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Exploring multiple-mode vibrations of capacitive micromachined ultrasonic transducers (CMUTs) You, Wei 2013

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Exploring Multiple-mode Vibrations of Capacitive Micromachined Ultrasonic Transducers (CMUTs) by Wei You B.Eng., Nanjing University of Science and Technology, 2005 M.ASc., The University of British Columbia, 2008 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in The Faculty of Graduate Studies (Electrical and Computer Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) April 2013 c© Wei You 2013 Abstract Capacitive Micromachined Ultrasonic Transducers (CMUTs) are considered advantageous over piezoelectric transducers for ultrasound imaging for the high bandwidth, ease of integration with electronics and miniaturization. Research efforts over the past two decades have been focusing on manufac- turing and system integration of CMUTs to achieve comparable and better performance than the piezoelectric counterparts, while the uniqueness of the CMUT structure and physics is barely exploited. This thesis explores the complex behavior of CMUTs from a mode super- position perspective, and demonstrates imaging applications using CMUTs’ multi-modal operation. The operation of CMUTs is first analytically mod- eled as a coupled electro-mechano-acoustical system using plate vibration theory. As the simplest case, the first symmetric and asymmetric modes of vibration can be excited simultaneously via asymmetric electrostatic actu- ation, resulting in a vibration profile with a shifted center. Finite element modeling (FEM) is used to verify the theoretical calculation, and an equiva- lent circuit consisting of two sub-circuits for the symmetric and asymmetric vibration modes is built to show the possibility of fast simulation of complex CMUT array behavior. Experimental characterization of fabricated CMUT chips show that asymmetric vibration can be achieved with multi-electrode ii CMUTs. Two imaging applications using the multi-modal operation of CMUTs are proposed. The first concept, tiltable transducers, explores the benefits of orienting each transducer element toward the focal point to concentrate the acoustic energy and reduce grating lobes and side lobes. Imaging simu- lation shows the grating lobes can be reduced by 20 dB while the main lobe energy is preserved. FEM simulation demonstrates that CMUTs capable of asymmetric vibration can be a viable candidate as tiltable transducers with careful design of the cell dimension and central frequency. The second imaging application takes advantage of the ringing response of a CMUT to off-axis acoustic sources to achieve super-resolution imaging with low computational cost. The differential responses across all CMUT cells form a more decorrelated pattern than the regular average responses, which leads to better estimation performance of the proposed super-resolution algorithm. While only preliminary experimental results for the proposed applica- tions are presented, the multi-modal operation concept shows potential in improving several aspects of ultrasound imaging. iii Preface A brief summary of the major contributions and related publications of this thesis is as below: Chapter 2 proposes an analytical model of a CMUT cell based on mode superposition, which was published as the following journal paper: W. You, E. Cretu, and R. Rohling. Analytical modeling of CMUTs in coupled electro-mechano-acoustic domains using plate vibration theory. IEEE Sensors Journal, 11(9):2159-2168, September. 2011. [124] A novel concept of Asymmetric CMUT that can be conveniently ana- lyzed by the analytical model, was then proposed and filed as the following United States patent application: R. Rohling, E. Cretu, and W. You. Method and system of shaping a CMUT membrane. United States Patent Application No.13/439, 537. Filed April 2012. The concept was applied to an ultrasound imaging method for reducing the side lobe artifact. This study is detailed in Chapter 3, and was published as the following journal paper: W. You, E. Cretu, R. Rohling, and M. Cai. Tiltable ultrasonic transduc- ers: Concept, beamforming methods and simulation. IEEE Sensors Journal, 11(10):2286-2300, October 2011. [128] iv The experimental characterization results of a multi-electrode CMUT array with asymmetric operation capability have been prepared for journal paper submission: M. Cai, W. You, E. Cretu, and R. Rohling. PolyMUMPs Implementation of Single and Multi-electrode CMUTs: VHDL-AMS Behavioral Modeling and Experimental Characterization. [11] The asymmetric mode of CMUTs has been explored in the receiving process of ultrasound imaging. A method of using the asymmetric mode for Direction of Arrival estimation was presented in a conference: W. You, E. Cretu, and R. Rohling. Direction of arrival (DOA) estima- tion using asymmetric mode frequency components of CMUTs. In IEEE International Ultrasonics Symposium, October 2012. [126] A series of super-resolution imaging methods using the same concept were proposed in Chapter 4, and submitted for journal publication. Fabrication of the CMUT chips used in this thesis was done by Ming Cai, MASc, who also collaborated in experimental characterization of the CMUT chips. v Table of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . vi List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . xxvii Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxix 1 Background and Motivation . . . . . . . . . . . . . . . . . . 1 1.1 Principle of Ultrasound Imaging Systems . . . . . . . . . . 2 1.2 Ultrasonic Transducers . . . . . . . . . . . . . . . . . . . . 4 1.3 Capacitive Micromachined Ultrasonic Transducers (CMUTs) 5 1.3.1 Operation Principle of CMUTs . . . . . . . . . . . . 7 1.3.2 Modeling of CMUTs . . . . . . . . . . . . . . . . . 8 1.3.3 Fabrication and Packaging of CMUTs . . . . . . . . 11 1.3.4 Characterization of CMUTs . . . . . . . . . . . . . 12 vi 1.3.5 Integrating CMUTs with an Imaging System . . . . 13 1.3.6 Applications of CMUTs . . . . . . . . . . . . . . . . 14 1.3.7 Issues with CMUTs . . . . . . . . . . . . . . . . . . 15 1.4 Motivation of the Thesis . . . . . . . . . . . . . . . . . . . 17 1.5 Contribution and Structure of the Thesis . . . . . . . . . . 18 2 Modeling of CMUTs Based on Mode Superposition . . . 19 2.1 CMUT Modeling Problem . . . . . . . . . . . . . . . . . . 20 2.2 Analytical Modeling of CMUTs Based on Mode Superposi- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1 Mechanical Modeling: the Plate Vibration Theory . 21 2.2.2 Electrostatic Modeling and Electro-mechanical Cou- pling . . . . . . . . . . . . . . . . . . . . . . . . . . 25 2.2.3 Mechano-acoustic Coupling . . . . . . . . . . . . . . 27 2.2.4 Harmonic Motion of Biased CMUTs . . . . . . . . . 29 2.3 Validation of Analytical Modeling Using Finite Element Mod- eling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 2.3.1 Construction of FEM . . . . . . . . . . . . . . . . . 30 2.3.2 Static Results Comparison . . . . . . . . . . . . . . 32 2.3.3 Harmonic Results Comparison . . . . . . . . . . . . 34 2.3.4 Frequency and Impulse Response Results Comparison 36 2.3.5 Electrostatic Effects . . . . . . . . . . . . . . . . . . 39 2.3.6 Far-field Pressure Comparison . . . . . . . . . . . . 39 2.4 The Concept of Symmetric and Asymmetric CMUTs . . . 42 2.5 Comparison of Analytical Modeling and FEM Results . . . 44 vii 2.5.1 Static Results Comparison . . . . . . . . . . . . . . 44 2.5.2 Harmonic Results Comparison . . . . . . . . . . . . 46 2.6 Equivalent Circuit Modeling of CMUTs Based on Mode Su- perposition . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 2.6.1 Equivalent Circuit Construction . . . . . . . . . . . 48 2.6.2 Equivalent Circuit Implementation . . . . . . . . . 52 2.6.3 Comparison Between Equivalent Circuit Simulation and FEM Result . . . . . . . . . . . . . . . . . . . . 53 2.7 Experimental Characterization of Symmetric and Asymmet- ric CMUTs . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 2.7.1 Optical Characterization . . . . . . . . . . . . . . . 58 2.7.2 Electrical Characterization . . . . . . . . . . . . . . 65 2.8 Conclusion and Discussion . . . . . . . . . . . . . . . . . . 68 3 Reducing Side Lobe Effects Using Asymmetrically Driven CMUTs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 3.1 Tiltable Transducers for Physical Focusing and Steering . . 76 3.1.1 Physical Focusing and Steering Using Tiltable Trans- ducer Elements . . . . . . . . . . . . . . . . . . . . 77 3.1.2 Simulation Results . . . . . . . . . . . . . . . . . . . 79 3.2 Embodiment of Tiltable Transducer Concept Using CMUTs 91 3.2.1 Equivalence of a Tilted Piston Element and an Asym- metrically Excited CMUT cell . . . . . . . . . . . . 94 3.2.2 Equivalence of Tilting a CMUT Element and Tilting CMUT Cells in the Element . . . . . . . . . . . . . 96 viii 3.2.3 Feasibility of Tilting Angles . . . . . . . . . . . . . 97 3.2.4 Simulation Results with Practical Tilting Angles . . 99 3.2.5 Layout Routing of Adaptive CMUT Arrays . . . . . 101 3.3 Other applications of Tiltable Transducers . . . . . . . . . 102 3.3.1 Spatial Compounding . . . . . . . . . . . . . . . . . 102 3.3.2 High Intensity Focused Ultrasound . . . . . . . . . 103 3.3.3 Future Applications . . . . . . . . . . . . . . . . . . 103 3.4 Conclusion and Discussion . . . . . . . . . . . . . . . . . . 105 4 Improving Image Resolution Using Asymmetric Mode . 107 4.1 Multiple Vibration Modes During CMUT Reception . . . . 109 4.1.1 Asymmetric Mode Operation in Reception . . . . . 109 4.1.2 Average and Differential Received Signals From Multi- electrode CMUTs . . . . . . . . . . . . . . . . . . . 111 4.2 Efficient Super-resolution Imaging . . . . . . . . . . . . . . 112 4.2.1 Imaging with a Ring Catheter . . . . . . . . . . . . 112 4.2.2 Super-resolution Imaging Using Differential Received Signals . . . . . . . . . . . . . . . . . . . . . . . . . 112 4.3 Simulation and Results . . . . . . . . . . . . . . . . . . . . 120 4.3.1 FEM Simulation . . . . . . . . . . . . . . . . . . . . 120 4.3.2 Ultrasound Imaging Simulation . . . . . . . . . . . 121 4.3.3 Comparison of Phased Array Imaging and the Pro- posed Method . . . . . . . . . . . . . . . . . . . . . 125 4.3.4 Discussion of Simulation Results . . . . . . . . . . . 131 4.4 Experimental Results Using a CMUT Probe . . . . . . . . 132 ix 4.4.1 Experiment Setup . . . . . . . . . . . . . . . . . . . 133 4.4.2 Experiment Procedure and Results . . . . . . . . . 134 4.4.3 Discussion of Experimental Results . . . . . . . . . 140 4.5 Conclusion and Discussion . . . . . . . . . . . . . . . . . . 142 5 Conclusion and Future Work . . . . . . . . . . . . . . . . . 144 5.1 Summary of the Thesis . . . . . . . . . . . . . . . . . . . . 144 5.2 Future Directions . . . . . . . . . . . . . . . . . . . . . . . 151 5.2.1 Experimental Characterization of CMUTs in Immer- sion . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.2.2 Experimental Study of the Asymmetrically Actuated CMUTs . . . . . . . . . . . . . . . . . . . . . . . . . 151 5.2.3 Experimental Study of the Super-resolution Imaging Method . . . . . . . . . . . . . . . . . . . . . . . . . 152 5.2.4 Imaging Application Using the Multi-modal Vibra- tion Concept . . . . . . . . . . . . . . . . . . . . . . 155 5.2.5 Application of Parametric Amplification to Multiple Vibration Modes . . . . . . . . . . . . . . . . . . . . 157 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 158 Appendices A Field II Implementation of a Tiltable Array . . . . . . . . 180 B Construction and Signal Processing of CMUTs in Field II 182 x B.1 Construction of CMUT Cells Capable of Symmetric and Asym- metric Vibrations . . . . . . . . . . . . . . . . . . . . . . . 182 B.2 Signal Processing Procedure to Obtain the Average and Dif- ferential Signals of the CMUTs . . . . . . . . . . . . . . . . 186 xi List of Tables 2.1 Frequently used variables. . . . . . . . . . . . . . . . . . . . 21 2.2 Natural frequency comparison. Unit:Hz . . . . . . . . . . . 32 2.3 Measured resonant frequencies compared with FEM analysis and analytical calculation. . . . . . . . . . . . . . . . . . . . 63 2.4 Spring softening effect from experimental characterization. . 64 3.1 Quantitative measure of transmit/receive beam profile for focusing with suboptimal spacing. . . . . . . . . . . . . . . 89 3.2 Quantitative measure of transmit/receive beam profile for focusing with optimal spacing. . . . . . . . . . . . . . . . . 90 3.3 Quantitative measure of transmit/receive beam profile for steering with suboptimal spacing. . . . . . . . . . . . . . . . 90 3.4 Quantitative measure of transmit/receive beam profile for steering with optimal spacing. . . . . . . . . . . . . . . . . . 90 4.1 B-mode image SNR comparison of different imaging methods (dB) for different target configurations shown in Fig. 4.11 to Fig. 4.14. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 xii 4.2 Proposed super-resolution methods and their corresponding received signals and required transducer array type. . . . . 132 xiii List of Figures 1.1 Basic ultrasound imaging system . . . . . . . . . . . . . . . 2 1.2 B-mode ultrasound image. . . . . . . . . . . . . . . . . . . . 4 1.3 CMUT cell and element structure. (a) Cross-section of a CMUT cell [89]. (b) Magnified view of a series of 5-cell wide elements [87] c©[2002] IEEE. . . . . . . . . . . . . . . . . . 8 1.4 Single-mode and multi-mode vibration of the CMUT cell membrane. . . . . . . . . . . . . . . . . . . . . . . . . . . . 18 2.1 Illustration of the analytical model. . . . . . . . . . . . . . . 22 2.2 Static rms deflection of the first mode vs. VDC : analytical result vs. FEM result. . . . . . . . . . . . . . . . . . . . . . 26 2.3 Finite element model in Comsol. . . . . . . . . . . . . . . . 31 2.4 Analytically calculated first three natural modes of a CMUT cell. (a) (0,1) mode. (b) (1,1) mode. (c) (0,2) mode. . . . . 32 2.5 Static deflection of a CMUT cell: analytical vs. FEM result (radial component of the axisymmetric deflection). . . . . . 33 2.6 In-vacuo harmonic deflection of a CMUT cell: analytical vs. FEM result (radial component of the axisymmetric deflection). 35 xiv 2.7 In-water harmonic deflection of a CMUT cell: analytical vs. FEM result (radial component of the axisymmetric deflection). 35 2.8 Frequency response of in-vacuo membrane center deflection: analytical vs. FEM result. . . . . . . . . . . . . . . . . . . . 37 2.9 Frequency response of in-water membrane center deflection: analytical vs. FEM result. . . . . . . . . . . . . . . . . . . . 37 2.10 Frequency response of in-water output pressure at the mem- brane center: analytical vs. FEM result, normalized with respective peak values. . . . . . . . . . . . . . . . . . . . . . 38 2.11 Impulse response of in-water membrane center deflection: an- alytical vs. FEM result, normalized with respective peak values. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 2.12 The influence of uniform electrostatic force with the original gap distance in cases of different bias voltages, gap distances and membrane radii. . . . . . . . . . . . . . . . . . . . . . . 40 2.13 Far-field pressure comparison: with 1 MHz driving frequency and 35µm radius ((a) FEM (b) Plate (c) Piston, data range adjusted to 0.0045 Pa), with 4 MHz driving frequency and 35µm radius ((d) FEM (e) Plate (f) Piston, data range ad- justed to 0.25 Pa), and with 1 MHz driving frequency and 70µm radius ((g) FEM (h) Plate (i) Piston, data range ad- justed to 0.16 Pa). . . . . . . . . . . . . . . . . . . . . . . . 43 2.14 Cross-section of in-vacuo asymmetric static deflection of a CMUT cell: analytical vs. FEM result. . . . . . . . . . . . . 45 xv 2.15 Cross-section of in-vacuo asymmetric harmonic deflection of a CMUT cell: analytical vs. FEM result. . . . . . . . . . . 46 2.16 Cross-section of in-water asymmetric harmonic deflection of a CMUT cell: analytical vs. FEM result. . . . . . . . . . . 47 2.17 Basic parallel-plate equivalent circuit model [27]. With per- mission from the author. . . . . . . . . . . . . . . . . . . . . 49 2.18 (0,1) mode and (1,1) mode equivalent circuit implemented in Multisim. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 2.19 FEM of a CMUT cell operating in an array. . . . . . . . . . 54 2.20 In-air equivalent circuit simulation result of a CMUT cell operating in an array. . . . . . . . . . . . . . . . . . . . . . 55 2.21 In-air FEM simulation result of a CMUT cell operating in an array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 2.22 In-water equivalent circuit simulation result of a CMUT cell operating in an array. . . . . . . . . . . . . . . . . . . . . . 56 2.23 In-water FEM simulation result of a CMUT cell operating in an array, averaged on half of the cell . . . . . . . . . . . . . 57 2.24 Cross section of the design of a CMUT cell using PolyMUMPs [10]. With permission from the author. . . . . . . . . . . . . 58 2.25 A die with a 2D CMUT array and standalone CMUTs fab- ricated using PolyMUMPs. . . . . . . . . . . . . . . . . . . 59 2.26 CMUT membrane displacement versus DC voltage. (a) FEM simulation of DC displacement. (b) Experimental character- ization of AC displacement. . . . . . . . . . . . . . . . . . . 60 xvi 2.27 The deflection profile and frequency response of a CMUT cell under symmetric actuation. (a) (0,1) mode deflection profile from experimental characterization. (b) (0,1) mode deflec- tion profile from FEM. (c) Frequency response with symmet- ric excitation from experimental characterization. . . . . . . 61 2.28 The deflection profile and frequency response of a CMUT cell under asymmetric actuation. (a) (1,1) mode deflection profile from experimental characterization. (b) (1,1) mode deflection profile from FEM. (c) Frequency response with asymmetric excitation from experimental characterization. . 62 2.29 The asymmetric deflection profile of an asymmetrically driven CMUT. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 2.30 Screenshot of the deflection profile and frequency response of a symmetrically driven CMUT cell immersed in olive oil. . . 65 2.31 Screenshot of the deflection profile and frequency response of an asymmetrically driven CMUT cell immersed in olive oil. 66 2.32 Experimental measurement of real and imaginary parts of the impedance of a row of CMUT cells with symmetric exci- tation in air. (a) Real part (resistance). (b) Imaginary part (reactance). . . . . . . . . . . . . . . . . . . . . . . . . . . . 67 2.33 Equivalent circuit simulation result of real part of the in-air electrical impedance of a CMUT cell from. . . . . . . . . . . 67 xvii 2.34 Experimental measurement of real and imaginary parts of the impedance of a single CMUT cell with asymmetric exci- tation in air. (a) Real part (resistance). (b) Imaginary part (reactance). . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 2.35 Experimental measurement of the impedance of a row of CMUT cells with symmetric excitation, and a single CMUT with asymmetric excitation in oil. (a) Impedance of a row of CMUT cells with symmetric excitation. (b) A single CMUT with asymmetric excitation. . . . . . . . . . . . . . . . . . . 69 3.1 Arrays of tiltable transducer elements. (a) 1D physical fo- cusing. (b) 1D physical steering. (c) 2D physical focusing. (d) 2D physical steering. . . . . . . . . . . . . . . . . . . . 77 3.2 Physical focusing. The dash lines denote the wave direction of each element, and long dashed curves denote collective beam traveling profile. (a) 1st scan line (b) 2nd scan line (c) N th scan line . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3 Physical steering. The dash lines denote the wave direction of each element, and long dashed curves denote collective beam traveling profile. (a) 1st scan line (b) 2nd scan line (c) N th scan line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79 3.4 Comparative transmit/receive beam profile for focusing with suboptimal spacing (Element spacing is 300µm, and element impulse response is 2 cycles of 8 MHz sinusoid). . . . . . . . 81 xviii 3.5 Phantom for simulation. 10 point targets are along the z- axis, and 10 point targets are +30◦ off the z-axis. . . . . . . 82 3.6 B-mode images of point targets with suboptimal spacing. (a) Electronic focusing. (b) Physical focusing. . . . . . . . . . . 83 3.7 Comparative transmit/receive beam profile for focusing with optimal spacing (Element spacing is 160µm, and element im- pulse response is 2 cycles of 8 MHz sinusoid). (a) 32-element group, focused at 30 mm. (b) 64-element group, focused at 30 mm. (c) 64-element group, focused at 20 mm. (d) 64- element group, focused at 10 mm. . . . . . . . . . . . . . . . 84 3.8 Comparative transmit/receive beam profile for steering with suboptimal spacing (Element spacing is 300µm, and element impulse response is 2 cycles of 8 MHz sinusoid). . . . . . . . 85 3.9 B-mode images of point targets with suboptimal spacing. (a) Electronic steering. (b) Physical steering. . . . . . . . . . . 86 3.10 Comparative transmit/receive beam profile for steering with optimal spacing (Element spacing is 80µm, and element im- pulse response is 2 cycles of 8 MHz sinusoid). (a) Steering to 15◦. (b) Steering to 30◦. (c) Steering to 45◦. . . . . . . . . 87 3.11 Comparative transmit/receive beam profile for composite steer- ing to 30◦ with optimal spacing. . . . . . . . . . . . . . . . 88 3.12 Comparative transmit/receive beam profile for combining phys- ical steering and physical focusing with suboptimal spacing. 89 xix 3.13 An example of an adaptive CMUT cell. The controlled driv- ing voltage changes the shape of the CMUT membrane which alters the wave propagation direction. . . . . . . . . . . . . 92 3.14 Adaptive CMUT cell structure. (a) Cross-sectional view of the adaptive membrane. The solid curve denotes the orig- inal position of the membrane. The dotted curve denotes a tilted membrane. (b)(c) Cross-sectional view of an adap- tive CMUT cell structure. (d)(e) Cross-sectional view of an adaptive CMUT cell with an alternative structure. (f)(g)(h) Top view of an adaptive CMUT element with lateral control (f), lateral and elevational control (g) and control along other axes (h). The gray areas denote tilting electrodes, and the bigger area denotes a transparent membrane. . . . . . . . . 93 3.15 Simulated transmit pressure of a tilted piston with a CMUT cell size at 2mm. The data was convolved with a filter that averages every 15 degrees of angle. . . . . . . . . . . . . . . 94 3.16 CMUT membrane deflection with different bias voltages (1 MHz case). (a) 180 V(left)/0 V(right). (b) 180 V(left)/180 V(right). (c) 0 V(left)/180 V(right) . . . . . . . . . . . . . . . . . . . . 95 3.17 Chosen surface and curve for beam tilting demonstration. (a) Top view of the chosen surface. (b) Top view of the chosen curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 xx 3.18 Beam tilting result, measured 1mm away from the CMUT. (a) 180 V/0 V result on the surface. (b) 180 V/180 V result on the surface. (c) 0 V/180 V result on the surface. (d)180 V/0 V result on the curve. (e) 180 V/180 V result on the curve. (f) 0 V/180 V result on the curve. . . . . . . . . . . . . . . . . . 97 3.19 A standard 2D CMUT array. Circles represent CMUT cells, and gray-scale coded hatching represents different elements [5]. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.20 (a) Conceptual diagram of tilting a CMUT element. (b) Im- plementation of tilting an element by uniformly tilting its cells. Only 5 cells are drawn for the sake of explanation. . . 98 3.21 Field II simulation of the beam profiles of a tilted element and tilted cells toward their focal point. The data was averaged every 4 degrees. . . . . . . . . . . . . . . . . . . . . . . . . . 98 3.22 Comparative relative main lobe and grating/side lobe level for different operation frequencies. All values are normalized by the main lobe amplitude of focusing/steering at 2 MHz.(a) Main lobe level for focusing. (b) Peak of grating/side lobe level for focusing. (c) Main lobe level for steering. (d) Peak of grating/side level for steering. . . . . . . . . . . . . . . . 101 4.1 Average displacement of the whole membrane, and left and right parts of the membrane subjected to an acoustic wave from an off-axis angle. . . . . . . . . . . . . . . . . . . . . . 