can still be implemented to dual-layer arrays to improve spatial resolution in the azimuth direction during 3-D imaging. Additionally, the performance of SMF beamforming with curved arrays will also be studied. The same as linear arrays, all of theoretical field analysis, Field II simulations and experimental tests are required to demonstrate the feasibility of SMF beamforming with curved arrays, which would eventually lead to the implementation of SMF beamforming to cylindrical dual-layer arrays for 3-D transrectal imaging. The ultimate goal of my thesis is to provide a real-time, 3-D ultrasound imaging system that has comparable image quality to systems with fully sampled 2-D arrays. Table 5 summarizes the comparisons between systems using fully sampled 2-D arrays and systems using dual-layer arrays with SMF beamforming implemented. In terms of fabrication and interconnection simplicity, the dual-layer design provides a more practical way of constructing transducer arrays for 3-D imaging. There are 4 dimensions of focusing involved in real-time, 3- D imaging, which are transmit (Tx) and receive (Rx) focusing in the azimuth direction and transmit and receive focusing in the elevation direction respectively. In the context of real-time, 3-D imaging, systems with fully sampled 2-D arrays can achieve receive focusing in both the azimuth and elevation direction through parallel receive processing. However, transmit focusing is compromised in both directions. For systems with dual-layer arrays, by using the “filtering before summing” approach, uniform transmit and receive focusing can be performed in the elevation direction. Transmit beamforming is done in the azimuth direction using transmit sub- apertures. In the meantime, receive beams can be narrowed if the “filtering after summing” approach is applied in this direction. The above facts indicate that systems using dual-layer 89 arrays with SMF beamforming has the potential to provide better overall focusing than systems using fully sampled 2-D arrays. Table 5: Comparison between real-time 3-D systems using fully sampled 2-D arrays and systems using dual-layer arrays with SMF beamforming implemented. Fully sampled 2-D arrays Dual-layer arrays with SMF beamforming Fabrication and interconnection simplicity × √ Focusing Azimuth Tx - √ Rx √ - Elevation Tx - √ Rx √ √ 90 Bibliography Chen, Y., Nguyen, M., & Yen, J. T. (2011). 7.5 MHz dual-layer transducer array for 3-D rectilinear imaging. 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Description: % Performs synthetic data acquisition with dual-layer transducers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all; %%%%% depth, determin PRF %%%%% clear depth depth = 155; save depth depth for ii =1:64 save ii ii load depth % aper = [zeros(1,ii-1),ones(1,1),zeros(1,256-ii)]; aper = [zeros(1,2*(ii-1)),ones(1,2),zeros(1,256-2*ii)]; SetUp_synthetic_yuling(depth,aper); VSX_yuling; close all; mat=cell2mat(RcvData); mat=double(mat); sz=size(mat); avg=zeros(sz(1),sz(2)); %%%%% averaging %%%%% for jj = 1:100 avg = avg + mat(:,:,jj); end avg = avg/100; tx = avg; load ii frr = ['save ',strcat('tx',num2str(ii)),' tx;']; eval(frr); end delete ii.mat 95 Appendix B: DAS beamforming with dual-layer transducers in Matlab %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: DualLayer_BF_GCF % 2. Description: % Delay-and-sum beamforming with dual-layer transducers %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all;clc; f_sample = 36; % sampling frequency, in MHz fs = f_sample*1e6; % sampling frequency, in Hz c = 1520; % sound speed, in m/s %%%%%%%% RX