111 xxi 4.2 (a) Visualization of manifold matrix V avg constructed from Savg. (b)Visualization of manifold matrix V diff constructed from Sdiff . The vertical axis represents LP hypothetical tar- get locations, and the horizontal axis representsNT temporal received samples. Each horizontal trace represents a column in the matrix. In this example, only 21 columns correspond- ing to 21 target locations in the matrices are shown. . . . . 115 4.3 (a) Correlation coefficient map of V avg. (b) Correlation coef- ficient map of V diff . The brightness of the pixels is mapped to the coefficient values. An ideal correlation coefficient map has zero off-diagonal values. . . . . . . . . . . . . . . . . . . 115 4.4 Workflow of the proposed method. [A] Manifold matrices construction. [B] MAP estimation of weight vectors. [C] Pruning of weight vectors. [D] Scan line reconstruction. [E] B-mode image reconstruction. . . . . . . . . . . . . . . . . . 116 4.5 Directional pruning process. For the weight vector estimated while the array steers to the ith angle θi, keep the values corresponding to θi and set the values at other angles to zero as they are more likely false estimates or result of side lobe energy. Note that multiple values for different axial locations at θi are all kept. . . . . . . . . . . . . . . . . . . . . . . . . 118 4.6 Frequency domain average and differential received signals for different source angles from the FEM simulation results. 121 4.7 Symmetric and asymmetric receiving impulse responses of membrane displacement. . . . . . . . . . . . . . . . . . . . . 122 xxii 4.8 Ring array with 48 CMUT cells constructed in Field II. . . 123 4.9 The relative scales of the CMUT array and the ROI for the imaging simulation. . . . . . . . . . . . . . . . . . . . . . . . 124 4.10 (a) TX/RX beam profile at 20 mm when focusing at 0 ◦. (b) TX/RX beam profile at 20 mm when focusing at 20 ◦. . . . . 126 4.11 Imaging results for two columns of point targets, calculated with manifold matrices of 21 by 6 hypothetical targets. (a) Idealized B-mode image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. . . . . . . . . . . . . . . . . . . . . . . . . . 127 4.12 Imaging results for targets with high spatial sampling rate, calculated with manifold matrices of 21 by 6 hypothetical tar- gets. (a) Idealized scan-converted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B- mode image result using SH. . . . . . . . . . . . . . . . . . 128 4.13 Imaging results of a simulated point targets phantom, calcu- lated with manifold matrices of 21 by 6 hypothetical targets. (a) Idealized scan-converted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. . . . . . . . . . . . . . . . . . . . . . 129 xxiii 4.14 Imaging results calculated with manifold matrices of 9 by 6 hypothetical targets, same targets as in Fig. 4.11. (a) Ide- alized scan-converted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. . . . . . . . . . . . . . . . . . . . . . . . . . 130 4.15 Experiment setup for super-resolution imaging. . . . . . . . 133 4.16 Relative scales of the CMUT probe, the active aperture, the beam width, and the imaging ROI of the linear array and phased array imaging tests. (a) Relative scales of the linear array imaging tests. (b) Relative scales of the phased array imaging tests. . . . . . . . . . . . . . . . . . . . . . . . . . . 135 4.17 Linear array imaging results using a CMUT probe. (a) Ideal- ized B-mode image for target No.1. (b) B-mode image result using delay-and-sum for target No.1. (c) B-mode image re- sult using SA for target No.1. (d) Idealized B-mode image for target No.2. (e) B-mode image result using delay-and-sum for target No.2. (f) B-mode image result using SA for target No.2. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 4.18 Phased array imaging results using a CMUT probe. (a) Ideal- ized B-mode image for target No.1. (b) B-mode image result using phased array for target No.1. (c) B-mode image result using SA for target No.1. (d) Idealized B-mode image for target No.2. (e) B-mode image result using phased array for target No.2. (f) B-mode image result using SA for target No.2. 139 xxiv 4.19 Visualization of manifold matrices using element-wise regu- lar and differential signals. (a) Manifold matrix constructed from element-wise regular echo data. (b) Manifold matrix constructed from element-wise differential echo data. . . . . 140 4.20 Phased array imaging results using element-wise differential signals. (a) Idealized B-mode image for target No.1. (b) B-mode image result using element-wise differential signals in SA for target No.1. (c) Idealized B-mode image for target No.2. (d) B-mode image result using element-wise differential signals in SA for target No.2. . . . . . . . . . . . . . . . . . 141 5.1 Illustration of reconstructing the temporal echo data from an element as a decaying exponential function. . . . . . . . . . 153 5.2 Examples of manifold matrices using reconstructed signals. (a) Manifold matrix constructed from reconstructed element- wise regular echo data. (b) Manifold matrix constructed from reconstructed element-wise differential echo data. . . . . . . 155 5.3 B-mode image results where reconstructed signals are used for weights estimation. (a) B-mode image result using re- constructed element-wise regular signals for target No.1. (b) B-mode image result using reconstructed element-wise differ- ential signals for target No.1. (c) B-mode image result using reconstructed element-wise regular signals for target No.2. (d) B-mode image result using reconstructed element-wise differential signals for target No.2. . . . . . . . . . . . . . . 156 xxv B.1 Illustration of constructing CMUT cells in Field II. . . . . . 183 B.2 Illustration of signal processing procedure of receiving aver- age and differential signals. ∗ denotes convolution. . . . . . 187 xxvi Acknowledgements I would like to express my gratitude to everyone who has helped me on my PhD journey. First, my most sincere thanks go to my supervisors Dr. Edmond Cretu and Dr. Robert Rohling, without whom this thesis can never be completed. They have always motivated and guided me through the bumpy course of the project with their profound and extensive knowledge in MEMS and ultrasound imaging, and supported all my wild ideas with faith and patience. They are also both the greatest life mentors I have ever hoped for, whose optimism, tenacity, integrity, and professionalism I will always respect and learn in years to come. Thank you both, for caring for me and believing in me. I would also like to thank the professors who have collaborated on the CMUT project: Dr. Shahriar Mirabbasi, Dr. Tim Salcudean and Dr. Kenichi Takahata, who provided valuable feedback on the project. Thanks to CMC Microsystems, Canada for providing the fabrication and simulation software support, and thanks to Vermon SA, France for provid- ing the CMUT probe for testing, and to Ultrasonix Medical Corporation, Canada for the technical support of the ultrasound machine. Special thanks to Professor Butrus (Pierre) T. Khuri-Yakub from Stan- xxvii ford University, and Professor Roger Zemp from University of Alberta for the insightful feedback on the project. Thanks to my group members Ming Cai for his help on the experiments, Mrigank Sharma for his knowledge on MEMS, members in the Robotic and Control Lab for their expertise in ultrasound machines, and all those in other fields of study who I have bugged for help. Last but not least, I am deeply indebted to my family, who have been through a lot when I should have been there. To my mother, Beiwei Feng, you are the strongest and most loving person in my life; and to my late father, Li You, thanks for always being proud of me. Thanks to my husband, Jingyuan Li, for your constant love and patience. xxviii Dedication To my family. xxix Chapter 1 Background and Motivation Ultrasound is a type of acoustic wave with frequencies above the audible range of human beings (>20 kHz). Medical ultrasound imaging uses the non-ionizing radiation of ultrasound to reveal the anatomy of the human body. Because of its safety, ultrasound imaging is particularly useful for obstetrical organs, cardiac and vascular systems, the fetus, and the eye. It is also used to measure the blood flow, and provide guidance for other imaging and therapeutic applications. Ultrasound imaging devices are portable and cost-effective than many other modalities, and typically offer images in real time. Hence ultrasound imaging is the most widely used medical imaging modality in the world. An ultrasound imaging system emits ultrasonic waves that penetrate, reflect and scatter at layers of human body tissues of different acoustic prop- erties, and subsequently receives and processes the reflected waves to form an image. The transducers inside an ultrasound imaging probe are the key part of an ultrasound imaging system, which convert electrical energy to acoustic energy and vice versa. When driven by electrical signals, transduc- ers vibrate to generate ultrasound waves that propagate into soft tissues. The echoes, the waves that partly reflect at boundaries of different tissues, 1 are received by the transducers and converted back to electrical signals. 1.1 Principle of Ultrasound Imaging Systems Fig. 1.1 is a block diagram of a typical B-mode ultrasound imaging system. A B-mode ultrasound image is a two-dimensional ultrasound image of the cross section of human tissues. The brightness at each image location rep- resents the strength of an ultrasound echo. In transmission, a transducer array is excited by electrical pulses and sends out ultrasound waves into the tissue; in reception, it acts as sensors that receives echoes from the tissue. The received echoes are converted to an image later. The ultrasound waves sent from, and received by, a group of elements are usually tuned with dif- ferent time delays and gains, so that waves from different elements meet at a certain focal point along a scan line. This process is generally referred to as beamforming. Figure 1.1: Basic ultrasound imaging system The transmit/receive switch isolates the high voltage in excitation from 2 the sensitive signals in reception. In transmission, the central controller generates pulses and sends beamforming information to the transmit beam- former. The beamforming information has two main components: beam steering and focusing. Steering refers to adjusting the direction of the beam, and focusing ensures that beams from multiple elements arrive at the fo- cal point concurrently. These two components can be combined for cer- tain imaging cases. Both are represented by time delays to the ultrasound beams. Other information, such as aperture selection and modulation, is also included in the beamforming information. The pulses with pre-set time delays and other beamforming information are converted to analog signals, amplified and sent to excite the group of elements before propagating into the tissue. During reception, the transducer converts the returning echoes along the scan line to electronic signals that are subsequently amplified and con- verted to digital signals. The amplitude of received echoes forms the basis of an ultrasound image. The received signals are delayed, apodized (applied different weighting factors on each element’s signal) and summed with the receive beamforming parameters. Once all echo signals along one scan line are received, the transducer array sends another set of ultrasound pulses and starts receiving echoes along another scan line. The central controller processes the summed signals, including detecting the envelopes of the signals and compressing them to reduce the dynamic range. Once echo data from all focal points along all scan lines are received, they are converted to a grid format (a B-mode image) and stored in the computer memory, ready for display. A B-mode ultrasound image and its 3 spatial relation with the probe is shown in Fig. 1.2. The direction parallel to the transducer array/probe is called the lateral direction; the direction along the beam or the penetration depth is called the axial direction. A third direction perpendicular to the B-mode imaging plane is called the elevational direction which is useful in 3D imaging. Figure 1.2: B-mode ultrasound image. 1.2 Ultrasonic Transducers Transducers are the energy converter of an ultrasonic imaging system. An ultrasound imaging probe typically contains many units of the transduc- ers (elements). Their sizes, output power, receive sensitivity, bandwidth, dynamic range and ways of excitation ultimately determine the quality of an ultrasound image. The current dominant type of transducers are based 4 on piezoelectric principles. The electrical voltage applied on the transducer produces the stress/strain that is passed into the tissue as pressure waves, making it a transmitter; in reverse, the impinging pressure field from the tis- sue is converted into strain and voltage signals, making it a receiver. Piezo- electric materials include the piezoelectric crystals (e.g., quartz), ceramics (e.g., barium titanate and lead zirconate titanate (PZT), most commonly used), and polymers (e.g., polyvinylidene fluoride (PVDF)) [23] [87]. Piezoelectric transducers is a mature technology that provides good bandwidth (up to 80%) and sensitivity [12], yet presents some limitations, one of which being the coupling efficiency with the tissue or the surrounding medium (typically fluid in medical applications). The mechanical impedance of the piezoelectric transducers is much larger than the acoustic impedance of the medium and a matching layer is required. The matching layer can be unavailable for high frequency transducers and is subjected to bandwidth restrictions [38]. The fabrication technology of piezoelectric transducers is expensive and offers limited geometric designs. It is also difficult to fabricate large two-dimensional arrays due to interconnect technologies [87] and lack of die-level integration with electronics. 1.3 Capacitive Micromachined Ultrasonic Transducers (CMUTs) An alternative transduction mechanism to piezoelectric effect is the elec- trostatic principle. The operation of electrostatic transducers is based on electrostatic transduction of a thin metalized membrane suspended over a 5 backplate. The recent development of microfabrication technology makes it possible to fabricate sub-micron gaps so that the GV/m electric field required by an electrostatic transducer can be achieved. Capacitive Micro- machined Ultrasonic Transducer (CMUT) technology, first introduced in the 1990s [43], is a desired combination of the microfabrication technology and the electrostatic principle. After two decades of development, it is consid- ered by the ultrasound imaging community as a potential replacement for piezoelectric transducers. A CMUT is made up of a silicon or silicon nitride membrane and a sub- strate using micromachining technology currently employed in micro-electro- mechanical systems (MEMS). Because of the mechanism of thin membrane vibration instead of bulk vibration, CMUTs have much lower mechanical impedance than the piezoelectric transducers which offers better coupling with the medium, and higher bandwidth. The high bandwidth not only improves imaging resolution, but also enables optimal performance in novel imaging techniques such as harmonic imaging [87]. The standard silicon Integrated Circuit (IC) technology allows easier and low-cost fabrication of large 2D arrays and arrays with tight space restrictions, such as those used for Intravascular Ultrasound (IVUS) and Intracardiac Echocardiography (ICE). Furthermore, CMUTs are advantageous in integration with electron- ics, compatibility with CMOS, and better thermal performance [71]. These features make CMUTs promising for improving many areas in ultrasound imaging, including three-dimensional imaging, high frequency imaging, and harmonic imaging. The research and industrial community is working to overcome several of the drawbacks of CMUTs discussed in Subsection 1.3.7. 6 1.3.1 Operation Principle of CMUTs The basic unit of CMUTs is a CMUT cell. As is shown in Fig. 1.3(a), the main parts of a CMUT cell are the membrane, the electrodes, the cavity (gap), and the substrate. A thin polysilicon or silicon-nitride membrane is suspended over a substrate separated by a small vacuum cavity. A top electrode and a bottom electrode are attached to the membrane and the substrate respectively. Alternatively the membranes and the substrate are made conductive. A DC voltage is applied between the electrodes to elec- trostatically attract the membrane to the substrate to increase mechanical sensitivity to subsequent voltage excitations. The electrostatic force is re- sisted by a mechanical restoring force due to the membrane stiffness. During transmit, the membrane is driven by an AC voltage and vibrates to gener- ate ultrasound. In reception, the acoustic pressure on the membrane results in a change in the capacitance between the electrodes, thus an alternating current signal can be detected. A CMUT element consists of hundreds of CMUT cells fabricated typi- cally in a grid on the same die, and usually actuated in phase to generate enough power for sufficient depth penetration into the human body. An example of five elements, each made up of five cells, is shown in Fig. 1.3(b). An ultrasound transducer/probe contains an array of such elements. The thickness, shape and the gap distance of the individual membrane determine the operating frequency of the CMUT cell, and multiple CMUT cells and elements can be arranged to form the desired geometry of the transducer with the suitable frequency. 7 (a) (b) Figure 1.3: CMUT cell and element structure. (a) Cross-section of a CMUT cell [89]. (b) Magnified view of a series of 5-cell wide elements [87] c©[2002] IEEE. 1.3.2 Modeling of CMUTs A CMUT is a complex electromechanical system that involves the energy coupling of three physical domains: the electrical domain, the mechanical (structural mechanics) domain, and the acoustic domain. The design and optimization of CMUTs require different types of modeling tools that serve different purposes. Analytical Modeling First, full theoretical analysis of the mechanism of each individual com- ponent of the CMUT cell and their interaction is needed. Seminal works such as [60] model the CMUT cell as a vibrating plate and laid out the CMUT operation equations. Then they simplify the CMUT behavior to a one-dimensional parallel plate capacitor model using the average displace- ment and velocity of the membrane, in order to analyze the system with equivalent circuit models. A few later works try to tackle the problem of a particular domain, such as computing the pull-in voltage of the CMUT by 8 sub-dividing the membrane into a series of capacitors [76], finding a close- form solution to the electromechanical equations [110], and computing the radiated pressure from one cell and the mutual acoustic influence from dif- ferent cells [16]. More sophisticated theoretical models analyze the detailed behavior and the radiation of CMUTs array in a unified fashion using the plate vibration theory and Fourier analysis [96]. Equivalent Circuit Modeling An electromechanical system can be analyzed in a unified circuit by replacing forces and velocity with voltage and current. A large amount of theoretical analysis of the CMUT operation is followed by an equivalent circuit model to validate the theory. The first works of CMUT equivalent modeling follow the Mason’s model [69] with an electrical port, a transformer, and a me- chanical port. The electrical port includes the resistance and capacitance of the CMUT as a capacitor, and the mechanical port includes the mechanical impedance, loss resistance and the acoustic load impedance. This 1D model involves two important simplifications: reducing the degree-of-freedom of the CMUT vibration, and considering the medium as a pure resistive load. Im- proved equivalent circuit models consider the position-dependent expression of the capacitance and acoustic impedance [100, 118], the self-and-mutual acoustic impedance [70], and the nonlinear effects [66, 82]. Equivalent cir- cuit models were also built for different operation regimes such as collapse operation. In contrast to regular mode operation when the CMUT mem- brane is brought close to the substrate by the electrostatic force, in the collapse mode, the CMUT membrane is attracted to touch the substrate by 9 a voltage stronger than the pull-in voltage and snaps back to produce higher output power [82, 84]. Equivalent circuits for multiple vibration modes of the membrane were also proposed [97] that offers convenient means of sim- ulation for more complex CMUT behavior, although the application of such a model was not further discussed. The equivalent circuit models offer fast simulation of the coupled system, and with its recent development, can very accurately approximate the CMUT behavior. Finite Element Modeling Another way of modeling and analyzing the CMUT behavior is the Finite Element Modeling (FEM), where a software computes the partial differential equations in each of the geometric division of the object (the finite element). FEM has been used for predicting and analyzing static and dynamic behav- ior of CMUTs[7, 121]. This numerical method produces the solution closest to the physical reality, but has the drawback of long computation time. Other modeling methods such as finite difference model were also pro- posed [17]. The most recent works employ a combination of analytical, equivalent circuit and FEM in order to achieve a higher modeling accuracy. The exact mode shape of the CMUT membrane is taken into account; the pressure emitted from a single cell, and mutual acoustic influence between different cells can be computed numerically, and the equivalent circuit pa- rameters can be extracted from FEM analysis [63]. The above simulation methods focus on the physical behavior of single CMUT cells or array. Imaging simulation of the CMUT array has been car- ried out in a linear acoustic field simulation software Field II [50, 51] where 10 a CMUT package was added to the code base. The package implements a simplified model of CMUTs, whose cell geometry is part of the spherical sur- face, and operates with electromechanical impulse response extracted from FEM or experiments [3]. 1.3.3 Fabrication and Packaging of CMUTs Fabrication technology spans the history of CMUT development and crit- ically influences the application of the CMUTs. In its early development, the fabrication was based on standard surface micromachining technology. There are two main approaches of CMUT fabrication: sacrificial release process (surface micromachining) [52, 53] and wafer-bonding method (bulk micromachining) [45] both originated from the CMUT group at Stanford University. The wafer-bonding method is more recently introduced and has exhibited shorter fabrication steps, greater ease of controlling parameters such as gap height, and mechanical properties. Other research groups, such as the one at University of Roma Tre, Italy [12] also developed their own fabrication technologies which are similar to the above two categories. The CMUT cells are usually fabricated into long thin elements, and a number of such elements are lined up to form CMUT arrays. In order to reduce the possibility of dielectric breakdown and solve the issue of high parasitic capacitance, several recent fabrication technologies were developed, such as local oxidation of silicon (LOCOS) [91], and using a thick buried oxide layer [57]. Other variations of CMUT structure were fabricated to approximate the performance of the CMUT membrane to that of a piston [46] [77]. 11 The transmit/receive electronics including the transmit pulsers and re- ceiving amplifiers need to stay close to the CMUT array in order to prevent the signal degradation from the capacitance of the cables. The integration with electronics can be categorized into monolithic and multi-chip meth- ods [55]. The monolithic approach includes building the CMUTs next to the electronics [31], and more recently on the finished CMOS wafers [20, 29, 63, 129]. The multi-chip method builds the CMUTs and the electronics on different substrates. The CMUT array elements are first electrically in- terconnected by means of through-wafer vias connects [19], and a flip-chip bonding process is used to bond the CMUT array to the electronics [119]. Other bonding methods using an intermediate substrate are developed for custom types of transducers [78, 114]. The transducer array is electrically insulated by a thin layer of elastic polymer that does not affect the performance significantly [64]. Instead of in-house fabrication, standard silicon foundry processes have been used, such as the multi-user microelectromechanical systems (MEMS) process (MUMPs) [10, 65, 81]. The MUMPs process is so far only successful in air-coupled CMUTs, and has the limitation such as the control of pull-in voltage and difficulty in sealing for immersion applications. 1.3.4 Characterization of CMUTs Experimental characterization of CMUTs are carried out after they are fabri- cated. CMUTs are measured both in air and in liquid, and the measurement methods include electrical impedance measurement, optical measurement using a Laser Doppler Vibrometer (LDV), and pulse-echo measurement in a 12 liquid environment. Measurement in air usually involves measuring the in- put impedance of the CMUT array through a bias-T (the real and imaginary part of the impedance peaks at the resonant frequency). The result is help- ful in determining parameters such as resonant frequency, collapse voltage (when bias voltage exceeds the mechanical restoring force), quality factor and so on [13, 60, 89]. Immersion experiments are performed to measure the imaging capabilities of CMUTs, such as input sensitivity, output pressure, fractional bandwidth and penetration depth. This is done by actuating the CMUTs by a wideband pulse voltage superimposed on a DC bias voltage. The ultrasound wave is either measured by a hydrophone or reflected by a planar reflector and transduced by CMUT into electrical signals that are read out by an oscilloscope [12, 54, 88]. The LDV measurement can be used for measuring the CMUT movement both in air and in immersion [7], and its ability to provide the vibration map provides detailed knowledge of the cell and the array behavior [68]. 1.3.5 Integrating CMUTs with an Imaging System The CMUT probes including the transducer array and the front-end elec- tronics are often built and packaged in-house for different applications, and are integrated into the imaging system where a control unit with the beam- forming information, and the processing unit for the received signal are included. Integration with a commercial imaging system dates back to 2003 [72], followed by a series of custom control and processing systems using FPGA and PCs [22, 98, 115], and more recently with a commercial system [63]. 13 1.3.6 Applications of CMUTs CMUTs have the potential for improving certain imaging applications due to the flexibility of transducer geometries, suitability for high frequency imag- ing of small structures such as the eye, and miniaturization for intravascular and intracardiac applications. The most commonly used ultrasound imaging type is the B-mode imag- ing. Usually a one-dimensional (linear) array of transducer elements is used that transmits acoustic pulses along one scan line into the tissue, and receives the echo from the tissue, before transmitting along the next scan line. Beam forming is often used for transmission and receiving. Linear CMUT arrays were built with comparable dimensions as those of piezoelectric arrays, and the imaging results show improved resolution but the penetration depth can be compromised [87]. Hitachi announced the world’s first commercialized linear CMUT probe in 2009 [44]. CMUT arrays offer special advantage over piezoelectric arrays in build- ing two-dimensional arrays for imaging three-dimensional volumes, because large CMUT arrays can be lithographically defined, and integrated with front-end electronics. 2D arrays for volumetric imaging were developed in [86] and [119]. Thanks to the microfabrication technology, CMUTs can be made into transducers of small sizes and different geometries, suitable for mounting at the tip of a catheter for intravascular and intracardiac applications, while producing an array of such small scale is challenging for the piezoelectric technology. Forward-looking ring arrays have been built [78, 123], and 14 the first in-vivo imaging results of a CMUT ring array were obtained re- cently [105]. CMUTs arrays have also been developed in more sophisticated and flex- ible geometries for minimally invasive medical imaging and therapies [18], and integrated with new imaging modalities such as photoacoustic imag- ing [56]. It is also used for therapeutic purposes such as High Intensity Focused Ultrasound (HIFU) [116] that benefits from the ability of large arrays and better thermal performance of the CMUT array. Apart from medical applications, CMUTs are also applied in the area of gas sensing [90] and fluid property sensing [106]. 1.3.7 Issues with CMUTs In spite of the advantages, CMUT arrays have a few issues that are under further investigation. Output Power and Receiving Sensitivity A major hurdle for the CMUTs to outperform its piezoelectric counterpart is the output power, which limits signal-to-noise-ratio (SNR) and penetration depth into the tissue, and in turn degrades the sensitivity in reception. Operating in collapse mode may improve the output pressure. During the collapse operation, the CMUT membrane is brought to contact with the substrate by a high voltage beyond its pull-in voltage, and released to emit much higher power. This approach was experimentally characterized [85] and theoretically analyzed [83], and an equivalent circuit was built for its analysis [84]. 15 Another way to improve the output pressure and the receiving sensitivity is to built novel CMUT structures, such as the dual-electrode structure [39, 40] that uses separate electrodes for transmission and reception. In transmit, the membrane is biased by the electrodes close to the edge of the membrane to increase its range of excursion, and hence the output pressure; in receive, the center electrode brings the membrane down to increase the receiving sensitivity. The output pressure can be further improved by adding a mass to the membrane center [41]. Cross Coupling One of the drawbacks of CMUT array is the cross coupling between cells that leads to degradation of image quality. The mechanism of cross cou- pling (crosstalk) include the leaky Lamb wave propagating in the substrate, the Stoneley wave that propagates at the silicon-fluid interface [54], and the dispersive guided modes which is the main part of crosstalk [6]. The crosstalk was experimentally observed as long ringing of the CMUT array element [54], and was observed in experiment and FEM as the excitation of neighboring element from the vibration of one element [6]. In the frequency spectrum, the crosstalk shows as dips or resonant peaks [14, 15]. The ef- fect was also observed with an optical interferometer [62]. Modeling of the crosstalk effects was carried out analytically [30, 113] and using an improved equivalent circuit model [15]. The crosstalk effect is more prominent when the array is steered to large angles [96]. Methods to reduce the crosstalk include adding a lossy top layer [8], and using a calibrated matrix [130]. 16 1.4 Motivation of the Thesis With two decades of development, a rich body of knowledge has been accu- mulated on the fabrication, theoretical analysis, simulation and experimen- tation of CMUTs, which are believed to become a strong competitor on the ultrasound imaging probe market soon as a matured technology. In spite of the success in matching up the performance with piezoelectric transducers, CMUTs are still being applied in the traditional imaging realm, and few imaging methods have been explored to take advantage of the unique struc- tural and physical features of the CMUTs. Most works treat CMUT arrays as piezoelectric arrays with smaller-scale elements, and view the softness of CMUT membranes as a source of acoustic crosstalk and image quality degradation. This thesis explores the usefulness of the “softness”: the pos- sibility of exciting multiple vibration modes of CMUTs, in contrast with the single-mode, piston-like bulk vibration of the piezoelectric elements. An il- lustration of the multi-mode vibration of the CMUT cell membrane is shown in Fig. 1.4. This thesis studies the modeling and applications of the voltage- driven complex vibrations of CMUTs that can be decomposed into multiple vibration modes. The usage of the multiple vibration modes first relies on the theoretical knowledge of the principle and influence of the excitation of such modes. Then appropriate analytical tools need to be employed to guide the design of novel applications of the modes. A physical structure capable of exciting the modes needs to be realized, and simulation and experiments need to be carried out to verify the novel application ideas. 17 Substrate Bottom electrode Single-mode membrane vibration V Controlled driving voltage + - Multi-mode membrane vibration Top electrode Figure 1.4: Single-mode and multi-mode vibration of the CMUT cell mem- brane. 1.5 Contribution and Structure of the Thesis This thesis explores the idea of exciting multiple vibration modes in CMUT cells and its applications in improving ultrasound imaging. In Chapter 2, the analytical model, finite element model and equivalent circuit models based on mode superposition are described and compared, and the con- cept of asymmetric CMUTs is introduced. Experimental characterization of fabricated CMUTs capable of vibrating in different modes is presented. In Chapter 3, the idea of using asymmetric CMUTs for reducing grating lobes in imaging is proposed and discussed, aided by imaging simulations and FEM simulations. Chapter 4 investigates the idea of super-resolution imaging by taking advantage of the resonant behavior resulting from the asymmetric mode of the CMUT cell. Imaging simulations and proof-of- concept experimental studies using a CMUT probe are presented. Future work involving further experimental verification of the proposed concepts, and ideas on applying the concept to other imaging aspects are discussed in Chapter 5. 18 Chapter 2 Modeling of CMUTs Based on Mode Superposition1 As introduced in Chapter 1, simplified equivalent circuit representations assume the CMUT dynamics is similar to that of a rigid parallel plate. Conversely, numerical finite element analysis, while more accurate, limits the ability to perform design optimization due to prohibitive computation time. This chapter proposes an analytical model based on mode superposition, and couples the electro-mechano-acoustic domains in order to provide the basis for analyzing complex behavior of CMUTs and thus designing novel applications. Experimental characterization of the fabricated CMUT cells were done to show the feasibility of multiple-mode vibrations of CMUTs, and to compare with the model. 1The Asymmetric CMUT concept proposed in this chapter was filed as a United States patent application [95]. The contents in Section 2.1 to Section 2.3 of this chapter were published in IEEE Sensor Journal [124]. Part of Section 2.4 and Section 2.7 was published in IEEE Sensor Journal [128]. Contents of Section 2.7 are in preparation for journal paper submission [11]. The fabrication of the CMUT arrays was done by Ming Cai, MASc., who also collaborated in the CMUT chip characterization. 19 2.1 CMUT Modeling Problem The physical model of a CMUT cell couples three interacting physical do- mains: electrostatic, mechanical and acoustic. The previous CMUT mod- eling methods typically focus on a limited subset of the interactions, while making strong simplifying assumptions on the remaining ones (for example, [60] and [13] focus on electromechanical interaction while not analyzing the radiation (acoustic coupling) except by assuming a resistive acoustic load; [4] simplifies the electromechanical interaction when analyzing radiation in water). It was only in the very recent years that authors start to analyze complex CMUT vibration behaviors [96, 124], compute the exact acoustic impedance [100], and combine analytical and numerical methods to achieve higher model accuracy [63]. They model the CMUT cell as either a rigid piston or a non-piston, such as a membrane or a plate. To provide a better understanding of the complex physical behavior and energy distribution of CMUTs, and to enable system level design leading to novel applications, we present an analytical model for the coupled domains of CMUTs. The mathematical notation for frequently used variables are listed in Table 2.1 with the typical values used in our simulation and calculation in the parentheses. The typical values come from the dimensions of the first batch of fabricated CMUT chips. The electrostatic field is considered as constant across the plate surface. This gap distance can be further estimated to be an equivalent/effective gap distance computed from static DC voltage excitation. The influence of this assumption is investigated in Subsection 2.3.5 with various bias voltages, 20 Table 2.1: Frequently used variables. Parameter Description a CMUT cell membrane radius (35µm) h CMUT cell membrane thickness (1.5µm) d CMUT cell zero-voltage vacuum gap distance (0.75µm) w vertical deflection of the CMUT cell membrane v velocity of the CMUT cell membrane ρp CMUT cell mass density (2320 kg/m 3) 0 permittivity in the vacuum gap (8.85× 10−12 F/m) D flexural rigidity of a plate E Young’s modulus (160× 109 Pa) ν Poisson’s ratio (0.22) Pe external (electrostatic) pressure to the CMUT membrane V driving voltage ω angular frequency P acoustic pressure emitted from the CMUT cell membrane ρm acoustic medium density (1000 kg/m 3) c speed of sound in the acoustic medium (1540 m/s) gap distances and membrane radii. The electromechanical coupling will be modeled in an equivalent circuit model and in future work. 2.2 Analytical Modeling of CMUTs Based on Mode Superposition 2.2.1 Mechanical Modeling: the Plate Vibration Theory There are at least three types of mechanical models available for a vibrating CMUT cell: the plate model, the membrane model, and the hybrid model of both (plate in tension) as summarized in [13]. Balancing the simplicity and accuracy among these models, we consider the CMUT cell membrane as a vibrating elastic circular plate. The plate is clamped at its edges, and 21 its dynamic behavior depends on its thickness, the density of the material, and its flexural rigidity. Since the deflection-to-thickness ratio of the CMUT considered in this work is around 16.7% (a CMUT plate with a deflection- to-thickness ratio of 15.2% does not show significant stress-stiffening effect [58]), explicit stress-stiffening effects are not included in this model. As shown in Fig. 2.1, we assume a top electrode is attached to the bottom of the plate, and a parallel bottom electrode is below the plate separated by a distance. When a voltage is applied to the electrode, the plate will deflect toward the bottom electrode. Plate radius a Plate deflection w Plate thickness h Bottom electrode CMUT membrane Top electrode Vacuum gap d r, ϕ V Figure 2.1: Illustration of the analytical model. Natural Vibration of Plates The equation governing the natural motion of a circular clamped plate in cylindrical coordinates (r, φ) is D∇4w + ρph∂ 2w ∂t2 + Pe = 0 (2.1) w(a, φ) = 0 (2.2) ∂w ∂r |r=a = 0 (2.3) 22 The flexural rigidity of the plate is D = Eh3 12(1− ν2) . (2.4) The simple harmonic solution to Eq. (2.1), assuming a position-independent Pe term, is w = ∑ m,n Fmψm(r, φ)e −iωt (2.5) ψm(r, φ) = cos (mφ)(Jm( λmn a r)− Jm(λmn) Im(λmn) Im( λmn a r)) (2.6) ψm is the characteristic function that represents the m th natural mode of the plate. Jm is the Bessel function of the first kind of order m, and Im is the hyperbolic Bessel function, defined by Im(z) = i −mJm(−z). Eq. (2.5) is called mode expansion [104] or mode superposition, a widely used method to express the plate motion. It allows construction of arbitrary motion shape of the plate with the sum of its natural mode shapes weighted by mode participation factors Fm. The characteristic functions are orthogonal to each other ( ∫ S ψmψndS = 0(m 6= n)), which decouples the motions and energies of the natural shapes. Each natural mode has a natural frequency ωmn = λ2mn a2 √ D ρph (2.7) 23 Forced Vibration of Plates When driven by a harmonic force, the motion of the plate can also be ex- pressed as a summation of natural modes, and the mode participation factor is determined by the type, frequency and spatial distribution of the applied force. Without considering damping, the mode participation factors Fm in the case of an external pressure q (can be one of (or the combination of) the electrostatic pressure and the acoustic pressure in the case of CMUT oper- ation) having both a static component qDC and a harmonic component qac are: (a) The factor corresponding to the static pressure component qDC [N/m 2] Fm,DC = F ∗m,DC ω2m (2.8) F ∗m,DC = 1 ρphNm ∫ S qDC · ψmdS (2.9) (b) The factor corresponding to the harmonic pressure component qac [N/m2] Fm,ac = F ∗m,ac ω2m − ω2 (2.10) F ∗m,ac = 1 ρphNm ∫ S qac · ψmdS (2.11) where qDC and qac are the vectors of force amplitude in three dimensions, and ψm is the characteristic function in these dimensions. dS is the area unit on the plate, and Nm is the integration of ψ 2 m on the plate. ω and ωm 24 are the driving frequency and the natural frequency of the mth mode. 2.2.2 Electrostatic Modeling and Electro-mechanical Coupling Due to the fact that the normal deflection across the plate surface is non- uniform, the electrostatic pressure Pe in Eq. (2.1) is position-dependent: Pe = 0V 2 2(d− w(r, φ))2 (2.12) where w(r, φ) is dependent on Pe at the same time. This bidirectional elec- tromechanical coupling adds complexity in the model. To our knowledge, the fully coupled model was only explicitly solved for the static pull-in case [110], or moderate DC bias voltage cases [1], using trial functions. In order to pro- vide a solution using the mode superposition expression for both static and harmonic cases, we consider a uniform electrostatic pressure, corresponding to an equivalent uniform displacement. In the simple case, this is computed for the zero-voltage position: Pe = 0V 2 2d2 (2.13) We can apply a two-step procedure to account for the effect of the DC bias. The root-mean-square (rms) membrane deflection wrms as a function of volt- age is firstly estimated from FEM results, and then used to correct the gap distance (from the zero-voltage value d to a net value d−wrms) for electro- static force calculation. This gives a hybrid model, but with an increased 25 validity. An expression of wrms vs. VDC for the first mode computed from mode superposition expression is derived from Eq. (2.5) and (2.8): wrms = √ 1 pia2 ∫ 2pi 0 ∫ a 0 w20,1rdrdφ = √ 1 pia2 ∫ 2pi 0 ∫ a 0 [F0,1ψ0,1(r, φ)]2rdrdφ = 1 2(d− wrms)2 0V 2 DC ρphN0,1ω20,1 ∫ S ψ0,1(r, φ)rdrdφ √ N0,1 pia2 (2.14) wrms can be solved as the most physically realistic root of the above poly- nomial equation. Fig. 2.2 shows the comparison of wrms vs. VDC obtained from FEM result and Eq. (2.14). The larger error close to the pull-in is due to the pronounced nonlinearity, which means that the total deformation en- ergy is spread across several mode shapes. We have analytically computed wrms considering only the energy contribution of the first mode. 0 50 100 150 200 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10−7 DC bias [V] rm s de fle ct io n [m ] Static rms deflection vs. DC bias   FEM result Plate model Figure 2.2: Static rms deflection of the first mode vs. VDC : analytical result vs. FEM result. 26 To maintain the tractable mode superposition expression, spring-softening effect [60] is therefore not included in this model. The mode participation factor can serve as an interface for integrating the electro-mechanical cou- pling into the model. 2.2.3 Mechano-acoustic Coupling The next step is to calculate the ultrasonic field generated by such a vibrat- ing plate. The far-field pressure of a certain transducer is the integration of the Green’s function for the velocity of each spherical source on transducer’s surface function [75]: Pω(R) = −ikρmc e ikR 2piR ∫ vω(x0, y0)e −ikxx0−ikyy0dx0dy0 (2.15) where k is the wave number, and R is the distance of the measuring point in the medium. In spherical coordinates, we get the far-field pressure with respect to the directivity angle ϑ: Pω(R) = ρmω 2 e ikR R ∑ m im ∫ a 0 Jm(kr0 sinϑ)Ym(r0)r0dr0 (2.16) where Ym = Fmψm(r, φ) is the radial component of the plate deflection. Eq. (2.16) shows that the far-field pressure can be expressed as a su- perposition of modes computed from integrating the characteristic function ψm with a Bessel function of the first kind, which provides considerable computational convenience. 27 For medical ultrasound applications, we assume water as the medium on one side of the plate. Motion of the plates interacting with the fluid medium can also be computed by summing the natural modes in vacuum, modified such that the influence from the inertial, damping and elastic fluid loading are included. In the case of a circular plate in an infinite medium, the literature usually treats the fluid medium as an added mass on the plate, which is equivalent to reducing the frequency of the natural modes by a factor: fme = fva√ 1 + β (2.17) β = Γ ρma ρph (2.18) where fme and fva are frequency in the medium and in vacuum respectively. Γ is known as Nondimensionalized Added Virtual Mass Factor (NAVMI) that depends on the type of boundary conditions of the vibrating plate and the natural mode [59]. Lax et al. [61] showed that when a plate interacts with the fluid, if the acoustic wavelength is larger than the plate dimension (ka  1), the inertial (mass) term dominates the fluid influence to the plate. The concept of added mass for plates interacting with fluid was also experimentally validated for microstructures, and the NAVMI factor was applied in analyzing the dynamics of microplates in water [117]. The influence from the fluid depends on the relative dimension of the CMUT cell and the acoustic wavelength, as well as the fluid domain bound- ary conditions. When a single CMUT cell vibrates in an infinite fluid medium, and the dimension of the CMUT is much smaller than the acoustic 28 wavelength (typically λ ≈ 1mm, therefore ka  1), the predominant fluid influence is the mass loading. When the CMUTs operate in an array, the fluid boundary condition changes to a periodic condition, and the major fluid influence is the radiation damping. The latter case will be explored by the equivalent circuit model and a different FEM model in Section 2.6.1. Derived from Lax et al.’s work [61], the mode participation factor in water, Fm,water is Fm,water = F ∗m (1 + β)(ω′2m − ω2) (2.19) where ω′2m = 2pifm,water is the angular frequency of the mth mode in water, and ω is the angular frequency of the driving voltage. 2.2.4 Harmonic Motion of Biased CMUTs The static and the harmonic actuations of CMUTs were separately discussed above. In the actual CMUT operation, the driving voltage V is composed of a bias voltage VDC and a harmonic voltage Vac. Therefore, the solution to Eq. (2.1) consists of two parts: w = wDC + wac (2.20) Since usually VDC  Vac, V 2 = (VDC + Vac) 2 ' V 2DC + 2VDCVac (2.21) Then wDC is the deflection caused by a static pressure alone 29 PDC = 0V 2 DC 2d2 (2.22) and wac is the harmonic deflection caused by an equivalent harmonic pres- sure Pac = 0(2VDCVac) 2d2 . (2.23) Eq. (2.15) shows that the far-field pressure only depends on the velocity of the vibrating CMUT, thus only depends on wac. Therefore, the harmonic motion of a biased membrane can be computed from a forced harmonic model (Eq. (2.10)) with the driving pressure Pac. 2.3 Validation of Analytical Modeling Using Finite Element Modeling (FEM) To show the validity of our analytical model, we use the geometric dimen- sions of the first batch of CMUT cells fabricated with PolyMUMPs technol- ogy shown in Table 2.1, and neglect the potential static pressure difference on both sides of the membrane. 