beamforming %%%%%%%% N_element = 256; % number of RX elements (channels) aper_sz = 128; % aperture size no_lines = 257; % number of image lines pitchRX = 0.150e-3; % pitch on RX makedir('RXBF_data') offset = 32; offset_mm = ceil((c/2/1000)*offset/f_sample); if offset_mm == 0 offset_mm = 1; end %%%% creating focal zone %%%% inc = 1; % increment of dynamic focusing, in mm dep_max = 51; % max depth of focal zone, in mm focal_zones = [offset_mm : inc : dep_max]'/1000; focus_times = (focal_zones-(inc/2)/1000)/(c/2); % in s focus_times1 = floor(focus_times*fs-offset); % in samples focus_times1(1) = 1; Nf = max(size(focal_zones)); % number of foci %%%% creating delay matrix %%%% ele_pos = (-(N_element-1)/2:(N_element-1)/2)*pitchRX; %%%% aper_start and line_pos for 257 image lines aper_start = [ones(1,65),2:128,129*ones(1,65)]; line_pos = (-(no_lines-1)/2:(no_lines-1)/2)*pitchRX; for line_no_rx = 1:no_lines for i = 1:Nf 96 aper_pos = ele_pos(aper_start(line_no_rx):aper_start(line_no_rx)+aper_sz-1); delays1(i,:,line_no_rx) = sqrt( (line_pos(line_no_rx)-aper_pos).^2 + focal_zones(i).^2 )/c - focal_zones(i)/c; end end delays = round(delays1*fs)+1; clear delays1 %%%% end creating delay matrix %%%% %%%% expanding aperture code %%%% NF_max = 3; fn = 2; % f-number New_aper_sz = round(focal_zones/(fn*pitchRX))+rem(round(focal_zones/(fn*pitchRX)),2); % second term is to make New_aper_sz even number for i = 1:Nf if New_aper_sz(i) > aper_sz New_aper_sz(i) = aper_sz; end end for line_no_rx = 1:no_lines aper_st_pos = ele_pos(aper_start(line_no_rx):aper_start(line_no_rx)+aper_sz-1)-pitchRX/2; % position of the START(left edge) of each element in the active aperture for depth = 1:Nf-NF_max clear pre post dd = focus_times1(depth+1)-focus_times1(depth)+1; if line_pos(line_no_rx) <= aper_st_pos(1+New_aper_sz(depth)/2) % translates to: if line position is <= the postion of the left edge of the center ele in the aperture pre = []; post = zeros(dd,aper_sz-New_aper_sz(depth)); elseif line_pos(line_no_rx) >= aper_st_pos(1+aper_sz- New_aper_sz(depth)/2) post = []; pre = zeros(dd,aper_sz-New_aper_sz(depth)); else shift1 = round((line_pos(line_no_rx)- aper_st_pos(1+New_aper_sz(depth)/2))/pitchRX); pre = zeros(dd,shift1); post = zeros(dd,aper_sz-New_aper_sz(depth)-shift1); end Exp_aper_mask(focus_times1(depth):focus_times1(depth+1),1:aper_sz, line_no_rx ) = ... logical([pre,ones(dd,New_aper_sz(depth)),post]); end end %%%% end expanding aperture code %%%% %%%% create LowPass for GCF %%%% m0 = 2; LPF = [zeros(1,(aper_sz-2*m0)/2),ones(1,2*m0),zeros(1,(aper_sz-2*m0)/2)]; 97 I = BandpassFilter2(4.8375,10.1625,f_sample); %%%% start beamforming %%%% for txID = 1:128 txID clear tx tx_f sub_rf delay_buffer total GCF load(['averagedRF/tx',num2str(txID),'.mat']) for ele_no = 1:N_element tx_f(ele_no,:) = conv(I,tx(1:3000,ele_no)); % tx_f(samples,ele_no) end tx_f = tx_f(:,33:end-31); for line_no_rx = 1:no_lines sub_rf = tx_f(aper_start(line_no_rx):aper_start(line_no_rx)+aper_sz- 1,:)'; for depth = 1:Nf-NF_max for ele_no = 1:aper_sz delay_buffer(focus_times1(depth):focus_times1(depth+1),ele_no) = sub_rf(delays(depth,ele_no,line_no_rx)+focus_times1(depth):delays(depth,ele_n o,line_no_rx)+focus_times1(depth+1),ele_no); end end delay_buffer = delay_buffer.*Exp_aper_mask(:,:,line_no_rx); total(line_no_rx,:) = sum(delay_buffer'); %%%%%%%%%% calculate GCF %%%%%%%%%% for iii = 1:length(delay_buffer) d_line = delay_buffer(iii,:); d_line_ft = fft(d_line); d_line_ft_f = d_line_ft.*fftshift(LPF); GCF(iii,line_no_rx) = sum(abs(d_line_ft_f).^2)./(eps^20+sum(abs(d_line_ft).