2.3.1 Construction of FEM We constructed a Finite Element Model of a CMUT cell in Comsol Multi- physics R© (Comsol Inc., Burlington, MA, USA) software, coupling the struc- tural mechanics subdomain, the electrostatics subdomain, and the pressure acoustics subdomain, as shown in Fig. 2.3. The structural mechanics sub- 30 domain consists of the CMUT cell, which is modeled as a circular membrane made of polysilicon. The air/vacuum gap directly underneath the membrane is the dielectric space for membrane deflection. The electrostatics subdomain includes the air/vacuum gap, the electrodes and the water medium. The top electrodes simplified as voltages are applied at the bottom of the membrane, relative to the bottom electrode as the reference voltage (at the bottom of the air gap). The pressure acoustics subdomain is the outer sphere with radius Rmedium=1 mm, which is used only for the simulation of harmonic movement of the CMUT interacting with the acoustic medium. The electrostatic force load is set as the boundary condition between the electrostatics subdomain and the structural mechanics subdomain. Normal acceleration and the pressure load from the pressure acoustics subdomain are used as the boundary condition between the structural mechanics subdomain and the pressure acoustics subdomain. The outer boundary of the pressure acoustics subdomain is set to be a radiation boundary. Figure 2.3: Finite element model in Comsol. 31 2.3.2 Static Results Comparison The static deflection computation helps identify the exact DC shape of the CMUT membrane, and describes the nonlinear properties of the CMUT be- havior better than the piston models typically employed. Using the CMUT parameters, we have calculated the natural frequencies of the CMUT cell with zero DC bias, while the gap distance with non-zero bias can be com- puted with the hybrid model described in Subsection 2.2.2. Comparison with the Comsol eigenfrequency analysis result is summarized in Table 2.2. The 3D shapes of the analytically calculated first three natural modes are shown in Fig. 2.4. Table 2.2: Natural frequency comparison. Unit:Hz Mode (m,n) Analytical FEM (0,1) 4.87 M 4.88 M (1,1) 10.19 M 10.13 M (0,2) 19.04 M 18.86 M −4 −2 0 2 4 x 10−5 −4 −2 0 2 4 x 10−5 0 0.5 1 1.5 2 x 10−7 x [m] Displacement of (0,1) mode y [m] di sp la ce m en t [m ] (a) −4 −2 0 2 4 x 10−5−4 −2 0 2 4 x 10−5 −4 −3 −2 −1 0 1 2 3 x 10−8 x [m] Displacement of (1,1) mode y [m] di sp la ce m en t [m ] (b) −4 −2 0 2 4 x 10−5 −4 −2 0 2 4 x 10−5 −2 −1 0 1 2 3 x 10−9 x [m] Displacement of (0,2) mode y [m] di sp la ce m en t [m ] (c) Figure 2.4: Analytically calculated first three natural modes of a CMUT cell. (a) (0,1) mode. (b) (1,1) mode. (c) (0,2) mode. The collapse (pull-in) voltage of our CMUT model is estimated to be around 210 V from FEM simulations, and we use a 200 V DC bias voltage in the static calculation and simulation. In the case of uniform static electro- 32 static pressure, the peak static displacement of the first axisymmetric mode (0,1) is calculated to be 55.03 times that of the second axisymmetric mode (0,2), so only the first two axisymmetric modes are used in the analytical cal- culation. To account for the electrostatic effects around the pull-in voltage, we calculate the electrostatic force by subtracting wrms from the original gap distance, i.e., Pe = 0V 2/2(d−wrms)2. We compared the radial compo- nent of the CMUT deflection of the analytical model result with the Comsol static analysis result, as plotted in Fig. 2.5. The root mean square error of the two results is 1.54× 10−8 m (6.25% of the peak displacement of the FEM result). The FEM result shows a higher amplitude than the analytical result. The discrepancy mainly comes from the nonlinear electromechanical coupling and our uniform electrostatic pressure assumption. 0 0.5 1 1.5 2 2.5 3 3.5 x 10−5 0 0.5 1 1.5 2 2.5 x 10−7 x [m] de fle ct io n [m ] In vacuo static deflection comparison   FEM data Plate model Figure 2.5: Static deflection of a CMUT cell: analytical vs. FEM result (radial component of the axisymmetric deflection). 33 2.3.3 Harmonic Results Comparison We continue to use only the first two axisymmetric modes in the analytic model in the case of uniform harmonic electrostatic pressure. This time nevertheless the amplitude depends as well on the difference between the driving frequency and the natural frequency of the axisymmetric modes. We firstly compare the analytically calculated harmonic displacement in vacuum with the corresponding FEM results using Comsol frequency re- sponse analysis. The amplitude of the harmonic voltage is set to 180 V, as an example. The driving frequency is set to 4 MHz, close to the first natural frequency. The comparison is shown in Fig. 2.6. The root mean square error of the two results is 9.7× 10−9 m (2.5% of the peak displacement of the FEM result). The reason that the FEM result is a bit smaller in amplitude than the analytical result is that we did not use the Comsol moving mesh (arbi- trary Lagrangian-Eulerian (ale)) option in harmonic analysis. The moving mesh keeps track of the moving parts more accurately, but does not give cor- rect amplitude results for the harmonic models. However, the two results are still in reasonable agreement with each other. The harmonic calculation in a fluid (water) medium is done next with the same driving voltage. The equivalent natural frequencies in water are calcu- lated to be f(0,1),water=2.04 MHz, f(1,1),water=5.27 MHz, f(0,2),water=10.91 MHz. The driving frequency is set to 1 MHz, close to the first equivalent natural frequency in water. Fig. 2.7 shows the comparison between the analytical result of deflection in water, and the FEM results in water. The root mean square error of the two results is 4.4× 10−9 m (2.5% of the peak displace- 34 0 0.5 1 1.5 2 2.5 3 3.5 x 10−5 0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 x 10−7 x [m] de fle ct io n [m ] In vacuo harmonic deflection comparison   FEM data Plate model Figure 2.6: In-vacuo harmonic deflection of a CMUT cell: analytical vs. FEM result (radial component of the axisymmetric deflection). ment of the FEM result). The good match between the two results validates the approach of added mass. 0 0.5 1 1.5 2 2.5 3 3.5 x 10−5 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 x 10−7 x [m] de fle ct io n [m ] In water harmonic deflection comparison   FEM data Plate model Figure 2.7: In-water harmonic deflection of a CMUT cell: analytical vs. FEM result (radial component of the axisymmetric deflection). 35 2.3.4 Frequency and Impulse Response Results Comparison The frequency response results are compared between the simple harmonic results from the analytical model, and FEM results from Comsol frequency response analysis, both with 180 V driving voltage. The comparative fre- quency response of in-vacuo membrane center deflection is shown in Fig. 2.8. The resonant frequencies of the plate model and the FEM result are shown to be very close. Although Fig. 2.6 shows an amplitude difference in har- monic in-vacuo deflection (rms error 2.5%), the difference is not sufficiently large to make a significant difference in resonant frequency. The compara- tive frequency response of in-water membrane center deflection is shown in Fig. 2.9. We also present the FEM results of the pre-biased membrane using a 180 V DC bias voltage, superposed over a 10 V amplitude harmonic volt- age in the frequency response analysis for the in-vacuo and in-water cases. Compared with pure harmonic driving results, the pre-biased FEM results show spring softening effects with lowered resonant frequencies, which are not yet captured in the current version of the analytical model. The compar- ative frequency response of the output pressure directly above the center of the CMUT membrane is shown in Fig. 2.10. The analytical output pressure is computed from the product of the harmonic membrane velocity and the radiation impedance of the (0,1) mode and (0,2) mode obtained from [61]. The deviation between the results of the two models may result from the fact that the FEM analysis computes more higher order modes than the analytical model. We computed the impulse response of a CMUT membrane in water 36 0 2 4 6 8 10 x 106 0 0.5 1 1.5 2 2.5 3 x 10−5 frequency [Hz] de fle ct io n [m ] Frequency response of in−vacuo membrane deflection   FEM frequency response FEM prestressed frequency response Plate model Figure 2.8: Frequency response of in-vacuo membrane center deflection: analytical vs. FEM result. 0 2 4 6 8 10 x 106 0 0.5 1 1.5 2 2.5 3 3.5 4 x 10−6 frequency [Hz] de fle ct io n [m ] Frequency response of in−water membrane deflection   FEM frequency response FEM prepressed frequency response Plate model Figure 2.9: Frequency response of in-water membrane center deflection: an- alytical vs. FEM result. by taking the inverse Fourier transform of the corresponding frequency re- sponse, as shown in Fig. 2.11. The impulse response shows that the CMUT cell is under-damped, which is consistent with the fact that the inertial water loading dominates the radiation impedance for a single CMUT cell 37 0 2 4 6 8 10 x 106 −90 −80 −70 −60 −50 −40 −30 −20 −10 0 frequency [Hz] n o rm a liz ed  o ut pu t p re ss ur e [dB ] Frequency response of normalized output pressure   FEM data Plate model Figure 2.10: Frequency response of in-water output pressure at the mem- brane center: analytical vs. FEM result, normalized with respective peak values. with low values of ka [61, 104]. The FEM result appears more damped than the plate model because the viscous damping was not considered in the analytical model. 0 1 2 3 4 5 x 10−6 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 0.6 0.8 1 time [s] n o rm a liz ed  d ef le ct io n Impulse response of normalized in−water membrane deflection   FEM data Plate model Figure 2.11: Impulse response of in-water membrane center deflection: an- alytical vs. FEM result, normalized with respective peak values. 38 2.3.5 Electrostatic Effects The electrostatic force in the proposed analytical model is assumed uniform, and is computed using the original gap distance, if the hybrid two-step pro- cess using wrms from FEM results (Subsection 2.2.2) is not applied. This subsection investigates the influence of this assumption on the analytical calculation, in comparison with the FEM results which account for the spa- tially varied membrane deflection in calculating the electrostatic forces. The static deflection is compared as an example. Fig. 2.12 shows the difference between FEM and analytical results for different conditions. As the DC bias voltage gets closer to the pull-in voltage (e.g. 200 V versus 150 V), the uni- form electrostatic force assumption leads to larger errors compared to FEM results. Similarly, the assumption causes larger discrepancies in results when the CMUT has a smaller gap distance (0.75µm rather than 1.5µm), or a larger membrane (a= 35µm rather than a= 17.5µm). These results suggest that the uniform electrostatic pressure simplification gives accurate results only when physical parameters do not produce strong electrostatic effects in the gap. In this later case, a hybrid solution is to be preferred, where the equivalent wrms as a function of bias voltage is extracted from FEM simulations and used afterward in the analytic model. 2.3.6 Far-field Pressure Comparison In this section we compute the far-field pressure of the CMUT using the analytical plate model, and compare it with the FEM and analytical piston model results. 39 0 0.5 1 1.5 2 2.5 3 3.5 x 10−5 0 0.5 1 1.5 2 2.5 x 10−7 x [m] de fle ct io n [m ] In−vacuo static deflection with varied bias voltages, gap distances and radii   FEM data with 200V Bias, 0.75um gap, 35um radius Plate model with 200V Bias, 0.75um gap, 35um radius −−−−−−−−−−−−−−−−−−−− FEM data with 150V Bias Plate model with 150V Bias −−−−−−−−−−−−−−−−−−−− FEM data with 1.5um gap Plate model with 1.5um gap −−−−−−−−−−−−−−−−−−−−− FEM data with 17.5um radius Plate model with 17.5um radius Figure 2.12: The influence of uniform electrostatic force with the original gap distance in cases of different bias voltages, gap distances and membrane radii. Piston Model Most current studies treat CMUTs as equivalent vibrating pistons in their coupled analysis, with a uniform velocity profile across the CMUT surface. The piston assumption was adopted because of its ease in modeling the cou- pling with other physical domains, similar to the theory used for piezoelectric transducers. This assumption ignores the influence of CMUTs’ plate-like behavior on other physical domains. To show the necessity of developing the analytical plate model, this subsection compares the acoustic far-field produced by a plate model with that of a piston model. Assume the CMUT parameters are the same as listed in Table 2.1. The 40 far-field radiation for a piston can be found in [75]: Pω(R) = −ikρmce ikR 2R a2ωwDω(ϑ) (2.24) Dω(ϑ) = 2J1(ka sinϑ) ka sinϑ (2.25) where w is the uniform deflection on the piston. Far-field Pressure Comparison We apply the same radius to the plate model and the piston model. To match the kinetic energy, we use the rms velocity of the plate model as the driving velocity for the piston model. The pressure is calculated at 1 m away from the CMUT, to match the far-field definition in Comsol simulation. The far-field pressure is compared among the FEM results, the ana- lytical results of the plate model and the analytical results of the piston model at different driving frequencies (1 MHz and 4 MHz), and with differ- ent plate/piston radii (35µm and 70µm), as shown in Fig. 2.13. The CMUT plate model has a far-field profile closer to the FEM re- sults both in amplitude and in shape. Comsol Multiphysics evaluates the far-field at a given distance R such that it ensures convergence when R increases to infinity. As a consequence, the far-field simulated by Comsol gives an approximated amplitude value and shows mainly the distribution of the acoustic pressure at 1 m distance. We thus adjusted the FEM data and our analytical results to refer to the same range for each combination of frequency and radius for the shape comparison. Together with Oguz’s result [82] showing the difference of radiation impedance between a clamped ra- 41 diator and a piston, our far-field comparisons between the plate model and the piston model suggest that it is improper to simplify the CMUT with a piston model due to the differences in radiation impedance and angular distribution of radiated energy, especially when certain types of design opti- mization are involved. For example, when trying to optimize the radiation efficiency of CMUTs using the radiation impedance, or the pitch between the cells using the far-field profile, approximating a CMUT cell as a piston may bring inaccuracies. 2.4 The Concept of Symmetric and Asymmetric CMUTs As can been seen in the Eq. 2.8 and Eq. 2.10, the participation of modes can be determined by the type of external force/pressure, i.e. if the force consists of components that produces non-zero mode participation factor of mode m, the vibration profile will include the mth component. Therefore, the electrostatic force applied on the CMUT membrane can be adjusted to be non-axisymmetric so that the membrane vibrates asymmetrically. For example, if we apply a voltage V1 on one half of the top electrode, and V2 on the other half of the top electrode, the electrostatic pressure on the two parts of the membrane becomes approximately Pe1 = 0V 2 1 2d2 , Pe2 = 0V 2 2 2d2 (2.26) and the total electrostatic pressure Pe expressed in cylindrical coordinate 42 −100 −50 0 50 100 0.698 0.6985 0.699 0.6995 0.7 0.7005 0.701 0.7015 0.702 0.7025 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure from FEM (a) −100 −50 0 50 100 0.7865 0.787 0.7875 0.788 0.7885 0.789 0.7895 0.79 0.7905 0.791 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure of the Plate Model (b) −100 −50 0 50 100 1.463 1.4635 1.464 1.4645 1.465 1.4655 1.466 1.4665 1.467 1.4675 directivity [degree] fa r− fie ld  p re ss ur e Far−field Pressure of the Piston Model (c) −100 −50 0 50 100 1.95 2 2.05 2.1 2.15 2.2 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure from FEM (d) −100 −50 0 50 100 4.35 4.4 4.45 4.5 4.55 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure of the Plate Model (e) −100 −50 0 50 100 4.25 4.3 4.35 4.4 4.45 4.5 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure of the Piston Model (f) −100 −50 0 50 100 3.9 3.92 3.94 3.96 3.98 4 4.02 4.04 4.06 Far−field Pressure from FEM directivity [degree] fa r− fie ld  [P a] (g) −100 −50 0 50 100 6.25 6.3 6.35 6.4 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure of the Plate Model (h) −100 −50 0 50 100 11.74 11.76 11.78 11.8 11.82 11.84 11.86 11.88 11.9 directivity [degree] fa r− fie ld  p re ss ur e [P a] Far−field Pressure of the Piston Model (i) Figure 2.13: Far-field pressure comparison: with 1 MHz driving frequency and 35µm radius ((a) FEM (b) Plate (c) Piston, data range adjusted to 0.0045 Pa), with 4 MHz driving frequency and 35µm radius ((d) FEM (e) Plate (f) Piston, data range adjusted to 0.25 Pa), and with 1 MHz driv- ing frequency and 70µm radius ((g) FEM (h) Plate (i) Piston, data range adjusted to 0.16 Pa). is Pe = Pe1 + Pe2 2 + Pe2 − Pe1 2 cos(φ) (2.27) where φ is the angular coordinate. In this way at least one axisymmet- ric mode (m=0,n=1) and one non-axisymmetric mode (m=1,n=1) in the 43 CMUT cell will be excited due to the integration of the axisymmetric force component and the non-axisymmetric force component with the respective characteristic equations. Other modes of vibration can be excited in a sim- ilar way. This type of fine control on the level of an individual CMUT cell could open opportunities for designing new imaging methods, which will be presented in Chapter 3 and Chapter 4. 2.5 Comparison of Analytical Modeling and FEM Results of Asymmetric CMUTs We apply the same CMUT parameters as in Table 2.1 to the analytical model developed in Section 2.2, and compare the results with those from FEM simulation. The FEM model is similar to the one constructed in Section 2.3 with two sections for the CMUT membrane, allowing two voltage levels to be applied on the bottom of the CMUT membrane to simulate the top electrodes. 2.5.1 Static Results Comparison In the case of asymmetric static electrostatic pressure, both the symmetric modes and the asymmetric modes will be excited. Two symmetric modes, (m=0,n=1) and (m=0,n=2), and one asymmetric mode, (m=1,n=1) are used in the analytical calculation. The pull-in (collapse) voltage of the CMUT cell was simulated to be 210 V. A pair of DC voltage 200 V/0 V was applied on the left and right half of the electrode respectively, for both analytical calculation and FEM simulation. To account for the electrostatic 44 effects around the pull-in voltage, we subtract the rms membrane deflection in FEM result (wrms) from the original gap distance, for the electrostatic force calculation of the analytical model, that is, Pe2 = 1/2(0V 2)/(2(d − wrms) 2). We compared the cross-sectional static deflection of the analytical model result with the Comsol static analysis result, as plotted in Fig. 2.14. The root mean square error between the two results is 3.69× 10−9 m (3.81% of the peak displacement of the FEM result). −4 −3 −2 −1 0 1 2 3 4 x 10−5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10−7 x [m] de fle ct io n [m ] In−vacuo static deflection comparison   FEM Plate model Figure 2.14: Cross-section of in-vacuo asymmetric static deflection of a CMUT cell: analytical vs. FEM result. The FEM deflection shows a bigger asymmetric effect than the analyt- ical calculation, mainly because the electrostatic pressure on the left half side actually forms a positive feedback with the membrane deflection (the membrane deflection reduces the gap distance which in turn increases the electrostatic effect), which is not captured by the analytical calculation. Therefore a larger asymmetric effect is observed in the FEM result. 45 2.5.2 Harmonic Results Comparison In the case of asymmetric harmonic electrostatic pressure, the amplitude is dependent also on the difference between the driving frequency and the natural frequency of the excited modes. We first show the comparison between analytically calculated harmonic displacement in vacuum and the corresponding FEM results. The har- monic voltage pair is set to 180 V/0 V, as an example. The natural fre- quencies of the first three modes are computed to be f(0,1),vac = 4.87 MHz, f(1,1),vac = 10.19 MHz, f(0,2),vac = 19.04 MHz. The driving frequency is set to 4 MHz, close to the first natural frequency. The cross section of the two results are compared in Fig. 2.15. The root mean square error of the two results is 6.82× 10−9 m (3.47% of the peak displacement of the FEM result). −4 −3 −2 −1 0 1 2 3 4 x 10−5 0 0.5 1 1.5 2 2.5 x 10−7 x [m] de fle ct io n [m ] In−vacuo hamonic deflection comparison   FEM Plate model Figure 2.15: Cross-section of in-vacuo asymmetric harmonic deflection of a CMUT cell: analytical vs. FEM result. The harmonic calculation in a liquid (water) medium is done next with the same driving voltage. The equivalent natural frequencies in water are calculated according to the NAVMI factor [59] and Eq. 2.19 which considers 46 the fluid loading as an added mass on the membrane: f(0,1),water=2.04 MHz, f(1,1),water=5.27 MHz, f(0,2),water=10.91 MHz. The driving frequency is set to 1 MHz, close to the first equivalent natural frequency in water. Fig. 2.16 shows the comparison between the analytical result of deflection in water, and the FEM result with the water medium. The root mean square error of the two results is 2.64× 10−9 m (2.89% of the peak displacement of the FEM result). −4 −3 −2 −1 0 1 2 3 4 x 10−5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10−7 x [m] de fle ct io n [m ] In−water harmonic deflection comparison   FEM Plate model Figure 2.16: Cross-section of in-water asymmetric harmonic deflection of a CMUT cell: analytical vs. FEM result. The comparison between analytical results and FEM results shows that the asymmetrically controlled motion can be analytically calculated. This is potentially very useful for designing novel control and signal processing methods for CMUTs as well as system level optimization. 47 2.6 Equivalent Circuit Modeling of CMUTs Based on Mode Superposition Equivalent circuit models are widely used for fast simulation of coupled electro-mechano-acoustic systems like CMUTs [60], but few works discuss the equivalent circuits for complex CMUT behavior beyond the first symmet- ric mode. In this section, an equivalent circuit model is built that captures the multi-mode behavior of CMUTs, using the analytical model based on mode superposition in Section 2.2. 2.6.1 Equivalent Circuit Construction The different modes of CMUT vibration are expressed by different sub- circuits, similar to what is proposed in [97]. In this work, only two sub- circuits were developed for (0,1) and (1,1) modes to constitute the asym- metric CMUT vibration. More sub-circuits can be added for different ap- plications. Each sub-circuit has an electrical port and a mechanical port, and follows a typical MEMS parallel-plate equivalent circuit model with the following constitutive equations and the corresponding circuit shown in Fig. 2.17 [27]. i = dQ dt = C(q) du dt + u dC(q) dq vq (2.28) fq = −1 2 u2 dC(q) dq where q is the displacement of the plate, and C(q) is the capacitance of the CMUT. There are two pairs of across-through variables (u, i) and (fq, vq). 