^2)); end end %%%%%%% apply GCF %%%%%%%%%%%% cmd = ['save RXBF_data/total',num2str(txID),' total GCF'];eval(cmd); total_RXBF(txID,:,:) = total(:,1:end).*GCF(1:end,:)'; end save total_RXBF total_RXBF %**************************************************************************** %%%%%%%% TX beamforming %%%%%%%% clear all load total_RXBF.mat 98 f_sample = 36; % sampling frequency, in MHz fs = f_sample*1e6; % sampling frequency, in Hz c = 1520; % sound speed, in m/s N_element = 128; aper_sz = 64; pitchTX = 0.30e-3; no_lines = 257; makedir('TXRXBF_data') offset = 32; offset_mm = ceil((c/2/1000)*offset/f_sample); if offset_mm == 0 offset_mm = 1; end inc = 1; % increment of dynamic focusing, in mm dep_max = 45; % max depth of focal zone, in mm focal_zones = [offset_mm : inc : dep_max]'/1000; focus_times = (focal_zones-(inc/2)/1000)/(c/2); focus_times1 = floor(focus_times*fs-offset); focus_times1(1) = 1; Nf = max(size(focal_zones)); %%%% creating delay matrix %%%% ele_pos = (-(N_element-1)/2:(N_element-1)/2)*pitchTX; %%%% aper_start and line_pos for 257 image lines aper_start1 = [ones(1,65),2:128,129*ones(1,65)]; aper_start = round(aper_start1/2); line_pos = (-(no_lines-1)/2:(no_lines-1)/2)*0.5*pitchTX; for line_no_tx = 1:no_lines for i = 1:Nf aper_pos = ele_pos(aper_start(line_no_tx):aper_start(line_no_tx)+aper_sz-1); delays1(i,:,line_no_tx) = sqrt( (line_pos(line_no_tx)-aper_pos).^2 + focal_zones(i).^2 )/c - focal_zones(i)/c; end end delays = round(delays1*fs)+1; clear delays1 %%%% end creating delay matrix %%%% %%%% expanding aperture code %%%% NF_max = 1; fn = 2; New_aper_sz = round(focal_zones/(fn*pitchTX))+rem(round(focal_zones/(fn*pitchTX)),2); % second term is to make New_aper_sz even number for i = 1:Nf 99 if New_aper_sz(i) > aper_sz New_aper_sz(i) = aper_sz; end end fnum = focal_zones./(New_aper_sz*pitchTX); for line_no_tx = 1:no_lines for depth = 1:Nf-NF_max clear pre post dd = focus_times1(depth+1)-focus_times1(depth)+1; aper_st_pos = ele_pos(aper_start(line_no_tx):aper_start(line_no_tx)+aper_sz-1)-pitchTX/2; % position of the START of each element in the active aperture if line_pos(line_no_tx) <= aper_st_pos(1+New_aper_sz(depth)/2); pre = []; post = zeros(dd,aper_sz-New_aper_sz(depth)); elseif line_pos(line_no_tx) >= aper_st_pos(1+aper_sz- New_aper_sz(depth)/2); post = []; pre = zeros(dd,aper_sz-New_aper_sz(depth)); else shift1 = round((line_pos(line_no_tx)- aper_st_pos(1+New_aper_sz(depth)/2))/pitchTX); pre = zeros(dd,shift1); post = zeros(dd,aper_sz-New_aper_sz(depth)-shift1); end Exp_aper_mask(focus_times1(depth):focus_times1(depth+1),1:aper_sz, line_no_tx ) = ... logical([pre,ones(dd,New_aper_sz(depth)),post]); end end %%%% end expanding aperture code %%%% %%%% create LowPass for GCF %%%% m0=2; LPF=[zeros(1,(aper_sz-2*m0)/2),ones(1,2*m0),zeros(1,(aper_sz-2*m0)/2)]; I=BandpassFilter2(4.8375,10.1625,36); for line_no_rx=1:no_lines line_no_rx clear sub_rf_rx delay_buffer total GCF sub_rf_rx=squeeze(total_RXBF(:,line_no_rx,:)); for line_no_tx=1:no_lines clear sub_rf sub_rf=sub_rf_rx(aper_start(line_no_tx):aper_start(line_no_tx)+aper_sz-1,:)'; for depth=1:Nf-NF_max for ele_no=1:aper_sz delay_buffer(focus_times1(depth):focus_times1(depth+1),ele_no) = 100 sub_rf(delays(depth,ele_no,line_no_tx)+focus_times1(depth):delays(depth,ele_n o,line_no_tx)+focus_times1(depth+1),ele_no); end end delay_buffer=delay_buffer.*Exp_aper_mask(:,:,line_no_tx); total(line_no_tx,:) = sum(delay_buffer'); %%%%% GCF for iii=1:length(delay_buffer) d_line=delay_buffer(iii,:); d_line_ft=fft(d_line); d_line_ft_f=d_line_ft.*fftshift(LPF); GCF(iii,line_no_tx)=sum(abs(d_line_ft_f).^2)./(eps^20+sum(abs(d_line_ft).^2)) ; end end cmd=['save TXRXBF_data/total',num2str(line_no_rx),' total GCF'];eval(cmd); end %**************************************************************************** clear disp(' ') no_lines = 257; %%%%%%%%% create a memory space, in order to avoid "out of memory" problem load TXRXBF_data/total1; total_RXTXBF = zeros(max(size(total)),min(size(total)),257); clear total %%%%%%%%% apply GCF on RX %%%%%%%%%%%%% for i=1:257 cmd=['load TXRXBF_data/total',num2str(i)];eval(cmd); total_RXTXBF(1:max(size(total)),1:min(size(total)),i)=total(1:min(size(total) ),1:max(size(total)))'.*GCF(1:max(size(total)),1:min(size(total))); end env_RXTXBF = zeros(max(size(total)),min(size(total)),257); tic for i=1:no_lines i cmd=['load TXRXBF_data/total',num2str(i)];eval(cmd); env=abs(hilbert(total')); env_RXTXBF(:,:,i)=env; toc end save env_RXTXBF env_RXTXBF 101 Appendix C: Program for implementing Rayleigh-Sommerfeld analysis in Matlab %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: RaySom_FilterBeforeSumApprox3 % 2. Description: % Implementation of equations derived based on the Rayleigh-Sommerfeld diffraction theory %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all; j = sqrt(-1); f0 = 5e6; % center frequency c = 1540; % sound speed lambda = c/f0; % wavelength k = 2*pi/lambda; % wave number Tzf = 40/1000; % transmit focal depth, [m] Rzf = 40/1000; % receive focal depth, [m] z = 40/1000; % observation depth, [m] TBeta = 1/(2*z)-1/(2*Tzf); RBeta = 1/(2*z)-1/(2*Rzf); % transmit transducer coordinate, transmit aperture size x0T = -.01:25e-6:.01; at = ones(size(x0T)); % transmit aperture function % receive transducer coordinate, receive aperture size x0R = -.01:25e-6:.01; ar = ones(size(x0R)); % receive aperture function x1 = -.01:25e-6:.01; % observation coordinate, filter size x2 = -.02:25e-6:.02; % observation coordinate, imaging field phiDASTot = zeros(1,length(x2)); % DAS phiSMFTot1 = zeros(1,length(x2)); % SMF, no focusing (no beta involved) phiSMFTot2 = zeros(1,length(x2)); % SMF, transmit focusing %%%%%%%%%% transmit setup %%%%%%%%%%%%%%% %%%%% Tx for filters for a = 1:length(x1) % along observation coordinate for b = 1:length(x0T) % transmit transducer %%%%% without paraxial approximation clear R R = sqrt((x0T(b)-x1(a))^2+z^2); Tintegrand(b) = at(b)*(exp(j*k*R))/R*(z/R); % Equation (1) clear Tfactor 102 Tfactor = sqrt(Tzf^2+(x0T(b))^2)-Tzf; % factor = Rf-zf Tintegrand_DAS(b) = at(b)*(exp(j*k*R))/R*(z/R)*exp(-j*k*Tfactor); %%%% with paraxial approximation % Tintegrand(b) = at(b)*exp(-j*k*x0T(b)*x1(a)/z)*exp(j*k*x0T(b)*x0T(b)/(2*z)); % Tintegrand_DAS(b) = at(b)*exp(-j*k*x0T(b)*x1(a)/z)*exp(j*k*x0T(b)*x0T(b)*TBeta); end Tintegrand_sum1(a) = sum(Tintegrand); Tintegrand_sumDAS1(a) = sum(Tintegrand_DAS); end %%%%% Tx for imaging field for a = 1:length(x2) % along observation coordinate for b = 1:length(x0T) %transmit transducer %%%%% without paraxial approximation clear R R = sqrt((x0T(b)-x2(a))^2+z^2); Tintegrand(b) = at(b)*(exp(j*k*R))/R*(z/R); % Equation (1) clear Tfactor Tfactor = sqrt(Tzf^2+(x0T(b))^2)-Tzf; % factor = Rf-zf Tintegrand_DAS(b) = at(b)*(exp(j*k*R))/R*(z/R)*exp(-j*k*Tfactor); %%%% with paraxial approximation % Tintegrand(b) = at(b)*exp(-j*k*x0T(b)*x2(a)/z)*exp(j*k*x0T(b)*x0T(b)/(2*z)); % Tintegrand_DAS(b) = at(b)*exp(-j*k*x0T(b)*x2(a)/z)*exp(j*k*x0T(b)*x0T(b)*TBeta); end Tintegrand_sum2(a) = sum(Tintegrand); Tintegrand_sumDAS2(a) = sum(Tintegrand_DAS); end %%%%%%%%%%%%%%%%%% receive setup and beamforming %%%%%%%%%%%%%%%%%%%% for d = 1:length(x0R) % receive transducer %%%%% Rx for filters for a = 1:length(x1) % observation %%%%% without paraxial approximation clear R R = sqrt((x0R(d)-x1(a))^2+z^2); Receive1(a) = ar(d)*(exp(j*k*R))/R*(z/R); % Equation (1) clear Rfactor Rfactor = sqrt(Rzf^2+(x0R(d))^2)-Rzf; % Pfactor = Rf-zf Receive_DAS1(a) = ar(d)*(exp(j*k*R))/R*(z/R)*exp(-j*k*Rfactor); 103 %%%%% with paraxial approximation % Receive1(a) = ar(d)*exp(-j*k*x0R(d)*x1(a)/z)*exp(j*k*x0R(d)*x0R(d)/(2*z)); % Receive_DAS1(a) = ar(d)*exp(-j*k*x0R(d)*x1(a)/z)*exp(j*k*x0R(d)*x0R(d)*RBeta); end %%%%% Rx for imaging field for a2 = 1:length(x2) % observation %%%%% without paraxial approximation clear R2 R2 = sqrt((x0R(d)-x2(a2))^2+z^2); Receive2(a2) = ar(d)*(exp(j*k*R2))/R2*(z/R2); % Equation (1) clear Rfactor2 Rfactor2 = sqrt(Rzf^2+(x0R(d))^2)-Rzf; % Pfactor = Rf-zf Receive_DAS2(a2) = ar(d)*(exp(j*k*R2))/R2*(z/R2)*exp(-j*k*Rfactor2); %%%%% with paraxial approximation % Receive2(a2) = ar(d)*exp(-j*k*x0R(d)*x2(a2)/z)*exp(j*k*x0R(d)*x0R(d)/(2*z)); % Receive_DAS2(a2) = ar(d)*exp(-j*k*x0R(d)*x2(a2)/z)*exp(j*k*x0R(d)*x0R(d)*RBeta); end phiDAS = Tintegrand_sumDAS2.*Receive_DAS2; % Equation (10), plot DAS phiDASTot = phiDASTot + phiDAS; % DAS %%%%%%%% PWT+SMF %%%%%%%% phi1 = Tintegrand_sum1.*Receive1; % Equation (10), for filters phi2 = Tintegrand_sum2.*Receive2; % Equation (10), for imaging field phiSMF1 = conv(phi2,fliplr(conj(phi1)),'same'); phiSMFTot1 = phiSMFTot1+phiSMF1; % add unfiltered results %%%%%%%% Tx focusing+SMF %%%%%%%% phiTx1 = Tintegrand_sumDAS1.*Receive1; % no Rx focusing, for filters phiTx2 = Tintegrand_sumDAS2.*Receive2;% no Rx focusing, for imaging field phiSMF2 = conv(phiTx2,fliplr(conj(phiTx1)),'same'); % no filter,filter size! = field size phiSMFTot2 = phiSMFTot2+phiSMF2; end phiDASTot = abs(phiDASTot)/max(abs(phiDASTot)); phiSMFTot1 = abs(phiSMFTot1)/max(abs(phiSMFTot1)); phiSMFTot2 = abs(phiSMFTot2)/max(abs(phiSMFTot2)); 104 Appendix D: SMF beamforming with PWT in Matlab %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: SMF_PWT % 2. Description: % SMF beamforming with plane wave transmissions %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all;clc; f_sample = 20; % samling rate, in MHz fs = f_sample*1e6; c = 1540; % sound speed N_element = 128; aper_sz = 64; pitch = 298e-6; dx = 298e-6; no_lines = 65; centFreq = 5; BW = 0.5; low_f = (2-BW)*centFreq/2; high_f = (2+BW)*centFreq/2; I = BandpassFilter2(low_f,high_f,f_sample); z_start = 10; offset_mm = z_start; offset = round(offset_mm/1000/c*2*fs); if offset_mm == 0 offset_mm = 1; end dep_mx = 50; % in mm focal_zones = [offset_mm:1:dep_mx]'/1000; focus_times = (focal_zones-0.5/1000)/(c/2); focus_times1 = floor(focus_times*fs-offset); focus_times1(1) = 1; % to BF data from 0 mm up to 1.5 mm with focus at 1 mm Nf = max(size(focal_zones)); for i = 1:length(focus_times1) if (focus_times1(i)<1) focus_times1(i) = 1; end end ele_pos = (-(N_element-1)/2:(N_element-1)/2)*pitch; aper_start = 1:65; % 65 lines line_pos = ( -(no_lines-1)/2:(no_lines-1)/2 )*dx; load cysts_LambdaPitch_Tx64Rx128.mat sta3d1 = v'; for kk = 1:128 sta3d(kk,:) = downsample(sta3d1(kk,:),10); end data_sz = max(size(sta3d)); % number of points per receive channel per Tx load('PWT_SMFfilter_NoBPF_20mm.mat') % load filters load('PWT_SMFfilter_NoBPF_30mm.mat') 105 load('PWT_SMFfilter_NoBPF_40mm.mat') SMFilter1 = sub_img_20mm; SMFilter2 = sub_img_30mm; SMFilter3 = sub_img_40mm; %%%%%%% filtering the raw RF data %%%%%%%%%% for ii = 1:128 sta3d_f(ii,:) = conv(squeeze(sta3d(ii,:)),I,'same'); % [tx,rx,samples] end sta3d_f1 = sta3d_f(:,150:408); sta3d_f2 = sta3d_f(:,409:667); sta3d_f3 = sta3d_f(:,668:926); for rx = 1:aper_sz sub_rf2_1 = squeeze(sta3d_f1(rx:rx+no_lines-1,:)); % sta3d_f1 [tx,rx,samples] sub_rf2_2 = squeeze(sta3d_f2(rx:rx+no_lines-1,:)); % sub_rf2_# [tx,rx (64 elements) ,samples] sub_rf2_3 = squeeze(sta3d_f3(rx:rx+no_lines-1,:)); channelRx_TxFocused1 = sub_rf2_1; channelRx_TxFocused2 = sub_rf2_2; channelRx_TxFocused3 = sub_rf2_3; sub_filter1 = squeeze(SMFilter1(rx,:,:)); %image line, samples sub_filter2 = squeeze(SMFilter2(rx,:,:)); sub_filter3 = squeeze(SMFilter3(rx,:,:)); %%%%% 2-D spatial matched filtering %%%%% sub_img_SMF1(rx,:,:) = conv2(channelRx_TxFocused1,fliplr(flipud(conj(sub_filter1))),'same'); sub_img_SMF2(rx,:,:) = conv2(channelRx_TxFocused2,fliplr(flipud(conj(sub_filter2))),'same'); sub_img_SMF3(rx,:,:) = conv2(channelRx_TxFocused3,fliplr(flipud(conj(sub_filter3))),'same'); end total1 = squeeze(sum(sub_img_SMF1,1)); total2 = squeeze(sum(sub_img_SMF2,1)); total3 = squeeze(sum(sub_img_SMF3,1)); total=[total1';total2';total3']; env = abs(hilbert(total(1:end,:))); env = env/max(max(env)); env_log = 20*log10(env); [r,d] = size(env); offset = offset+667; rx_axis = ((1:(d-1))*dx-d*dx/2)*1000; ax_axis = (c/2000)*(offset:offset+r)/f_sample; figure;imagesc(rx_axis,ax_axis,20*log10(env),[-40 0]);colormap(gray); 106 Appendix E: SMF beamforming with DAX applied in Matlab %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % 1. Filename: Txfocusing_SMF_DAX66 % 2. Description: % SMF beamforming with fixed transmit focusing % DAX processing %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% clear all;clc; f_sample = 20; % sampling rate, in MHz fs = f_sample*1e6; c = 1540; % sound speed N_element = 128; aper_sz = 64; pitch = 298e-6; dx = 298e-6; no_lines = 65; centFreq = 5; BW = 0.5; low_f = (2-BW)*centFreq/2; high_f = (2+BW)*centFreq/2; I = BandpassFilter2(low_f,high_f,f_sample); z_start = 30; offset_mm = z_start; offset = round(offset_mm/1000/c*2*fs); if offset_mm == 0 offset_mm = 1; end dep_mx = 50; % in mm focal_zones = [offset_mm:1:dep_mx]'/1000; focus_times = (focal_zones-0.5/1000)/(c/2); focus_times1 = floor(focus_times*fs-offset); focus_times1(1) = 1; % to BF data from 0 mm up to 1.5 mm with focus at 1 mm Nf = max(size(focal_zones)); for i = 1:length(focus_times1) if (focus_times1(i)<1) focus_times1(i) = 1; end end ele_pos = (-(N_element-1)/2:(N_element-1)/2)*pitch; aper_start = 1:65; % 65 lines line_pos = ( -(no_lines-1)/2:(no_lines-1)/2 )*dx; %%%%%%%%%% creating delay matrix %%%%%%%%%% for line_no = 1:no_lines for i = 1:Nf aper_pos = ele_pos(aper_start(line_no):aper_start(line_no)+aper_sz- 1); delays1_dyn(i,:,line_no) = sqrt( (line_pos(line_no)-aper_pos).^2 + focal_zones(i).^2 )/c - focal_zones(i)/c; end 107 end delays_dyn = round(delays1_dyn*fs)+1; zf = 30e-3; % focal depth for Tx focusing at a fixed depth, in meter for line_no = 1:no_lines for j = 1:Nf aper_pos = ele_pos(aper_start(line_no):aper_start(line_no)+aper_sz- 1); delays1_fixed(j,:,line_no) = sqrt( (line_pos(line_no)-aper_pos).^2 + zf^2 )/c - zf/c; end end delays_fixed = round(delays1_fixed*fs)+1; %%% fixed f-number = 2 %%% fn = 2; NF_max = 1; %%%%%%%%%%% expanding aperture %%%%%%%%%% New_aper_sz = round(focal_zones/(fn*pitch))+rem(round(focal_zones/(fn*pitch)),2); for i = 1:Nf if New_aper_sz(i) > aper_sz New_aper_sz(i) = aper_sz; end end for line_no_rx=1:no_lines aper_st_pos=ele_pos(aper_start(line_no_rx):aper_start(line_no_rx)+aper_sz-1)- pitch/2; for depth=1:Nf-NF_max clear pre post dd=focus_times1(depth+1)-focus_times1(depth)+1; if line_pos(line_no_rx)<=aper_st_pos(1+New_aper_sz(depth)/2) pre=[]; post=zeros(dd,aper_sz-New_aper_sz(depth)); elseif