48 Figure 2.17: Basic parallel-plate equivalent circuit model [27]. With per- mission from the author. u and i are the across (voltage) and through (current) variables at the elec- trical port, representing the electrostatic input to the system. fq and vq are the force and velocity at the mechanical port where the force is the through variable (current) and velocity is the across variable (voltage), dif- ferent from several of the CMUT equivalent circuit models [60, 118] derived from Mason’s model [69]. The parameters of the circuit are calculated as follows: Parallel capacitance from the equivalent mass The parallel equiv- alent capacitance CM at the mechanical port is related to the equivalent mass of the mode. The equivalent mass for a mode can be calculated from the total kinetic energy T ∗: T ∗ = ρph 2 ∫ 2pi 0 ∫ a 0 (v01(r, t) + v11) 2rdrdφ (2.29) = ρph 2 ∫ 2pi 0 ∫ a 0 v01(r, t) 2rdrdφ+ h 2 ∫ 2pi 0 ∫ a 0 v11(r, t) 2rdrdφ = ρph 2 (v2rms,01S + v 2 rms,11S) 49 where v01 and v11 are orthogonal characteristic velocity functions of the two modes, so the cross integral becomes zero. The equivalent masses for the two modes are M01 = d dt ∂T ∗ ∂vrms,01 / d dt vrms,01 (2.30) M11 = d dt ∂T ∗ ∂vrms,11 / d dt vrms,11 Therefore, the equivalent mass for both modes are the physical mass of the membrane: M01 = M11 = MCMUT = ρphpia 2 (2.31) The parallel equivalent capacitance representing the mass is then com- puted as CM,01 = M01 (2.32) CM,11 = M11 Parallel inductance from the equivalent spring constant The par- allel equivalent inductance L at the mechanical port represents the spring constants of the mode, and is related to the in-air resonant frequency of the two modes: L01 = 1/k01 = ω 2 01M01 (2.33) L11 = 1/k11 = ω 2 11M11 50 Capacitance and resistance from medium loading The loading from the medium for both modes include the mass loading from the medium, and the radiation damping. The mass loading from the medium, represented by another capacitance can be computed from [34] Cfl,01 = Sρm/K01 (2.34) Cfl,11 = Sρm/K11 where Kmn = 4 √ ω2mnρph/D is the structural wave number of the mode. The radiation damping is calculated the radiation impedance of the medium, as typically considered in literature. It appropriately describes the case of a large number of CMUT cells operating in phase in an array. The medium is considered as a fluid column on top of each CMUT cell and has periodic or sound-hard boundary conditions on its periphery [121]. This is a different assumption than the model in Section 2.2, which was an earlier elemental analysis of each individual cell. The fluid column assumption used in this section leads to a more advanced model for practical CMUT array operation. The radiation damping is significant for the (0,1) mode, and minimal for the (1,1) mode because the anti-symmetric pressure field does not propagate to the far field if the dimension of the membrane is much smaller than the acoustic wavelength [34]. Therefore, Rrad,01 = 1/(ρmcS) (2.35) 51 Parameters from electromechanical interaction According to the constitutive equation, the rest of the circuit parameters resulting from the electromechanical interaction are calculated as follows: C0,01 = 0S d− wrms,01 (2.36) dC0,01 dwrms,01 = 0S (d− wrms,01)2 = 0S d2 (1 + 2wrms,01 d ) f0,01 = 0Su 2 2d2 (1 + 2wrms,01 d ) C0,11 = 0S 2(d− wrms,11) dC0,11 dwrms,11 = 0S 2((d− wrms,11)2) = 0S 2d2 (1 + 2wrms,11 d ) f0,11 = 0Su 2 4d2 (1 + 2wrms,11 d ) Because the net vibration of the (1,1) mode is minimal, the mechanical vibration and the capacitance of half of the membrane is modeled for (1,1) mode. 2.6.2 Equivalent Circuit Implementation The equivalent circuits are implemented in NI Multisim 12.0 R© (National In- strument, Austin, TX, USA), and the electromechanical interaction behavior is expressed using the virtual elements such as voltage-controlled-capacitors and voltage-controlled-resistors. A screen shot of the schematic of the two sub-circuits for the two modes is shown in Fig. 2.18. The voltage ampli- tude for (0,1) and (1,1) modes are the same, representing the case when one side of the membrane has a net excitation of 0 V and the other side has an 52 excitation of 2(VDC + Vac). 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 A A B B C C D D E E F F G G C1 24.2pF L1 143.8µH C2 24.2pF L2 32.9µH R1 93.5Ω C3 102.3pF C4 70.7pF I3 I = { 1.09e-7/2*V(3)^2*(1+2*sdt(V(1))/0.75e-6) }V1 10 Vpk 1MHz 0° I1 I = { 5.5e-8/2*V(3)^2*(1+2*sdt(V(2))/0.75e-6) } V2 V = { 6.14e-20/(0.75e-6-sdt(V(1))) } U1 1 F/V 0.064p 5 4 U2 1 Ω/V V3 V = { 1/(1.09e-7*(1+2*sdt(V(1))/0.75e-6)*(V(1)==0?1e-12:V(1))) } 7 6 V5 V = { 3.07e-20/(0.75e-6-sdt(V(2))) } U3 1 F/V 0.041p U4 1 Ω/V V6 V = { 1/(5.5e-8*(1+2*sdt(V(2))/0.75e-6)*(V(2)==0?1e-12:V(2))) } 9 8 11 10 3 0 2 0 1 Figure 2.18: (0,1) mode and (1,1) mode equivalent circuit implemented in Multisim. 2.6.3 Comparison Between Equivalent Circuit Simulation and FEM Result The results from the equivalent circuits simulation are compared with FEM simulation with the same parameters. Note that the CMUT membrane ra- dius here is 47µm, different from the one used in Section 2.3, while other parameters stay the same2. The calculated resonant frequencies for (0,1) mode and (1,1) mode in air, according to Eq. 2.7 are f(0,1),vac=2.70 MHz, 2This is to comply with a batch of successfully fabricated CMUT chips, while the previous batch with the 32µm radius was defected. 53 f(1,1),vac=5.65 MHz; and the central frequencies for the two modes in water, considering the mass loading from the water (Eq. 2.19), are f(0,1),water=0.90 MHz, f(1,1),water=2.38 MHz respectively. We built an FEM model in Comsol Multiphysics simulating the CMUT cell operating in an array of cells excited in phase. The FEM model is shown in Fig. 2.19. The only difference with the previous FEM model is that the acoustic medium is changed to a fluid column above the CMUT cell membrane, and the boundary conditions of the periphery of the column is set to sound-hard (or alternatively periodic). The fluid column serves as a wave guide since the waves emitted from neighboring cells can be deemed as reflection of the self-emitted waves at the fluid column periphery. The end of the fluid column is set to radiation condition. The CMUT cell membrane has two sections for applying different level of voltages. Figure 2.19: FEM of a CMUT cell operating in an array. A parametric sweep of DC voltage (from VDC=100 V to VDC=160 V) 54 with AC analysis (Vac=5 V) was performed in Multisim for both in-air and in-water conditions. The medium load impedance are open circuited for in-air simulations. The frequency response for the mode (0,1) sub-circuit and the mode (1,1) sub-circuit is shown in Fig. 2.20 where V (1) and V (2) are the voltage equivalence of the output velocity of the two modes. In the FEM analysis, the voltage is only applied on half of the CMUT membrane, and a linearized perturbation analysis was performed. The FEM result of the average velocity amplitude on half of the CMUT membrane is shown in Fig. 2.21. Printing Time:Thursday, August 16, 2012, 12:01:15 PM  V(2), vv1 dc=100  V(1), vv1 dc=100  V(2), vv1 dc=120  V(1), vv1 dc=120  V(2), vv1 dc=140  V(1), vv1 dc=140  V(2), vv1 dc=160  V(1), vv1 dc=160 Device Parameter Sweep: in-air Frequency (Hz) 0.0000 6.0000M500.0000k 1.0000M 5.0000M1.5000M 4.5000M2.0000M 4.0000M2.5000M 3.5000M3.0000M M a g n i t u d e  ( d B ) -75.0000 75.0000 -50.0000 50.0000 -25.0000 25.0000 0.0000  V(2), vv1 dc=100  V(1), vv1 dc=100  V(2), vv1 dc=120  V(1), vv1 dc=120  V(2), vv1 dc=140  V(1), vv1 dc=140  V(2), vv1 dc=160  V(1), vv1 dc=160 Frequency (Hz) 0.0000 6.0000M500.0000k 1.0000M 5.0000M1.5000M 4.5000M2.0000M 4.0000M2.5000M 3.5000M3.0000M P h a s e  ( d e g ) -100.0000 100.0000 -50.0000 50.0000 0.0000 Figure 2.20: In-air equivalent circuit simulation result of a CMUT cell op- erating in an array. The FEM results show two resonant peaks in the velocity of half of the CMUT membrane, which means it is a superposition of two modes. This is verified by the two resonant peaks in the equivalent circuit model. It also shows the down-shift of resonant frequency with the increase of DC voltage resulting from spring softening effect. Note that the DC voltage can pass the calculated pull-in voltage if it is only applied on half of the CMUT cell. The equivalent circuit and FEM results in water are shown in Fig. 2.22 55 Figure 2.21: In-air FEM simulation result of a CMUT cell operating in an array. and Fig. 2.23 respectively. It can be seen that the (0,1) mode is considerably damped with a wide band behavior in water whereas the (1,1) mode is still resonant in water, which can be seen on the average velocity on half of the CMUT membrane. This is an important feature which will be explored for novel imaging method in Chapter 4. Printing Time:Thursday, August 16, 2012, 11:40:58 AM  V(2), vv1 dc=100  V(1), vv1 dc=100  V(2), vv1 dc=120  V(1), vv1 dc=120  V(2), vv1 dc=140  V(1), vv1 dc=140  V(2), vv1 dc=160  V(1), vv1 dc=160 Device Parameter Sweep: in-water Frequency (Hz) 0.0000 3.0000M250.0000k 500.0000k 2.5000M750.0000k 2.2500M1.0000M 2.0000M1.2500M 1.7500M1.5000M M a g n i t u d e  ( d B ) -75.0000 75.0000 -50.0000 50.0000 -25.0000 25.0000 0.0000  V(2), vv1 dc=100  V(1), vv1 dc=100  V(2), vv1 dc=120  V(1), vv1 dc=120  V(2), vv1 dc=140  V(1), vv1 dc=140  V(2), vv1 dc=160  V(1), vv1 dc=160 Frequency (Hz) 0.0000 3.0000M250.0000k 500.0000k 2.5000M750.0000k 2.2500M1.0000M 2.0000M1.2500M 1.7500M1.5000M P h a s e  ( d e g ) -100.0000 100.0000 -50.0000 50.0000 0.0000 Figure 2.22: In-water equivalent circuit simulation result of a CMUT cell operating in an array. To summarize, the equivalent circuit model results and the FEM results 56 Figure 2.23: In-water FEM simulation result of a CMUT cell operating in an array, averaged on half of the cell agree with each other, as well with the theoretical calculation of the reso- nant frequencies. The equivalent circuit model is useful in fast simulation of complex CMUT movements which can be decomposed into orthogonal modes. 2.7 Experimental Characterization of Symmetric and Asymmetric CMUTs We experimentally tested the symmetric and asymmetric behavior of the CMUTs fabricated using the PolyMUMPs process, a three-layer polysil- icon micromachining process offered by MEMSCAP Inc.(North Carolina, USA) [10]. The design of a CMUT cell using the PolyMUMPs layers is shown in Fig. 2.24. The 2.0µm Poly1 layer was used as the bottom elec- trode, the 0.75µm second oxide layer was used as the air gap, and the 1.5µm Poly2 layer was used as structural layer. The silicon nitride layer is 0.6µm 57 in thickness. Each CMUT cell has a membrane radius of 53µm, and an electrode radius of 47µm. The cell dimensions are the same with the pa- rameters used in FEM simulation and analytical calculation in Section 2.4. Voltage signals are applied on the membrane, and the bottom electrodes are connected to ground. Figure 2.24: Cross section of the design of a CMUT cell using PolyMUMPs [10]. With permission from the author. Each packaged die contains a 2D CMUT array of 71 rows by 71 columns of regular cells with complete circular bottom electrodes, and several stan- dalone cells whose bottom electrodes are split in half for applying different voltages 3, as shown in Fig. 2.25. 2.7.1 Optical Characterization The CMUT array was characterized using a Laser Doppler Vibrometer (LDV) Polytec Micro System Analyzer (MSA-500) (Polytec Inc., CA, USA). Pull-in Voltage The pull-in (collapse) voltage of a CMUT is the DC voltage beyond which the electrostatic force exceeds the mechanical restoring force, and the mem- 3termed Adaptive CMUTs in [128] 58 Adaptive CMUT cell Regular CMUT cells 10 mm Figure 2.25: A die with a 2D CMUT array and standalone CMUTs fabri- cated using PolyMUMPs. brane collapses to the substrate. The pull-in voltage can be theoretically calculated as Vpi = √ 8kd3/270S [60] which is 118.96 V for our CMUT chip. When the voltage of pull-in has occurred, and gradually returns to lower val- ues, the membrane snaps back to a suspended position, a process known as hysteresis [60]. Because the MSA-500 cannot measure static displacement, we chose a low frequency, low amplitude AC voltage superimposed on an increasing DC voltage in order to find the pull-in voltage. A 2.5 V, 300 kHz sinusoidal signal (far from the expected resonant peak) is chosen as the AC voltage, and a DC offset starting from 10 V with a 10 V step is superimposed to observe the pull-in. We observed that the measured displacement of the CMUT membrane dropped to a very small value after a dramatic increase, and consider the DC voltage at this point the pull-in voltage. The small displacement suggests that the membrane collapses to the substrate. In our experiment, when the DC voltage is later reduced, the AC displacement does not increase. The reason may be that the membrane adheres to the bottom electrode as it collapses due to the viscous residue in the gap between the 59 bottom electrode and the CMUT membrane after hydrofluoric release [10]. Tests on multiple CMUT chips all showed a pull-in voltage between 90 V and 100 V. The voltage-displacement curves from the FEM simulation and the experimental characterization are shown in Fig. 2.26. The linear behav- ior at low voltages in Fig. 2.26(b) may be the result of the resistance of the interconnects on the chip. 0 20 40 60 80 100 120 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 x 10−7 VDC [V] st at ic  d isp la ce m en t [m ] (a) 10 20 30 40 50 60 70 80 90 0 1 2 3 4 5 6 7    u  test o  C U                 VDC [V] A C  d is pl ac em en t [ nm ] (b) Figure 2.26: CMUT membrane displacement versus DC voltage. (a) FEM simulation of DC displacement. (b) Experimental characterization of AC displacement. Vibration Modes and Resonant Frequencies in Air A periodic chirp excitation voltage is used for the frequency response char- acterization. The amplitude of the periodic chirp is set to 10 V, and the frequency ranges from 1000 Hz to 10 MHz. A scanning measurement was performed on a CMUT cell with 2 bottom electrodes in order to observe its frequency response under both symmetric (equal voltage on both electrodes) and asymmetric (voltage on only one electrode) actuation. The measured 60 and simulated vibration profile of one CMUT cell in (0,1) mode, and the frequency response under symmetric actuation are shown in Fig. 2.27. The measured and simulated vibration profile of (1,1) mode, and the frequency response under asymmetric actuation are shown in Fig. 2.28. The CMUT membrane clearly shows two vibration modes under asymmetric actuation, represented by resonant peaks from asymmetric excitation. (a) (b) (c) Figure 2.27: The deflection profile and frequency response of a CMUT cell under symmetric actuation. (a) (0,1) mode deflection profile from exper- imental characterization. (b) (0,1) mode deflection profile from FEM. (c) Frequency response with symmetric excitation from experimental character- ization. The measured resonant frequencies are compared with the resonant fre- quencies from the eigen-mode analysis in FEM as well as the analytical model, shown in Table 2.3. The result shows that the analysis and the 61 (a) (b) (c) Figure 2.28: The deflection profile and frequency response of a CMUT cell under asymmetric actuation. (a) (1,1) mode deflection profile from exper- imental characterization. (b) (1,1) mode deflection profile from FEM. (c) Frequency response with asymmetric excitation from experimental charac- terization. experimental characterization are in good agreement. The error in the ex- perimental measurement may be a result of the idealization of the structure in the analytical and the FEM models, e.g. the electrode size is not identical to the membrane size in the actual fabricated structure. Unlike piezoelectric transducers array whose errors in resonant frequencies cannot be corrected once fabricated, the resonant frequencies of CMUT cells can be tuned after fabrication to achieve higher level of uniformity using the DC voltages. The asymmetric vibration behavior of a CMUT cell was further tested by applying a 10 V, 5 kHz simple sinusoid signal on one half of the bottom 62 Table 2.3: Measured resonant frequencies compared with FEM analysis and analytical calculation. Mode (m,n) Measurement Analytical FEM (0,1) 2.57 MHz 2.70 MHz 2.72 MHz (1,1) 4.84 MHz 5.65 MHz 5.69 MHz Measurement grid points Figure 2.29: The asymmetric deflection profile of an asymmetrically driven CMUT. electrode. The CMUT shows an asymmetric movement at 1 MHz in the frequency spectrum with a maximum harmonic deflection of 0.25 nm. The deflection amplitude of a grid of measurement points on the membrane of a single CMUT cell is shown in Fig. 2.29. A superimposed DC bias or a higher AC actuation would increase the amplitude of deflection. The experimental measurement shows that CMUT cells applied with asymmetric voltage excitation exhibit a shift in vibration center, which will be used in Chapter 3 and Chapter 4. Spring Softening Effect The electrostatic spring softening effect was observed by fixing the amplitude of the periodic chirp at 2.5 V, and changing the DC offset from 10 V to 60 V. The first resonant frequency of one CMUT cell drops as the DC bias increases, as shown in Table 2.4. 63 Table 2.4: Spring softening effect from experimental characterization. DC bias (V) first resonant frequency (MHz) 10 2.565625 20 2.565625 30 2.564063 40 2.551563 50 2.528125 60 2.503125 Frequency Response in Oil Immersion Since the air gaps are not sealed in the fabricated array, we performed the immersion tests of the CMUT array in olive oil. Olive oil has high viscosity that may delay in filling up the air gap through the unsealed etch holes. It also has similar acoustic impedance to water (1.391 MRayl for olive oil vs. 1.483 MRayl for water), and provides electrical insulation for the array. The CMUT array was immersed in 5 mm depth of olive oil, biased by a DC voltage of 30 V-40 V to improve output power and sensitivity, and actuated by a periodic chirp with an amplitude of 5 V. Symmetrically excited cell First, a single CMUT cell was tested with same electrical excitation on both of its bottom electrodes, i.e. symmetric excitation. Fig. 2.30 shows the vibration shape and the frequency response of the cell. The CMUT has a highly damped behavior in oil, with its center frequency around 1 MHz, which aligns with the FEM analysis of a CMUT array in Section 2.6.1. The damping partly results from acoustic radiation, and partly from the viscous damping of the oil. Although we did not observe a significant drop of amplitude within a few hours of operation, the pressure 64 output efficiency must have been lowered in the first place due to the open gap. Figure 2.30: Screenshot of the deflection profile and frequency response of a symmetrically driven CMUT cell immersed in olive oil. Asymmetrically excited cell We then applied the DC voltage and the periodic chirp only on the right bottom electrode. The vibration shape from this asymmetric excitation is shown in Fig. 2.31. The result suggests that asymmetric excitation can excite resonant asymmetric modes in fluid despite the high damping factor. This characteristic will be used in Chapter 4. 2.7.2 Electrical Characterization The electrical characterization of the CMUT was also performed with an Agilent 4294A Precision Impedance Analyzer (Agilent Technologies Canada 65 Figure 2.31: Screenshot of the deflection profile and frequency response of an asymmetrically driven CMUT cell immersed in olive oil. Inc., Mississauga, ON., Canada). An AC sweep voltage with an amplitude of 0.5 V and a 33 V DC offset was applied to the CMUT chip through a bias- T. The resistance and reactance of a row of CMUT with 71 cells are shown in Fig. 2.32. A resonance can be observed at 2.61 MHz, which agrees with the optical measurement and theoretical analysis. Ideally, the resistance should peak at the resonant frequency and remain flat for other frequencies, as shown in the equivalent circuit simulation result (Fig. 2.33). The exper- imental result, however, shows that resistance decreases with frequency. A similar result was published in [122], which was attributed to the parasitic DC leakage. To test the asymmetric excitation, an AC sweep voltage with an ampli- tude of 0.5 V and a 20 V DC offset is applied to only half of the electrode of 66 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 x 106 1290 1300 1310 1320 1330 1340 1350 1360 1370 1380 Frequency [Hz] R es is ta nc e [oh m] (a) 1.6 1.8 2 2.2 2.4 2.6 2.8 3 3.2 x 106 −1100 −1050 −1000 −950 −900 −850 −800 −750 −700 Frequency [Hz] R ea ct an ce  [o hm ] (b) Figure 2.32: Experimental measurement of real and imaginary parts of the impedance of a row of CMUT cells with symmetric excitation in air. (a) Real part (resistance). (b) Imaginary part (reactance). Printing Time:Tuesday, November 27, 2012, 3:52:01 PM  re(V(3)/I(V1)) Impedance (Real part) Frequency (Hz) 1.60M 3.20M1.83M 2.97M2.06M 2.74M2.29M 2.51M M a g n i t u d e -10k 80k 20k 50k  im(V(3)/I(V1))  re(V(3)/I(V1))  V(3)/I(V1) Frequency (Hz) 1.50M 3.25M1.75M 3.00M2.00M 2.75M2.25M 2.50M P h a s e  ( d e g ) -150 200 -100 150 -50 100 0 50 Figure 2.33: Equivalent circuit simulation result of real part of the in-air electrical impedance of a CMUT cell from. a standalone CMUT cell. The resistance and reactance of the cell is shown in Fig. 2.34. A few ripples at 4 MHz-5 MHz can be observed in this result instead of a clear resonant peak. The reason may be that the asymmetric resonance of the single cell is so small that it is buried in the much larger parasitic impedance. Further electrical measurement on the asymmetric mode needs to be done with future fabrication of arrays of multi-electrode CMUTs. 67 1 2 3 4 5 6 7 8 9 x 106 −3000 −2000 −1000 0 1000 2000 3000 4000 5000 6000 Frequency [Hz] R es is ta nc e [oh m] (a) 1 2 3 4 5 6 7 8 9 x 106 −5 −4.5 −4 −3.5 −3 −2.5 −2 −1.5 −1 −0.5 x 104 Frequency [Hz] R ea ct an ce  [o hm ] (b) Figure 2.34: Experimental measurement of real and imaginary parts of the impedance of a single CMUT cell with asymmetric excitation in air. (a) Real part (resistance). (b) Imaginary part (reactance). The real and imaginary parts of a row of symmetrically excited CMUTs, and a single asymmetrically excited CMUT immersed in oil are shown in Fig. 2.35. The oil damps the resonance, as was observed in optical measure- ment, and the small resonant rippled seen in Fig. 2.35(b), although at the resonance of the (1,1) mode, may be an artifact and needs further investi- gation. 2.8 Conclusion and Discussion The analytical, FEM and equivalent circuit models of CMUTs were de- scribed in this chapter, and the results of these models were compared with each other, together with the experimental characterization results of the fabricated CMUT chips. An analytical model of the CMUT cell operation was first proposed in the coupled mechanical, electrostatic and acoustic domains. The static and 68 1 1.5 2 2.5 3 3.5 4 4.5 5 x 106 −1000 −500 0 500 1000 1500 frequency [Hz] Im pe da nc e [oh m]   oil, sym, real oil, sym, imag (a) 1 1.5 2 2.5 3 3.5 4 4.5 5 x 106 −4 −3 −2 −1 0 1 x 104 frequency [Hz] Im pe da nc e [oh m]   oil, asym, real oil, asym, imag (b) Figure 2.35: Experimental measurement of the impedance of a row of CMUT cells with symmetric excitation, and a single CMUT with asymmetric ex- citation in oil. (a) Impedance of a row of CMUT cells with symmetric excitation. (b) A single CMUT with asymmetric excitation. harmonic shapes of the CMUT vibration were modeled from a mode superpo- sition perspective. The electro-mechanical interaction, mainly reflected on the electrostatic force, was modeled with a hybrid step using the rms static displacement from FEM analysis. The acoustic pressure was also calculated using the mode characteristic functions, and the type of loading from the acoustic medium on the mechanical vibration could be modeled differently depending on the acoustic boundary conditions. The analytical results of the single CMUT cell operating in an infinite acoustic domain were compared with an FEM model with the same condi- tions in static and harmonic cases in air and in water, and the results of the vibration shape, resonant frequencies and pressure profile agreed between the models. It was also shown that the plate-vibration based analytical model provided a better fit to the CMUT output pressure than the piston model with only 1-degree-of-freedom operation. 69 Then the Asymmetric CMUT concept was proposed that the CMUT cell can vibrate with an asymmetric shape when actuated by non-axisymmetric voltages. The simplest case is the superposition of the (0,1) mode and (1,1) mode vibrations when excited by two different voltages on two parts of the CMUT membrane. The analytical results of the asymmetric vibrations of a CMUT cell were compared with an FEM model, and the static and harmonic results in air and in water also showed good agreement. The mode superposition perspective was also applied to the construc- tion of an equivalent circuit model, for fast simulations of electro-mechano- acoustic interactions of multiple vibration modes. The (0,1) and (1,1) modes were integrated into a generic CMUT equivalent circuit as multiple sub- circuits with corresponding equivalent mass, spring constant, fluid mass loading, and radiation damping. The equivalent circuit model was used to model CMUTs operating in an array, where the (0,1) mode sub-circuit included a radiation impedance with the periodic acoustic boundary con- dition, and therefore showed over-damped behavior; the (1,1) mode only exchanged kinetic energy locally, and radiated little into the far field, and therefore its sub-circuit included only the capacitance representing the fluid mass loading, and the frequency response remained resonant. The equiva- lent circuit simulation results were compared with an FEM model with the same acoustic boundary conditions, and the in-air and in-water behavior agreed well between the results. The CMUT chip fabricated using the PolyMUMPs technology was char- acterized optically and electrically both for its regular operation, and asym- metric operation. The results of the pull-in voltage, spring-softening effect, 70 in-air frequency response of both symmetric and asymmetric excitations agreed well with the model results. The symmetric and asymmetric vibra- tion shapes were observed in oil immersion, but the results were not validated with the model because of the unsealed etch holes of the chip. The para- sitic impedances of the chip needs to be considered in an improved model, and the immersion characterization, including the vibration shape, acoustic pressure profile, and electrical impedance of a vacuum-sealed CMUT chip is one of the future directions. The modeling work presented in this chapter serves as the theoretical basis for this thesis, and the mode superposition approach was shown to be a useful tool for analyzing complex CMUT vibrations. The model provides the understanding of the CMUT vibration, and can guide the design of imaging applications using multiple-mode CMUT vibrations, as well as the optimization of novel device design. The encouraging characterization re- sults of the multi-electrode CMUTs showed the feasibility of the developing novel devices using the Asymmetric CMUT concept. 