line_pos(line_no_rx)>=aper_st_pos(1+aper_sz- New_aper_sz(depth)/2) post=[]; pre=zeros(dd,aper_sz-New_aper_sz(depth)); else shift1=round((line_pos(line_no_rx)- aper_st_pos(1+New_aper_sz(depth)/2))/pitch); pre=zeros(dd,shift1); post=zeros(dd,aper_sz-New_aper_sz(depth)-shift1); end Exp_aper_mask(focus_times1(depth):focus_times1(depth+1),1:aper_sz, line_no_rx )=... logical([pre,ones(dd,New_aper_sz(depth)),post]); Exp_aper_mask1(1:aper_sz, line_no_rx,focus_times1(depth):focus_times1(depth+1) )=... logical([pre,ones(dd,New_aper_sz(depth)),post]'); end end 108 %%%%%%%%%%% end expanding aperture %%%%%%%%%% load point40mm_reshape.mat sta3d = avg_re(:,:,1:end); % cut off main bang data_sz = max(size(sta3d)); % number of points per receive channel per Tx %%%%%%% filtering the raw RF data %%%%%%%%%% for ii = 1:128 for jj = 1:128 sta3d_f(ii,jj,:) = conv(squeeze(sta3d(ii,jj,:)),I,'same'); % [tx,rx,samples] end end %%%%% load filters load Tx30mm_filter_40mm_f2.mat SMFilter3 = sub_img_40mm; for rx = 1:aper_sz for line_no = 1:no_lines sub_rf2 = squeeze(sta3d_f(aper_start(line_no):aper_start(line_no)+aper_sz- 1,aper_start(line_no)+rx-1,:)); sub_rf = sub_rf2'; % sub_rf = [samples,Tx]; for depth = 1:Nf-1 for tx = 1:aper_sz %%%%% fixed Tx focusing delay = delays_fixed(depth,tx,line_no); delay_buffer(focus_times1(depth):focus_times1(depth+1),tx) = sub_rf(delay+focus_times1(depth):delay+focus_times1(depth+1),tx); end end delay_buffer = delay_buffer.*Exp_aper_mask(:,:,line_no); delay_buffer3 = delay_buffer(40:506,:); channelRx_TxFocused3(line_no,:) = sum(delay_buffer3'); end channelRx_TxFocused3 = channelRx_TxFocused3.*squeeze(Exp_aper_mask1(rx,:,40:506)); sub_img3(rx,:,:) = channelRx_TxFocused3; sub_filter3 = squeeze(SMFilter3(rx,:,:)); %%%%% 2-D spatial matched filtering %%%%% sub_img(rx,:,:) = conv2(channelRx_TxFocused3,fliplr(flipud(conj(sub_filter3))),'same'); end total = squeeze(sum(sub_img,1)); %%%%%%%%%% DAX %%%%%%%%%% 109 clear temp1 temp2 for stagger_ind = 1:6 temp1(stagger_ind,:,:) = squeeze(sum(sub_img(stagger_ind:12:end,:,:),1)); temp2(stagger_ind,:,:) = squeeze(sum(sub_img(stagger_ind+6:12:end,:,:),1)); end total5(:,:) = sum(temp1,1); total6(:,:) = sum(temp2,1); rf_matrixe = total5'; rf_matrixf = total6'; thr = 0.001; % threshold center_freq = 5e6; % typically 2 to 3 wavelengths are used as segment for xcorr segment = round(2.5*fs/center_freq); mean_rf = total'; mean_rf = mean_rf/max(max(mean_rf))+1e-20; rf_matrixe = rf_matrixe/max(max(rf_matrixe))+1e-20; rf_matrixf = rf_matrixf/max(max(rf_matrixf))+1e-20; cc6_6 = ones(size(rf_matrixa)); rf_matrixnla3 = zeros(size(rf_matrixa)); tic for j = 1:min(size(rf_matrixa)) for i = 1+segment:max(size(rf_matrixa))-segment; % cross-correlation e = rf_matrixe(i-segment:i+segment,j); f = rf_matrixf(i-segment:i+segment,j); cc6_6(i,j) = xcorr(e,f,0,'coeff'); % thresholding if (cc6_6(i,j)<thr) cc6_6(i,j)=thr; end end end %%%%% Median Filter %%%%% cc6_6f = medfilt2(cc6_6(:,1:65),[25 8]); rf_matrixnla3 = mean_rf.*cc6_6; for fi = 1:min(size(rf_matrixa)) mean_rf1(:,fi) = conv(mean_rf(:,fi),I,'same'); rf_matrixnla3_1(:,fi) = conv(rf_matrixnla3(:,fi),I,'same'); end mean_detected = abs(hilbert(mean_rf1)); nla_detected3_1 = abs(hilbert(rf_matrixnla3_1)); mean_detected = mean_detected/max(max(mean_detected)); nla_detected3_1 = nla_detected3_1/max(max(nla_detected3_1)); 110 c = 1540; [r,d] = size(mean_detected); rx_axis = ((1:(d-1))*dx-d*dx/2)*1000; ax_axis = (c/2000)*(offset:offset+r)/f_sample; DR=50; figure;imagesc(rx_axis,ax_axis,20*log10(mean_detected),[-DR 0]); colormap(gray);axis('image'); figure;imagesc(rx_axis,ax_axis,20*log10(nla_detected3_1),[-DR 0]); colormap(gray);axis('image');