71 Chapter 3 Reducing Side Lobe Effects Using Asymmetrically Driven CMUTs4 Transducer arrays have long been used in ultrasonic imaging for the ability to form a focused ultrasound beam along a selected scan line direction. Focusing of the transmitted beam is achieved by electronically controlling the time delays of individual elements during group excitation. Focusing of the received echoes is done by electronically controlling the time delays when combining the signals received from a group of elements. The direction of the transmitted/received beams can also be controlled through time delays in the beam steering process. For a typical transducer, the set of transducer elements are arranged in a fixed position (e.g. 128 elements equally spaced along a 35mm line), so only the timing of the transmit/receive delays and the weights of the aperture (apodization) are adjustable. The fixed arrangement causes inherent compromises in the ability to focus and steer the beam. For example, in order to increase the field of view covered by the scan 4A version of this chapter was published in IEEE Sensors Journal [128]. 72 lines, the transducer elements are commonly arranged in a curvilinear array so that the scan lines emanate radially, like the spokes of a wheel. Since the directional elements tend to transmit the beam in different directions, such curvilinear arrays make it even more difficult to steer and focus the beam, and often suffers from a loss of efficiency [2]. For applications such as inter-rib imaging of the heart, a small footprint phased array (a transducer array that steers all its elements to different angles using electronic delays) with the need for large beam steering angles is used. This type of phased arrays has sensitivity and resolution problems at the outer edge of the sector, because of the decrease of effective aperture at large steering angles [2]. Another of the problems with transducer arrays are the grating lobes arising from the periodic layout of the array elements [26]. Grating lobes are reduced amplitude copies of the main lobe of the beam that propagate with different angles from the main beam lobe and subsequently create ar- tifacts in the image. The current approach is to fix the elements in an array with the element spacing chosen to minimize grating lobes. The typ- ical design criteria for the element spacing in a linear array is to make it no greater than the ultrasound wavelength λ for arrays without the need for beam steering, and λ/2 if beam steering is involved [5]. This criteria leads to tradeoffs in other parameters such as element size. Small size ele- ments are favored according to the criteria, but since the width of a single element determines the envelope of the array beam profile [26], the small width contributes to a broader main lobe [24], reduction in directivity, and degradation in lateral resolution and SNR. Moreover, high-frequency imag- 73 ing applications are limited because the spacing required by this criteria is usually unachievable. Researchers have designed numerous ways to circum- vent these tradeoffs, such as by positioning elements in an optimized pattern to break the periodicity[36, 48]. Yet the current mature piezoelectric mate- rial fabrication technology makes it difficult to fabricate arrays of elements with arbitrary shape and geometry, and the reduction in the active area is likely to result in a poor SNR [5]. If it is possible to manipulate the shape and emitting angle of individual elements in a transducer array, the collective shape of the element group (or aperture) could be tuned to direct the beam to a greater angle than using the time-delay based steering, while the beam power and resolution is preserved. The controlled shape of an individual element can also be considered as a shift in its center of vibration. If the “shift” is adjusted differently from one element to another, the periodicity of the array can be broken and the grating lobes can be reduced. One important advantage of such a tunable array is during wide-band transmission/reception. Unlike current transducer arrays whose geometry is usually optimized for minimal grating lobes up to a certain frequency, the tunable array that relies on breaking the periodicity may still provide grating lobe reduction at higher frequencies, and can be further tuned to optimize transmit/receive efficiency for each frequency. In this chapter, we propose a transducer whose shape and orientation is dynamically adjustable (in the simplest case, tiltable), so that more pa- rameters (such as the tilting angle) can be added to the conventional beam- forming process, and in principle applied together with the time-delay based 74 techniques. The goal is to constrain the beam from an element to a certain location better than simply using time delays. The outcome should be a reduction in image artifacts and an overall increase in SNR. The development of CMUT has brought in a number of new possibilities for improving ultrasonic image quality, apart from the benefits in trans- ducer characteristics. For example, Bavaro et al. [5] proposed to design the cell layout in a CMUT element to reduce grating lobes. A distinct yet hardly explored property of CMUTs is the ability to control the individual cell membrane shape or orientation through the driving electric field. This property may bring extra degrees of freedom to the movement of CMUTs, resulting in different ultrasonic waveforms than those from the traditional piston-like vertical vibration of piezoelectric transducers. For example, the extra degrees of freedom in the one-dimensional case can be the ability to physically shift the center of movement of a CMUT’s membrane by judi- ciously applying different voltages at different locations on the membrane, as was shown theoretically and experimentally in Chapter 2. In this way the emitted ultrasound wave can be directed toward a certain direction. More importantly, the control of direction can be nearly instantaneously done by sending control signals from a digital processing unit depending on the current imaging requirements. The dynamically and adaptively tun- able CMUT through electrical excitation may be a good candidate for the adjustable transducer concept. We are aware that a rich body of literature has been devoted to tackle the problems associated with the transducer arrays discussed above, many of which with solutions through beamforming and post-processing. The 75 present work provides an alternative solution to improve the signal quality from the front-end using physical tuning of individual elements, and may inspire new approaches when combined with the state-of-the-art techniques. In this chapter, we first investigate the benefits of using an array of tiltable ultrasonic transducers for focusing and steering, which we call phys- ical focusing and steering in Section 3.1. Results of simulated imaging pro- cesses with a tiltable transducer array are presented. Next, an embodiment of such transducers using CMUT technology, adaptive CMUTs, is described in Section 3.2. Other applications of tiltable transducer arrays are discussed in Section 3.3, followed by a discussion of the concept in Section 3.4. 3.1 Tiltable Transducers for Physical Focusing and Steering In this section, the concept of tiltable transducers is proposed, and two beamforming approaches using these transducers, physical focusing and physical steering, are developed. As compared to time-delay based electronic focusing and steering, physical focusing and steering are done by physically tuning the orientations of individual elements dynamically to form a desired pattern of the element group, in order to concentrate the beam energy, and reduce side lobes and grating lobes artifacts. A conceptual example of one- dimensional and two-dimensional tiltable arrays is illustrated in Fig. 3.1. Both 1D and 2D arrays can apply our physical focusing and physical steer- ing approaches explained next. Although more sophisticated beamforming is often used, we demonstrate 76 −2 −1 0 1 2 −1 0 1  x [mm]y [mm]  z [m m] (a) −2 −1 0 1 2 −1 0 1  x [mm]y [mm]  z [m m] (b) −1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1  x [mm] y [mm]  z [m m] (c) −1 −0.5 0 0.5 1 −1 −0.5 0 0.5 1  x [mm]y [mm]  z [m m] (d) Figure 3.1: Arrays of tiltable transducer elements. (a) 1D physical focusing. (b) 1D physical steering. (c) 2D physical focusing. (d) 2D physical steering. beamforming with a small group of elements. To explain the principle of the proposed beamforming approach, we assume that a 1D linear imaging array is used. The first group of elements is excited to form the first scan line. The next group, shifted by one element, is then excited. This process continues until all scanlines are acquired. We describe the proposed physical focusing and physical steering in detail as below. 3.1.1 Physical Focusing and Steering Using Tiltable Transducer Elements Physical Focusing The idea for physical focusing is that, when a group is excited, each element in this group is adaptively tilted toward the focus on the scan line with its respective angle α = atan(x/f), where x is the distance from the element 77 center to the group center, and f is the focal distance. Time-delay based electronic focusing is used at the same time. This directs the wave toward the focal point for each scan line, and breaks the periodic pattern of the array. The time sequence for physical focusing is illustrated in Fig. 3.2. Scan line 1 Group 2 Group 1 Group N (a) Scan line 2 Group 2 Group N Group 1 (b) Scan line N Group N Group N-1Group 1 (c) Figure 3.2: Physical focusing. The dash lines denote the wave direction of each element, and long dashed curves denote collective beam traveling profile. (a) 1st scan line (b) 2nd scan line (c) N th scan line Physical Steering Assume the scan lines should be steered to a specific angle β. The idea of physical steering is that when a group is excited, all elements in this group are uniformly tilted in the same direction as the scan line by β. Electronic and physical focusing may be used simultaneously. In this way the physi- cal positions of elements direct the wave toward the scan line orientation. The time sequence for physical steering (without focusing for simplicity of illustration) is illustrated in Fig. 3.3. The physical focusing and steering concept can be linked to the Fresnel lens concept in optics, where a conventional lens is divided into a set of con- centric annular sections. The Fresnel lens reduces the amount of material required for large aperture lens, and can capture more oblique light from a 78 Scan line 1 Group 2 Group 1 Group N (a) Scan line 2 Group 2 Group N Group 1 (b) Scan line N Group 1 Group N Group N-1 (c) Figure 3.3: Physical steering. The dash lines denote the wave direction of each element, and long dashed curves denote collective beam traveling profile. (a) 1st scan line (b) 2nd scan line (c) N th scan line light source [112]. The physical focusing and steering method is neverthe- less fundamentally different in terms of the signal source (pulsed ultrasonic signal versus continuous light signal), and in nature facilitates dynamic and instantaneous control of the transducer array. 3.1.2 Simulation Results Our ideas were tested by simulating imaging processes in Field II where each element is assumed to vibrate as a piston with a tunable orientation for simplicity. A linear array with 64/128 elements was created whose el- ements are adjustable in width, length, spacing, axial direction displace- ment, and tilting angles. An implementation of such an array is shown in Appendix A. The central frequency of the array is set to 8 MHz, similar to previous work [39], and the wavelength λ in the medium (assumed water in this work) is 192.5µm. In the first configuration where the element spacing s is suboptimal for reducing grating lobes (s > λ), element width is set to 250µm, element length is set to 2.4 mm, and element spacing is set to 300µm. In the second configuration, where the element width and spacing 79 are optimized to avoid grating lobe artifacts (s < λ for the non-steering case, and s < λ/2 for the steering case), the element width and element spacing are set to 150µm and 160µm respectively for the focusing test, and 75µm and 80µm respectively for the steering test, and element length is set to 2.4 mm. The arrays are excited with 4 cycles of a sinusoid, and the impulse response is set to 2 cycles of a sinusoid at the frequency of 8 MHz with a Hanning weighting. Transmit/receive (TX/RX) beam profile plots, B-mode images and quantitative measures will be shown to compare the conventional approach (electronic focusing/steering) and the proposed idea (physical focusing/steering). The transmit/receive (TX/RX) beam profile plots are log plots that represent the spatial distribution of the ultrasonic beam on the focal plane. Since this beam is generated from the transducer, it measures the ability of the transducer in concentrating the beam energy toward the focal point. Physical Focusing Results Configuration I (Suboptimal spacing) Parameters of the first configu- ration are used in this test to demonstrate the improvement in beam focusing using an array of tiltable transducers with suboptimal element spacing. The transmit/receive beam profile of a 32-element group of an array with elec- tronic focusing and with physical focusing is plotted in Fig. 3.4. The beam is focused at a point (0,0,30) mm away from the transducer array. The x- axis corresponds to the lateral direction, where the array lies. The z-axis is the axial direction into the imaging target. The intensity of grating lobes is reduced in the physical focusing case. 80 −80 −60 −40 −20 0 20 40 60 80 −550 −540 −530 −520 −510 −500 −490 −480 −470 −460 −450 −440 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of focusing at 30mm   electronic focusing physical focusing Figure 3.4: Comparative transmit/receive beam profile for focusing with suboptimal spacing (Element spacing is 300µm, and element impulse re- sponse is 2 cycles of 8 MHz sinusoid). We created a simulated phantom with 10 point targets on the z-axis and 10 point targets +30◦ off z-axis, similar to one created in [5], as shown in Fig. 3.5. Because the first grating lobe of the array is at +40◦, the grating lobes of several element groups will hit the off-axis targets while scanning the on-axis targets, creating false images of off-axis targets alongside on-axis targets. This phantom was used to create B-mode images using both conventional electronic focusing, and proposed physical focusing. An 128-element linear array with Configuration I (suboptimal spacing) was used where 32 elements were excited at a time. The B-mode image result has a 40dB dynamic range. The comparative results are shown in Fig. 3.6. The shadowy regions are false images of off-axis targets or on-axis targets caused by grating lobes. It is shown that the physical focusing approach introduces fewer false image artifacts than the electronic focusing approach. 81 1 2 3 4 On-axis targets Off-axis targets Figure 3.5: Phantom for simulation. 10 point targets are along the z-axis, and 10 point targets are +30◦ off the z-axis. Configuration II (Optimal spacing) Parameters of the second config- uration are used in this test, i.e. when the array spacing is set to the value that does not generate grating lobes. The transmit/receive beam profile for electrical focusing and physical focusing with different numbers of elements in a group, and different focal distances is shown in Fig. 3.7. The results show that the larger the number of elements in the group (64 elements rather than 32 elements), or the closer the focal point is to the array (10 mm rather than 30 mm), the more improvement physical focusing brings, in terms of main beam intensity and reduction in side lobe intensity. The reason is that, the physical focusing effect is more dramatic when the average tilting angles of the elements are larger (e.g., a maximum of 27◦ tilting angle rather than 9◦), which corresponds to wider arrays and closer focal points. 82 False image of 1 False images of 2 to 4 Correct images of on-axis targets Correct images of off-axis targets (a) False image of 1 False image of 2 Correct images of off- axis targets Correct images of on- axis targets (b) Figure 3.6: B-mode images of point targets with suboptimal spacing. (a) Electronic focusing. (b) Physical focusing. Physical Steering Results Configuration I (Suboptimal spacing) Parameters for the first con- figuration are used in this test to demonstrate the improvement in beam steering using tiltable transducers when the array spacing is suboptimal. The transmit/receive beam profile of a 16-element group of an array with 83 −80 −60 −40 −20 0 20 40 60 80 −550 −540 −530 −520 −510 −500 −490 −480 −470 −460 −450 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of focusing at 30mm, 32 elements   electronic focusing physical focusing (a) −80 −60 −40 −20 0 20 40 60 80 −540 −530 −520 −510 −500 −490 −480 −470 −460 −450 −440 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of focusing at 30mm, 64 elements   electronic focusing physical focusing (b) −80 −60 −40 −20 0 20 40 60 80 −530 −520 −510 −500 −490 −480 −470 −460 −450 −440 −430 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of focusing at 20mm, 64 elements   electronic focusing physical focusing (c) −100 −50 0 50 100 −530 −520 −510 −500 −490 −480 −470 −460 −450 −440 −430 −420 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of focusing at 10mm, 64 elements   electronic focusing physical focusing (d) Figure 3.7: Comparative transmit/receive beam profile for focusing with optimal spacing (Element spacing is 160µm, and element impulse response is 2 cycles of 8 MHz sinusoid). (a) 32-element group, focused at 30 mm. (b) 64-element group, focused at 30 mm. (c) 64-element group, focused at 20 mm. (d) 64-element group, focused at 10 mm. electronic steering and with physical steering is plotted in Fig. 3.8. The beam is focused at a point (8, 0, 30) mm from the transducer array, equiva- lent to steering the beam by 15◦. The level of grating lobes is much lower in the physical steering case than the electronic steering case. We use the aforementioned phantom to create B-mode images using both conventional electronic steering, and the proposed physical steering. 84 −80 −60 −40 −20 0 20 40 60 80 −550 −540 −530 −520 −510 −500 −490 −480 −470 −460 −450 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of steering to 15 degrees   electronic steering physical steering Figure 3.8: Comparative transmit/receive beam profile for steering with sub- optimal spacing (Element spacing is 300µm, and element impulse response is 2 cycles of 8 MHz sinusoid). Electronic focusing is performed for both approaches. A 64-element linear array with the suboptimal parameters was used where a 16-element group is excited at a time. The focal point is -5 mm off each linear scan line, equivalent to steering −9◦. The B-mode images are geometrically corrected and are shown in Fig. 3.9. It is shown that physical steering considerably reduces the amplitude and area of false images of off-axis point targets. Configuration II (Optimal spacing) Parameters for the second config- uration are used in this test. The beam profile of electronic steering versus physical steering for different steering angles is shown in Fig. 3.10. For an array with optimal spacing, the physical steering method can provide higher main lobe level and reduce the side lobe level (equivalent to reducing the beam width) for steering angles larger than 30◦. Fig. 3.11 shows the beam profile of using three different approaches to 85 False images of off-axis targets Correct images of on- axis targets (a) False images of 2 to 4 Correct images of on- axis targets (b) Figure 3.9: B-mode images of point targets with suboptimal spacing. (a) Electronic steering. (b) Physical steering. steer to 30◦. One is through pure electronic steering, one is through pure physical steering, and the other is through composite steering - physically steering to 45◦ and electronically steering back to 30◦. The last approach 86 −80 −60 −40 −20 0 20 40 60 80 −560 −550 −540 −530 −520 −510 −500 −490 −480 −470 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of steering to 15 degrees   electronic steer physical steer 1.5dB (a) −80 −60 −40 −20 0 20 40 60 80 −560 −550 −540 −530 −520 −510 −500 −490 −480 −470 directicity [degree] TX /R X be am  p ro file  [d B] Beam profile of steering to 30 degrees   electronic steering physical steering 10.70dB (b) −80 −60 −40 −20 0 20 40 60 80 −560 −550 −540 −530 −520 −510 −500 −490 −480 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of steering to 45 degrees   electronic steering physical steering 11.30dB (c) Figure 3.10: Comparative transmit/receive beam profile for steering with optimal spacing (Element spacing is 80µm, and element impulse response is 2 cycles of 8 MHz sinusoid). (a) Steering to 15◦. (b) Steering to 30◦. (c) Steering to 45◦. can reduce the side lobe level even more than physical steering alone to 30◦. This test shows that physical steering can be combined with electronic steering in different ways to change the beam shape. 87 −80 −60 −40 −20 0 20 40 60 80 −560 −550 −540 −530 −520 −510 −500 −490 −480 −470 directivity [degree] TX /R X be am  p ro file Beam steering to 30 degrees   physical steering physical steering +backward electronic steering electronic steering Figure 3.11: Comparative transmit/receive beam profile for composite steer- ing to 30◦ with optimal spacing. Combining Physical Focusing and Physical Steering Results The results of combining physical focusing and physical steering for beam steering using suboptimal spacing is shown in Fig. 3.12, in comparison with electronic steering + electronic focusing, and physical steering + electronic focusing. Combining physical focusing and physical steering reduces the side lobe level of the beam profile at the steering side, compared to physical steering + electronic focusing. Quantitative Results The quantitative results of the transmit/receive beam profile for both fo- cusing and steering with suboptimal spacing are measured and summarized in Tables 3.1 and 3.3, and results with optimal spacing are summarized in Tables 3.2 and 3.4. The measurements include relative grating lobe levels for suboptimal focusing and steering, relative main lobe levels, relative peak of side lobe levels for the optimal spacing configuration of focusing, and rel- 88 −80 −60 −40 −20 0 20 40 60 80 −540 −520 −500 −480 −460 −440 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of steering to 15 degrees   electronic steering + electronic focusing physical steering + electronic focusing physical steering + physical focusing Figure 3.12: Comparative transmit/receive beam profile for combining phys- ical steering and physical focusing with suboptimal spacing. ative side lobe levels for the optimal spacing configuration of steering. The measurements are done based on a common 0dB point of the same compari- son test. Due to the lack of clearly defined side lobe for the optimal steering case, the locations for the quantitative data are shown in Figs. 3.10. Table 3.1: Quantitative measure of transmit/receive beam profile for focus- ing with suboptimal spacing. Beamforming approach Relative main lobe (dB) Relative peak of grating lobe (dB) 64-group electronic -2.00 -44.57 physical 0.00 -63.70 32-group electronic -0.20 -48.50 physical 0.00 -56.28 16-group electronic 0.00 -44.98 physical 0.00 -46.47 Discussion of Simulation Results The simulated imaging results suggest that physical focusing and steering can reduce grating lobe level considerably when the array spacing is subop- 89 Table 3.2: Quantitative measure of transmit/receive beam profile for focus- ing with optimal spacing. Beamforming approach Relative main lobe (dB) Relative peak of side lobe (dB) 64-group,f=10 mm electronic -1.90 -61.30 physical 0.00 -78.40 64-group,f=20 mm electronic -2.90 -79.40 physical 0.00 -83.50 64-group,f=30 mm electronic 0.00 -91.10 physical 0.00 -96.10 32-group,f=30 mm electronic 0.00 -49.50 physical 0.00 -58.80 Table 3.3: Quantitative measure of transmit/receive beam profile for steer- ing with suboptimal spacing. Beamforming approach Relative main lobe (dB) Relative peak of grating lobe (dB) 32-group electronic -4.30 -23.47 physical 0.00 -43.78 16-group electronic -4.70 -17.61 physical 0.00 -40.26 Table 3.4: Quantitative measure of transmit/receive beam profile for steer- ing with optimal spacing. Beam forming approach Relative main lobe (dB) Relative mid-point side lobe (dB) 16-group,45◦ electronic -2.30 -38.30 physical 0.00 -62.40 16-group,30◦ electronic -1.90 -38.30 physical 0.00 -49.60 16-group,15◦ electronic 0.00 -30.90 physical 0.00 -32.40 timal. For optimal spacing, these approaches could preserve beam intensity and reduce side lobe levels, when the element group is wide or the focal point is close, and when steering the beam to large angles. The tiltable 90 transducer elements we proposed have shown promise of mitigating the con- flicts of avoiding grating lobes, optimizing emitting power, and maintaining high frequency, as analyzed in the introduction of this chapter. Moreover, the results show that physical focusing and steering can be combined with electronic beamforming methods that can potentially improve the image quality more than used alone. 