Abstract (if available)

Abstract The difficulties associated with fabrication and interconnection have limited the development of 2-D ultrasound array transducers with a large number of elements (>9000). The dual-layer array design provides an alternative solution to the problem by substantially reducing the fabrication complexity as well as the channel count, making 3-D ultrasound imaging more realizable. This dissertation presents the design, fabrication, tests and imaging experiments of two dual-layer array transducers for different 3-D ultrasound applications. One is a planar transducer for 3-D rectilinear imaging, which has a -6 dB fractional bandwidth of 71% with a center frequency of 7.5 MHz. The measured lateral beamwidths are 0.521 mm and 0.482 mm in azimuth and elevation, respectively, compared with a simulated beamwidth of 0.43 mm. The other one is a cylindrical transducer for 3-D transrectal imaging, with a center frequency of 5.7 MHz and a -6 dB fractional bandwidth of 62%. The measured lateral beamwidths are 1.28 mm and 0.91 mm in transverse and longitudinal directions, whereas simulated beamwidths in these directions are 0.92 mm and 0.74 mm. For both transducers, 3-D synthetic aperture data sets were acquired by interfacing them with a Verasonics Data Acquisition System (VDAS). Offline beamforming was performed using the conventional delay-and-sum (DAS) beamforming method to obtain volumes of wire phantoms and cyst phantoms, which were used for spatial resolution and image contrast evaluation. Generalized coherence factor (GCF) was applied to the beamformed data to improve the contrast of cyst images. Preliminary real-time volumetric data acquisition was realized with the planar dual-layer array. ❧ The nature of the dual-layer design determines that there is only one-way focusing can be achieved in each of the azimuth and elevation directions, which indicate the directions of the transmit array and receive array respectively. For instance, in the elevation direction of the dual-layer design, transmit pulses emitted from the elongated elements are unfocused, plane wave pulses. Image quality is consequently worse compared to fully-sampled 2-D arrays, which are capable of two-way, or transmit-receive, focusing in both lateral directions. A novel beamforming method by spatially matched filtering (SMF) the echo signals was investigated in this dissertation to compensate for the degradation of image quality. With plane wave pulses used on transmit, the validity of SMF beamforming was demonstrated by analysis based on the Rayleigh-Sommerfeld diffraction theory. The performance of SMF beamforming was evaluated by spatial resolution and contrast of images beamformed from both computer simulations and experimentally acquired data with a one-dimension (1-D) linear array transducer. Simulation results showed a -6 dB beamwidth of 0.63 mm and an image contrast-to-noise ratio (CNR) of 5.34 with SMF beamforming, comparing to those of dynamic receive DAS beamforming, which were 0.74 mm and 2.00. In experiments, SMF beamforming gave a -6 dB beamwidth of 0.66 mm and an image CNR of 3.81. Experimental measurements of these values with dynamic receive DAS beamforming were 0.83 mm and 2.29 respectively. Furthermore, dual apodization with cross-correlation (DAX) was implemented on SMF beamforming to improve image contrast. The performance of the method was evaluated using both computer simulations and experiments. With a single transmit focus, DAX increased the CNR of anechoic cyst images of SMF beamforming at all depths without introducing any artifacts that might arise in the DAX-processed images using DAS beamforming.

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University of Southern California Dissertations and Theses

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Asset Metadata

Creator Chen, Yuling (author)

Core Title Novel beamforming with dual-layer array transducers for 3-D ultrasound imaging

School Viterbi School of Engineering

Degree Doctor of Philosophy

Degree Program Biomedical Engineering

Publication Date 04/23/2013

Defense Date 03/06/2013

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

Tag 3-D ultrasound imaging,beamforming by spatial matched filtering,dual-layer array transducers,OAI-PMH Harvest

Format application/pdf (imt)

Language English

Contributor Electronically uploaded by the author (provenance)

Advisor Yen, Jesse T. (committee chair), Shung, Kirk. K (committee member), Wang, Pin (committee member), Zhou, Qifa (committee member)

Creator Email yul.chen02@gmail.com,yuling@usc.edu

Permanent Link (DOI) https://doi.org/10.25549/usctheses-c3-241141

Unique identifier UC11294757

Identifier etd-ChenYuling-1576.pdf (filename),usctheses-c3-241141 (legacy record id)

Legacy Identifier etd-ChenYuling-1576.pdf

Dmrecord 241141

Document Type Dissertation

Format application/pdf (imt)

Rights Chen, Yuling

Type texts

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

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

Repository Name University of Southern California Digital Library

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