3.2 Embodiment of Tiltable Transducer Concept Using CMUTs Because of the difficulty of fabricating dynamically tiltable transducer ele- ments using piezoelectric technology, we propose an implementation using the CMUT technology described in Chapter 2. This novel type of adjustable CMUT is named Adaptive CMUT. A cell of the current design of an Adaptive CMUT is illustrated in Fig. 3.13. The CMUT cell membrane is modeled as a clamped circular plate, whose shape and orientation can be dynamically and adaptively adjusted by the driving electric field. While ideally we expect the membrane to be physically tilted and vibrate at an angle, the present work approximates tilting by asymmetric electrostatic bias or actuation, so that the membrane vibrates with a shifted center toward the direction of tilting, and transmits the beam with an angle from the origin of the cell. In future we hope to separate the tilting and lateral shift of vibration center as different types of deformation. An array of such cells can be tuned to form a variety of overall shapes for different imaging requirements. Fig. 3.14(a) shows the design of an adaptive CMUT cell whose membrane 91 SubstrateBottom electrode Untilted membrane V Controlled driving voltage + - Tilted membrane Top electrode Figure 3.13: An example of an adaptive CMUT cell. The controlled driving voltage changes the shape of the CMUT membrane which alters the wave propagation direction. can be tuned to tilt an angle by subdividing and controlling its electrodes. Fig. 3.14(b) and 3.14(c) show the cross-section of the conceptual control structure where one pair of electrodes is responsible for actuating the mem- brane to generate ultrasound, and two other pairs of electrodes are applied different bias voltages to deform the membrane so that the membrane vi- brates at an angle. The actuating electrodes are ideally “tilted” with the membrane to ensure that the vibration direction is also tilted. Fig. 3.14(d) and 3.14(e) shows an alternative structure, where the actuating electrodes are not all tilted with the membrane. We expect tilting to be done in two dimensions with two degrees of free- dom: roll, pitch along lateral and elevational axes. Figs. 3.14(f) to 3.14(h) shows the top views of the control structure. Two electrodes underneath the vibrating membrane (shown transparent) can be used to tilt the membrane in one dimension (Fig. 3.14(f)). Four electrodes can tilt the membrane in two dimensions (Fig. 3.14(g)), i.e., combining electrode 1 and 2, 3 and 4 for one dimension, and electrode 1 and 3, 2 and 4 in another dimension. By extension of this concept, different numbers of electrodes can be used to deform the membrane into different shapes (such as with the design in 92 Fig. 3.14(h)). top electrode bottom electrodes membrane Tilted membrane substrate (a) Actuating electrodes Tilting electrodes Tilting electrodes Membrane Vibrating direction (b) Tilting electrodes Actuating electrodes Tilting electrodes Membrane Vibrating direction (c) Membrane Actuating electrodes Tilting electrodes Vibrating direction Tilting electrodes (d) Membrane Actuating electrodes Tilting electrodes Vibrating direction Tilting electrodes (e) (f) (g) (h) Figure 3.14: Adaptive CMUT cell structure. (a) Cross-sectional view of the adaptive membrane. The solid curve denotes the original position of the membrane. The dotted curve denotes a tilted membrane. (b)(c) Cross- sectional view of an adaptive CMUT cell structure. (d)(e) Cross-sectional view of an adaptive CMUT cell with an alternative structure. (f)(g)(h) Top view of an adaptive CMUT element with lateral control (f), lateral and ele- vational control (g) and control along other axes (h). The gray areas denote tilting electrodes, and the bigger area denotes a transparent membrane. 93 3.2.1 Equivalence of a Tilted Piston Element and an Asymmetrically Excited CMUT cell To show the feasibility of using an asymmetrically excited CMUT cell to approximate a tilted piston element, the simulated beam profile of a piston with the size of a CMUT cell is presented. The width and height of the piston are set to 70µm (the diameter of a CMUT cell example used in Section 2.2), and the piston is physically tilted by 20◦ along y-axis. The peak of the transmit beam profile measured at 2 mm distance is shown to shift to the side by around 10◦ (Fig. 3.15). −60 −40 −20 0 20 40 60 −7 −6 −5 −4 −3 −2 −1 0 directivity [degree] Tr as nm it pr es su re  a t 2 m m  [d B] Far−field pressure of a tilted piston   Figure 3.15: Simulated transmit pressure of a tilted piston with a CMUT cell size at 2mm. The data was convolved with a filter that averages every 15 degrees of angle. We then use a FEM model of a CMUT cell similar to the one in Sec- tion 2.4 to show that a CMUT cell can achieve similar beam profile with proper driving voltages. The frequency response package of the Comsol structural mechanics module and the time-harmonic package of the pressure acoustics module 94 for frequency response analysis were used in the FEM analysis. A paramet- ric analysis is applied over a range of vibration frequencies (from 1 MHz to 10 MHz). The harmonic driving voltage of the membrane is set to three dif- ferent cases: 180 V (left) / 0 V (right), 180 V (left) / 180 V (right), 0 V (left) / 180 V (right). The figures are created based on 1 MHz results. The mem- brane deflection simulation results for all three cases are shown in Fig. 3.16. The top boundary surface of the water medium and a semicircular curve on the top boundary surface are chosen to demonstrate the “tilted” acous- tic field resulting from asymmetrically actuated CMUT cell, as shown in Fig. 3.17. Result of the total acoustic pressure on the boundary and along the semicircular curve are shown in Fig. 3.18 in angular coordinates. The ultrasonic beam can be tilted around 7◦ in the medium toward the side with higher bias voltage. The 7◦ tilting was the largest tilting effect obtained from the FEM simulation with the 0 V applied on one side of the membrane, and a maximum voltage applied on the other side. (a) (b) (c) Figure 3.16: CMUT membrane deflection with different bias voltages (1 MHz case). (a) 180 V(left)/0 V(right). (b) 180 V(left)/180 V(right). (c) 0 V(left)/180 V(right) The simulation results show that asymmetric excitation voltages are able 95 (a) (b) Figure 3.17: Chosen surface and curve for beam tilting demonstration. (a) Top view of the chosen surface. (b) Top view of the chosen curve. to direct the acoustic beam to a certain angle. 3.2.2 Equivalence of Tilting a CMUT Element and Tilting CMUT Cells in the Element As shown in Fig. 3.19, a typical CMUT array consists of a number of CMUT elements, and each CMUT element is composed of several CMUT cells. We have just shown the similarity of beam profile between a tilted piston and an asymmetrically excited CMUT cell. Though geometric tuning is done on the cell level, we can “tilt” a CMUT element (Fig. 3.20(a)) by means of uniformly tilting the CMUT cells in the element (Fig. 3.20(b)) with the same angle. From our preliminary simulation in Field II, the two approaches generate similar ultrasound wavefronts. This result complements the recent work in [3], which demonstrates that CMUT elements can be well 96 (a) (b) (c) −100 −80 −60 −40 −20 0 20 40 60 80 100 −235 −230 −225 −220 −215 −210 −205 −200 −195 directivity [degree] To ta l a co us tic  p re ss ur e [P a] Total acoustic pressure of 180V/0V combination (−6.5, −231) (d) −100 −80 −60 −40 −20 0 20 40 60 80 100 −480 −470 −460 −450 −440 −430 −420 −410 directivity [degree] To ta l a co us tic  p re ss ur e [P a] Total acoustic pressure of 180V/180V combination (0,−472) (e) −100 −80 −60 −40 −20 0 20 40 60 80 100 −235 −230 −225 −220 −215 −210 −205 −200 −195 directivity [degree] To ta l a co us tic  p re ss ur e [P a] Total acoustic pressure of 0V/180V combination (7.6,−232) (f) Figure 3.18: Beam tilting result, measured 1mm away from the CMUT. (a) 180 V/0 V result on the surface. (b) 180 V/180 V result on the surface. (c) 0 V/180 V result on the surface. (d)180 V/0 V result on the curve. (e) 180 V/180 V result on the curve. (f) 0 V/180 V result on the curve. approximated in Field II by neglecting their cell structure, when only the element-level pressure profile is considered. The beam profiles of an element tilting toward its focal point, and the cells in the element tilting to the same direction are shown in Fig. 3.21. Therefore, the beamforming approaches by physically tilting element proposed in Section 3.1 can be achieved by physically tilting cells in each element. 3.2.3 Feasibility of Tilting Angles In order to achieve the image quality improvement presented in Section 3.1, large tilting angles are desired. We showed in Subsection 3.2.1 that a beam tilting angle of 7◦ is feasible with the present clamped CMUT parame- 97 CMUT cell CMUT element CMUT array Figure 3.19: A standard 2D CMUT array. Circles represent CMUT cells, and gray-scale coded hatching represents different elements [5]. −0.1 −0.05 0 0.05 0.1 −0.1 −0.05 0 0.05 0.1 −0.02 0 0.02  x [mm]y [mm]  z [m m] (a) −0.1 −0.05 0 0.05 0.1 −0.1 −0.05 0 0.05 0.1 −5 5 x 10−3  x [mm]y [mm]  z [m m] (b) Figure 3.20: (a) Conceptual diagram of tilting a CMUT element. (b) Im- plementation of tilting an element by uniformly tilting its cells. Only 5 cells are drawn for the sake of explanation. −60 −40 −20 0 20 40 −600 −590 −580 −570 −560 −550 −540 directivity [degree] TX /R X be am  p ro file  [d B] Beam profile of a tilted element and tilted cells   tilted element tilted cells Figure 3.21: Field II simulation of the beam profiles of a tilted element and tilted cells toward their focal point. The data was averaged every 4 degrees. 98 ters. A larger angle may be achieved by a similar structure with different physical or electrical parameters. A different physical design might achieve greater tilting angles, such as a suspended or supported structure like the MEMS micromirrors that operate with similar electrostatic principles [103]. The state-of-the-art micromirror may produce up to 20◦ physical tilting an- gles [111]. More recent CMUT structures with flexural central posts [77] are also promising candidates. Beamforming methods of tiltable transducers should be designed within the tilting angle constraints of the corresponding structure. 3.2.4 Simulation Results with Practical Tilting Angles To show the practicality of using adaptive CMUTs as an embodiment of tiltable transducers, further Field II simulations were carried out in this subsection with tilting angles restricted to 7◦, which is relatively small, but feasible angle. We constructed an array with the same physical size and type of excita- tion as the one described in [39]. The array consists of 64 elements, each of which has a width of 100µm, a height of 2.4 mm, and an element spacing of 105µm. In [39], the operating frequency band of the CMUT array was tested to be 2-16 MHz centered at 8 MHz, and the array spacing is optimal for min- imizing grating lobes up to 14.7 MHz for non-steering cases, and 7.3 MHz for steering cases. The array was driven with 15 cycles of 10 MHz sinusoid signals. In order to study the behavior of the array with different driving frequencies, we repeated both focusing and steering simulations similar to Section 3.1 with 2 MHz to 20 MHz sinusoidal driving signals. The array is 99 by default electronically focused at 10 mm in front of the transducer. Phys- ical focusing is done by scaling the necessary tilting angles of each element (computed using the method in Section 3.1) so that the maximum tilting angle (the angle for the outermost element) is 7◦. Fig. 3.22 (a) and (b) show that physical focusing can maintain a higher main lobe level from 4 MHz to 20 MHz than electronic focusing alone. The peak of grating/side lobe level is lower from 8 MHz to 20 MHz when physical focusing is used. Physical steering is done by tilting all elements by 7◦ toward the focal point at (1.23, 0, 10) mm (equivalent to 7◦ looking direction). Fig. 3.22 (c) and (d) show that physical steering results in a higher main lobe level from 10 MHz to 20 MHz, and a lower grating/side lobe level from 8 MHz to 20 MHz. The results for different operating frequencies show that despite the tilt- ing angle restrictions of clamped-membrane based adaptive CMUTs, the physical focusing and steering approaches provide advantages in terms of power level and grating lobe reduction for a wide band of frequencies higher than the resonant or central frequency. While the conventional arrays are physically optimized to minimize grating/side lobes for a frequency band (usually up to a frequency around the resonance), the optimization does not hold and can not be altered for higher frequency, wide band applica- tions. The physical focusing and steering approaches, however, can be used to adaptively tune the array to optimize the main lobe level and the sup- press the grating lobe levels for each frequency. These approaches can also potentially reduce the array sampling requirements and thereby lower the channel counts and the system cost. 100 2 4 6 8 10 12 14 16 18 20 −45 −40 −35 −30 −25 −20 −15 −10 −5 0 Excitation frequency [MHz] R el at iv e m ai n lo be  le ve l [d B] Relative main lobe level   electronic focusing physical focusing (a) 2 4 6 8 10 12 14 16 18 20 −100 −90 −80 −70 −60 −50 −40 −30 −20 Excitation frequency [MHz] R el at iv e pe ak  o f s id e/ gr at in g lo be  le ve l [d B] Relative peak of side/grating lobe level   electronic focusing physical focusing (b) 2 4 6 8 10 12 14 16 18 20 −40 −35 −30 −25 −20 −15 −10 −5 0 Excitation frequency [MHz] R el at iv e m ai n lo be  le ve l [d B] Relative main lobe level   electronic steering physical steering (c) 2 4 6 8 10 12 14 16 18 20 −90 −80 −70 −60 −50 −40 −30 −20 Excitation frequency [MHz] R el at iv e pe ak  o f s id e/ gr at in g lo be  le ve l [d B] Relative peak of side/grating lobe level   electronic steering physical steering (d) Figure 3.22: Comparative relative main lobe and grating/side lobe level for different operation frequencies. All values are normalized by the main lobe amplitude of focusing/steering at 2 MHz.(a) Main lobe level for focusing. (b) Peak of grating/side lobe level for focusing. (c) Main lobe level for steering. (d) Peak of grating/side level for steering. 3.2.5 Layout Routing of Adaptive CMUT Arrays The multi-electrode control structure of adaptive CMUTs may complicate the layout routing of a CMUT array, especially a large 2D array if the conventional flat routing approach is adopted. This problem can be solved with a vertical approach, such as a recently proposed integrated CMOS- 101 based technology [129]. Since the electronic circuit is placed beneath the membranes in this technology, the high number of interconnects has no effect on routing. Therefore it facilitates the deployment of various adaptive and dynamic control algorithms for the adaptive CMUTs. 3.3 Other applications of Tiltable Transducers Transducers whose shape and orientation can be electronically adjusted can bring about more applications, discussed as follows. 3.3.1 Spatial Compounding The idea of spatial compounding, as investigated in [107], is to image a region of interest from different angles, and average these images to reduce the speckle noise of the overall image. Electronically controlled steering is normally used in spatial compounding to obtain images from different angles. Usually, there is a tradeoff between the steering angle and the image quality. We want large angles to get uncorrelated measurements (ultrasound echoes), but large angle steering results in degraded resolution and sensitivity, and different levels of distortion [37]. So currently we stick to a compromise of steering about 15 degrees and see a small improvement in SNR. If the transducer elements are physically directed to the intended angle, the quality of each image to be compounded may be improved, meaning larger steering angles can be achieved with less quality loss incurred, and thus the quality of the compounded image could be improved. Yet the usable field of view is compromised when imaging at large angles. 102 3.3.2 High Intensity Focused Ultrasound Apart from improving pulse-echo image quality, transducers of variable ge- ometry are also promising for use in High Intensity Focused Ultrasound (HIFU) intended for minimally invasive thermal therapy for treatment of cancer and other pathologies. In a HIFU system, ultrasound beams are concentrated to deliver high acoustic power to a target to achieve localized therapeutic effects. Various geometries of HIFU arrays have been developed to achieve higher accuracy, power efficiency and resolution, such as concave, spherical and cylindrical geometries [99]. Systems of variable focus have also been developed [49]. Optimized beamforming is needed to alleviate non-uniformities in the field of view introduced by directive elements [120]. Application of tiltable transducer arrays in HIFU can produce geometries that better concentrate ultrasound beams, form lens-free variable focus by dynamically adjusting element orientations, and make a more uniform field of view combined with beamforming techniques. Use of CMUTs in HIFU has been reported in [116] but the elements were non-adjustable. 3.3.3 Future Applications Tiltable transducers and adaptive CMUTs have the potential of being useful in other areas of ultrasound imaging. Adaptive Imaging Adaptive imaging techniques are those that restore image coherence by com- pensating beamforming errors resulting from tissue-induced aberrations [28]. 103 It is usually done by dynamically adjusting the transmit time difference among different array elements based on the time difference of received sig- nals. Ries et al. [93, 94] proposed a method that tilts the element in elevation with a piezoelectric actuator to compensate for the phase aberration. The ability of shape control offered by tiltable transducers may permit physical adjustment of corrections in addition to time delays, and the adjustment could be dynamically altered based on the received signals. Harmonic Imaging Harmonic imaging is the method of extracting the higher frequency com- ponent from the echo signal generated from the tissue or contrast agents. Usually the second harmonics with respect to the central frequency of trans- mitted pulse is used. The harmonic component has a potentially higher focus-to-clutter-ratio than the fundamental frequency, provides better lat- eral and axial resolution than the fundamental mode, and improves the visualization of lower frequency signals at depth [108]. The extraction of higher-order harmonics is currently done using linear or non-linear filters. By manipulating the receiving bias voltage of an adaptive CMUT cell, cer- tain vibration modes, for example, the (1,1) mode of the CMUT that is sensitive to a higher frequency can be excited, and can be selectively re- ceived as the harmonic receiving signal. The physical focusing method can further make the array more sensitive to higher frequency components. Us- ing higher order symmetric modes of CMUTs for harmonic imaging has been proposed in [42], but the use of asymmetric modes has not been discussed in literature. 104 3.4 Conclusion and Discussion This chapter proposes the concept of an ultrasonic transducer whose shape and orientation is dynamically adjustable. In its simplest form, it can be considered as a tiltable transducer. Imaging simulation was done to test the benefit of an array of such transducers in improving beam focusing and steering. The results show promise for reducing grating lobe and side lobe artifacts, and preserving beam power to mitigate some of the array design tradeoffs. An embodiment of this type of transducer is Adaptive CMUTs, whose “tilting” capability via electrical excitation is demonstrated by FEM. In practice, the Adaptive CMUTs can be implemented by the asymmetric CMUT structure proposed in Chapter 2, which vibrates with a shifted center under asymmetric actuation. In the current CMUT technology, the dimension of the CMUT cells is much smaller than that of the wavelength, so only a minimal part of the asymmetric pressure component may propagate into the far field [34]. While the present technology limits the tilting of the acoustic wave, with different physical structures such as one with large cell size or high operating fre- quencies, the asymmetric acoustic pressure component can influence the far field. Further development is needed to extend the tiltable transducer idea for image quality improvement within the constraints of the current fabri- cation technology, and to combine with other beamforming techniques. The properties of asymmetrically vibrating CMUTs, such as the acoustic radia- tion efficiency, and the far-field distribution are under further investigation. The proposed tiltable transducer concept opens up new possibilities for im- 105 proving image quality from the front-end, especially with the incorporation of on-chip electronics for control and processing. 106 Chapter 4 Improving Image Resolution Using Asymmetric Mode of CMUTs in Reception5 Capacitive Micromachined Ultrasonic Transducers (CMUTs) have several potential benefits over traditional piezoelectric transducers in some appli- cations. For example, CMUTs have been recently used in ring arrays for forward-looking intracardiac echocardiography and intravascular ultrasound imaging applications [22, 105]. When a ring array is used to image targets at a distance much larger than its aperture, the classic phased array imaging approach produces a broad beam and high side lobes [26]. As an alternative, therefore, Synthetic Aperture Array imaging with various techniques such as aperture weighting [79, 80] and spatial/temporal coding [21, 73] have been applied to improve the image quality. These techniques can add a considerable computational load that limits the overall frame rate in certain implementations [22]. Fast imaging using a broad beam or plane wave transmission [67, 74, 101] 5Part of this chapter has been presented in 2012 IEEE Ultrasonics Symposium [126]. A version of this chapter has been submitted for publication [127]. 107 may improve the frame rate substantially but further degrades the image resolution. Compounding multiple transmitted plane waves from a range of angles [74] can yield comparable quality with the focused B-mode images, so it is considered in [22] for a ring array system. In a related research direction, super-resolution imaging techniques have also been proposed to overcome the diffraction limit in ultrasound imag- ing [47]. Various approaches have been be developed in this field [25, 33, 35, 92, 102, 109]. qTONE [33] is one example based on RADAR and SONAR literature [9]. During the calibration process, this method first transmits a plane wave, and records the temporal channel responses from individual hypothetical point targets in the Region of Interest (ROI) to form a mani- fold matrix. During the imaging process, it solves a maximum a posteriori (MAP) problem to obtain the weights of each hypothetical target. To make an accurate estimation of the weights, especially in the case of a small aper- ture array with a broad beam pattern and high side lobes, millions of calibra- tion targets need to be modeled resulting in high computation complexity. Considerable efforts have been made to manage this complexity [32]. In this chapter, we propose a new series of super-resolution imaging methods and demonstrate using a phased ring arrays in acoustic simulations, and a linear array in experimental studies. It is based on focused transmis- sion and the differential received signals 6 obtained by the multi-electrode CMUT structure developed in Chapter 2. Because of the clamped-plate structure of a CMUT cell, off-axis targets can excite asymmetric resonant 6The term differential is used to describe the subtraction of temporal signals on the two parts of the electrode, namely X1(t)−X2(t), rather than the differential signal with respect to time. 108 modes on CMUTs that could be captured by subtracting signals on their partial electrodes. The differential received signals from all CMUTs form decorrelated temporal patterns for different beam directions and have the potential to lead to a more accurate estimation result at reflector locations than using the same amount of received data averaged on the single elec- trode. The methods can also benefit from focused transmissions in terms of computation load, since the echo data to be processed can be limited to the focal zone. Therefore the new methods can improve the image resolution over the standard phased array method, and achieve super-resolution with relatively low computational effort. Section 4.1 briefly explains the source of the resonant components in the differential received signals from a mode decomposition perspective. Sec- tion 4.2 described the new super-resolution method. The imaging simulation results using a multi-electrode CMUT ring array are shown in Section 4.3 and discussed in Section 4.5. The experimental studies using a CMUT probe is presented and discussed in Section 4.4. 4.1 Multiple Vibration Modes During CMUT Reception 4.1.1 Asymmetric Mode Operation in Reception The CMUT behavior can be analyzed using the mode superposition method both mathematically [96, 124] and using a multi-modal equivalent circuit model [97], as described in Chapter 2. When the force acted on the CMUT 109 plate is non-uniform, the CMUT behavior is the superposition of axially symmetric and asymmetric mode shape components. Higher order symmet- ric mode components were reported as undesirable dips in the frequency spectrum [42], and higher order asymmetric components were observed as a result of the acoustic crosstalk [100] or manufacturing defect of the CMUT cell [68]. There has been little work to date on making use of the higher order symmetric modes. For example, in [42], additional mass loadings were placed on the CMUT membrane to adjust the frequency of the third mode, and the harmonic signal of this mode was selectively detected from the side electrode of a multi-electrode structure [40] to enable harmonic imaging. In this chapter, we will leverage the resonant behavior of the asymmetric mode ((1,1) mode). As shown in Chapter 2, asymmetric mode components exists when a non-axisymmetric force is exerted on the membrane, e.g. dif- ference in electrostatic forces exerted on the left and the right part of the membrane in transmission, or difference in acoustic pressure in reception. The asymmetric mode is a local exchange of kinetic energy between the parts of the CMUT membrane, and does not radiate significant acoustic pressure given the CMUT dimension and frequency range of the present technology (Chapter 2 and [34, 96]). Although the displacement (velocity) sensed on the entire membrane is non-resonant (thus making dips in the spectrum), the local measurement integrated on each half of the membrane appears resonant and in opposite phase with one another. The proposed method makes use of the relations between the acoustic pressure difference and the differential received signal between the left and right half of the membrane, which is a direct reflection of the asymmetric mode. The multi-electrode 110 CMUT structure with half-membrane-sized electrodes described in Chap- ter 2 is used to separately obtain the signals from the left and right parts of the electrode. 4.1.2 Average and Differential Received Signals From Multi-electrode CMUTs Fig. 4.1 shows an example of the average displacement of the whole CMUT membrane, the left part and the right part of the membrane due to a sim- ulated off-axis acoustic pressure source from the Finite Element simulation (see Section 2.3 for details). The differential signal is then a harmonic sig- nal with the resonant frequency of the asymmetric mode, which may be deemed as unwanted in regular imaging, but is used in our method for super-resolution imaging. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 x 10−5 −6.5 −6 −5.5 −5 −4.5 −4 −3.5 −3 x 10−8 time [s] a ve ra ge  d isp la ce m en t [m ]   whole membrane left part right part Figure 4.1: Average displacement of the whole membrane, and left and right parts of the membrane subjected to an acoustic wave from an off-axis angle. 111 4.2 Efficient Super-resolution Imaging Based on Differential Received Signals of CMUTs The goal of this section is to develop a super-resolution image method with relatively low computational complexity. 4.2.1 Imaging with a Ring Catheter In [22], a ring catheter made of CMUT elements was described, and several imaging methods using the catheter were compared. In summary, due to the ring geometry, plane wave transmission (flash imaging) resulted in poor off- axis image quality, and the phased array beamforming method generated high side lobes. The synthetic phased array with Hadamard coding and aperture weighting provided the best image quality and decent frame rate, but had a large computational load. 4.2.2 Super-resolution Imaging Using Differential Received Signals In summary, the difficulties with catheter imaging is the off-axis image qual- ity falloff in fast imaging, and high side lobes in phased array imaging. In this study, we propose a new focused super-resolution imaging method with a directional pruning step, and compare the performance between using av- erage received signals and differential received signals. An overview of the method is shown in Fig. 4.4. 112 Manifold Matrices and Estimation of Imaging Target Locations The proposed approach first defines a grid of hypothetical point targets in the ROI, and constructs manifold matrices V , similar to the approach in [9, 109]. Each column of V is the concatenation of the T temporal received samples at each of the N array elements for each hypothetical target. The matrix consists of LP columns, L and P being the number of hypothetical targets in two dimensions. When new signals are received and concatenated into a NT vector, the target locations and the amplitudes (weights) can be estimated using an iterative method [33]: fk+1 = CfkV H(V CfkV H + Cn) −1x (4.1) where V is the NT ×LP manifold matrix, f is a LP -dimension vector rep- resenting the weights of the hypothetical targets, C is the covariance matrix of f , Cn is the noise covariance matrix, and x is the new NT -dimension concatenated temporal signals received at all N elements. Temporal Signature of Differential Received Signals As discussed in Section 4.1, the signal received at the left and right electrode alone (SL and SR) is a superposition of the broad-band, symmetric mode, and the narrow-band, asymmetric mode, which shows a longer ringing ef- fect than the regular single-electrode CMUT received signal. The regular received signal, which is the average signal on the left and right electrodes, Savg = (SL + SR)/2, appears as time-delayed pulses across all elements/- cells when concatenated, and the time delays are tiny for a small aperture 113 transducer. Conversely, the differential signals across all the elements/cells, Sdiff = SL − SR, have a more visually distinct amplitude signature. Define V avg and V diff as the manifold matrices constructed using the average and differential signals respectively. A visualization of V avg and V diff is shown in Fig. 4.2. It is preferred that each column of V be unique from other columns so that one point scatterer can be distinguished from the others. We consider the correlation coefficients of V as the measure of its quality. A map of correlation coefficients of the LP columns of V avg and V diff is shown in Fig. 4.3 where the pixel brightness is mapped to the values of the correlation coefficients. The mapping shows a wide band of high correlation coefficients around the diagonal for V avg, and only a narrow band for V diff . This means that the columns of V diff are more decorrelated than those of V avg, therefore when V diff is used, Eq. 4.1 can be solved more accurately due to the separation of the manifold vectors in space. Multi-focus Manifold Matrices Construction Plane wave transmission suffers from lower resolution and image contrast than focused transmit and receive beamforming [74]. To obtain simultaneous higher resolution and lower side lobes, we propose a focused super-resolution imaging approach. One NT × LP manifold matrix is constructed off-line for each of the M scan lines or angular positions (Fig. 4.4, Step [A]). A set of manifold matrices V avg consisting of the average received signals, and a set of manifold matrices V diff consisting of the differential received signals, 114 0 2000 4000 6000 8000 Concatenated temporal received samples from N channels hy po th et ica l t ar ge t l oc at io ns (a) 0 1000 2000 3000 4000 5000 6000 7000 8000 Concatenated temporal received samples from N channels hy po th et ica l t ar ge t l oc at io ns (b) Figure 4.2: (a) Visualization of manifold matrix V avg constructed from Savg. (b)Visualization of manifold matrix V diff constructed from Sdiff . The verti- cal axis represents LP hypothetical target locations, and the horizontal axis represents NT temporal received samples. Each horizontal trace represents a column in the matrix. In this example, only 21 columns corresponding to 21 target locations in the matrices are shown.   20 40 60 80 100120 20 40 60 80 100 120 0 0.5 1 (a)   20 40 60 80 100120 20 40 60 80 100 120 −0.5 0 0.5 1 (b) Figure 4.3: (a) Correlation coefficient map of V avg. (b) Correlation coeffi- cient map of V diff . The brightness of the pixels is mapped to the coefficient values. An ideal correlation coefficient map has zero off-diagonal values. are constructed for all scan lines: V avg = {V avgi , i = 1, 2, ...,M} V diff = {V diffi , i = 1, 2, ...,M} (4.2) 115 Weight vector 1 Weight vector 2 Weight vector M Imaging targets … Pruned weight vector 1 Pruned weight vector 2 Pruned weight vector M Scan line 1 Scan line 2 Scan line M … … Manifold matrix 1 Manifold matrix 2 Manifold matrix M Hypothetical targets … Reconstructed image Calibration and manifold matrices construction Imaging process [A] [B] [C] [D] if ipf , iV ix [E] Figure 4.4: Workflow of the proposed method. [A] Manifold matrices con- struction. [B] MAP estimation of weight vectors. [C] Pruning of weight vectors. [D] Scan line reconstruction. [E] B-mode image reconstruction. This approach can potentially reduce the size of the manifold matrix by restricting the data analysis to the focal region, instead of using the data from a large area in the plane wave scheme proposed in [33]. This benefit comes with a trade-off in memory space. Multi-focus MAP Solution of the Weight Vector During the imaging process, the array focuses at multiple angular positions in transmission. After the reception from the ith angle, an iterative MAP process similar to Eq. 4.1 is performed to obtain the optimal weight vector of the ith scan line, fi (Fig. 4.4, Step [B])). 116 Pruning of Weight Vectors Next, a directional pruning step is applied to fi to further reduce the effect of side lobes. fi is the estimated weights of all hypothetical targets in the grid when the beam is focused at the ith angle. It includes the weights within the ith angle resulting from the main lobe of the transmit/receive beam, and the weights at other angles resulting largely from the energy of the side lobe. When fi is used for the reconstructing the current scan line, the mixture of main lobe energy and side lobe energy will both contribute, causing false images. In order to remove the part of the signals contributed by the side lobe, we set to zero the weights of the targets outside the current ith focal angle, keeping only the estimates at positions corresponding to the ith angle (Fig. 4.4, Step [C]). The resulting pruned weight vector is defined as fp,i. A detailed illustration of the pruning process is shown in Fig. 4.5. As a future direction, a weighted average of fi from n neighbors of the current focal angle can be used to further improve robustness and reduce false negatives. Image Reconstruction The image is then reconstructed using the pruned weight vector fp of each scan line multiplied by the manifold matrix of the average signal: xi = V avg i fp,i (4.3) where xi is the result RF data of the ith scan line, and fp,i is the pruned f of the ith scan line (Fig. 4.4, Step [D]). Instead of directly displaying the weights of the hypothetical targets as brightness in the image, our method 117 ip M i i i f , 1 1 1 ... ... 0 ... 0 67.0 0 ... 0 θ θ θ θ θ + −                       i M i i i f θ θ θ θ θ ... ... 05.0 ... 01.0 67.0 05.0 ... 10.0 1 1 1 + −                       Directional pruning Figure 4.5: Directional pruning process. For the weight vector estimated while the array steers to the ith angle θi, keep the values corresponding to θi and set the values at other angles to zero as they are more likely false estimates or result of side lobe energy. Note that multiple values for different axial locations at θi are all kept. attempts to preserve some of the texture information in the RF data by weighting the manifold RF data in the B-mode image reconstruction. The scan lines are envelope detected, log-compressed, and scan converted to form an image (Fig. 4.4, Step [E]). Hybrid Method Using Weight Vectors from the Average and Differential Signals We propose a new alternative method for calculating the weight vector fp,i to benefit from both the average and the differential signals. Since the signature of the regular concatenated channel data largely relies on the temporal delays between different locations of the hypothetical targets, the average received signals are well-suited for detecting targets along the axial direction. On the other hand, the differential signals have a more unique signature between angles, providing better lateral discernibility. We propose to fuse these two 118 advantages by taking the element-wise product of the two weighting vectors: fp,i,j = f avg p,i,j × fdiffp,i,j , where fp,i,j is the jth element of the pruned f vector of the ith scan line. As will be shown in the result section, this operation aims to remove false positives from both the solutions. We will hereafter term the methods using the proposed imaging process with the average received signal (Savg), the differential received signal (Sdiff), and the hybrid weight vector as Super-Avg (SA), Super-Diff (SD), and Super-Hybrid (SH ) respectively. Scaling and Interpolation In a regular phased array, the lateral or angular resolution is limited by the width of the scan line. While the proposed method is also scan line based, the resolution is instead limited by the density of the hypothetical targets. When the beam is steered to an angle, all weights in f are estimated. The RF signals from the targets falling between the scan lines can be interpolated by combining the weights estimated from the neighboring scan lines. Assume the scan lines only sample the hypothetical target matrix at every other angle, i.e., the beams are only steered to θi−1, θi+1, θi+3, .... One way to interpolate the lines at θi, θi+2, ... could be weighting manifold matrices at the neighboring scan lines using the respective weight vectors, and taking the average to construct the interpolated line: xi = (V avg i−1 f i p,i−1 + V avg i+1 f i p,i+1)/2 (4.4) 119 where xi is the RF data for the interpolated scan line, f i p,i−1 and f ip,i+1 are the weight vectors estimated at θi−1 and θi+1, pruned only to keep the elements at θi. 4.3 Simulation and Results This section shows the simulation and results of the proposed imaging method using Finite Element Modeling (FEM) and the ultrasound field simulation program Field II. 4.3.1 FEM Simulation First, the received signals on the multi-electrode CMUT cell in response to acoustic sources from different angles are simulated with Comsol Multi- physics. The FEM model (similar to Fig. 2.23) has the same dimensions as the fabricated multi-electrode CMUT structure (Section 2.7). A 100 V DC bias voltage is applied at the bottom of the membrane, and the acoustic field is a 1 mm long cylinder filled with viscous fluid (µ = 5.0 Pa · s) with sound hard boundary on the peripheral and radiation boundary at the end, simulating a CMUT cell vibrating in an array. The receiving scenario is analyzed in the FEM. The incoming plane wave pressure pulse P from an angle φ is simulated by applying a 10 ns Gaussian- shaped unipolar pulse with a continuous angle-dependent time delay across the CMUT cell membrane: P = P0(t− (l +R)/(2R)t0sin(φ)) (4.5) 120 where P0 is a constant pressure, l is the lateral distance, R is the radius of the CMUT cell, t0 = 2R/c where c is the speed of sound. The differential displacement on the left and right half of the membrane, and the average displacement of the whole membrane is measured. The frequency domain average and differential signals are shown in Fig. 4.6. 1 1.5 2 2.5 3 3.5 4 4.5 5 x 106 −40 −35 −30 −25 −20 −15 −10 −5 0 frequency [Hz] di sp la ce m en t [d B]   avg, −10o diff, −10o avg, −5o diff, −5o avg, 0o diff, 0o Figure 4.6: Frequency domain average and differential received signals for different source angles from the FEM simulation results. 4.3.2 Ultrasound Imaging Simulation We revised the CMUT version of Field II so that each quarter of the CMUT membrane is a standalone unit of actuation and reception. The receiving impulse responses of the symmetric mode and the asymmetric mode, defined as the displacement or capacitance response to a acoustic pressure impulse, are extracted respectively from the FEM simulation. Assuming that the superposition of the two modes is linear, we have the following equation: S = Ssym + Sasym = Pavg ∗ IRsym + Pdiff ∗ IRasym (4.6) 121 where S is the received signal, i.e. displacement or capacitance, Ssym and Sasym are the symmetric/asymmetric components. Pavg and Pdiff are the av- erage/differential pressure on the left and right part of the membrane, IRsym and IRasym are symmetric/asymmetric impulse response in reception, and ∗ denotes convolution. As a simplification, the asymmetric impulse response is chosen so that the ratios of Sasym between a few small angles in Field II simulation align with those of the FEM simulation. An example of the sym- metric and asymmetric impulse response of the membrane displacement is shown in Fig. 4.7. A detailed description of the construction of such CMUT cells in Field II can be found in Appendix B. 0 0.2 0.4 0.6 0.8 1 1.2 1.4 x 10−5 −20 −15 −10 −5 0 5 x 10−9 time [s] di sp la ce m en t [m ]   symmetric impulse response asymmetric impulse response Figure 4.7: Symmetric and asymmetric receiving impulse responses of mem- brane displacement. 122 Simulated Ring Array and Imaging Targets A ring array consisting of 48 CMUT cells with the aforementioned dimen- sions are constructed in Field II to demonstrate the new method (Fig. 4.8). The array has similar dimensions as the one fabricated in [22]. The static displacement of the individual CMUT cells in the Field II simulation are set from a cell profile extracted from a FEM simulation where the DC bias voltage is 100 V. The CMUT cells has a central frequency of 1.8 MHz when operating in the symmetric mode in immersion, and a resonant frequency of 2.7 MHz in the asymmetric mode. The ring array is excited using three cy- cles of a 3 MHz sinusoid, and the imaging targets are at depths of 18 mm to 23 mm. The relative scales of the CMUT array and the ROI for the imaging simulation is shown in Fig. 4.9. −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 −0.8 −0.6 −0.4 −0.2 0 0.2 0.4 x [mm] y [mm] Figure 4.8: Ring array with 48 CMUT cells constructed in Field II. Extracting Differential Received Signals For both manifold matrix construction and the imaging process, the CMUT ring array is excited with symmetric voltages, and the average and differen- 123 Region of Interest CMUT probe Beam width Figure 4.9: The relative scales of the CMUT array and the ROI for the imaging simulation. tial received signals from the targets are recorded as Sdiff = SL − SR, and Savg = (SL + SR)/2, where SL and SR are the received signal on the left and right half of the CMUT membrane. Manifold Matrix Construction The manifold matrices are constructed using 126 targets in an ROI centered around z = 20 mm. There are 21 targets angularly distributed from −20◦ to 20◦ with 2◦ separation, and 6 targets distributed in the axial direction from 18 mm to 23 mm with 1 mm separation. For both Savg and Sdiff , a manifold matrix set is calculated by focusing at each of the 21 angular directions at z = 20 mm and stored in the memory. To reduce the NT -dimension row space of the matrices, responses of cells at the same lateral position in the ring are averaged, and the responses are 124 recorded for every other cell in the lateral direction, thus making the rows a concatenation of 12 channel data. The temporal signals are sampled at 10 MHz. Weight Vector Computation and Image Formation In an imaging simulation, point targets are placed in the ROI, and the ring array transmits and receives with 21 focal points consecutively. In each transmit/receive, the f vector is computed and pruned, and an RF scan line is reconstructed using the method described in Section 4.2. The scan line matrix is then envelope detected, log-compressed, and scan-converted into a sector image. 4.3.3 Comparison of Phased Array Imaging and the Proposed Method The TX/RX beam profile of the ring array at z = 20 mm when focusing at 0 ◦ and 20◦ are shown in Fig. 4.10(a) and Fig. 4.10(b) respectively. The scale of the beam width with respect to the ROI is shown in Fig. 4.9. The side lobes contribute to the blurred appearance during classic phased array imaging. The idealized image of each simulated phantom is reconstructed assum- ing that imaging is done with the same number of angles (scan lines) as the proposed method, and the elements in fi corresponding to the true targets at θi have the value 1, and others being 0; therefore these images shows only the interpolation effects between the scan lines. The phased array beam forming is done by focusing the ring array at 21 focal points, and collect- ing the sum of the per-element echo data, each delayed according to their 125 −20 −15 −10 −5 0 5 10 15 20 −35 −30 −25 −20 −15 −10 −5 0 Lateral position [mm] TX /R X Be am  p ro file  [d B] (a) −20 −15 −10 −5 0 5 10 15 20 −40 −35 −30 −25 −20 −15 −10 −5 0 Lateral position [mm] TX /R X Be am  p ro file  [d B] (b) Figure 4.10: (a) TX/RX beam profile at 20 mm when focusing at 0 ◦. (b) TX/RX beam profile at 20 mm when focusing at 20 ◦. distance to the focal point. The imaging results for a simulated phantom of two columns of point targets 10◦ apart are shown in Fig. 4.11. For comparison, the imaging results of the same targets but calculated using a coarser hypothetical point target grid (9 by 6) are shown in Fig. 4.14. To show a more rigorous imaging scenario, a simulated phantom with half the maximum spatial sampling frequency of the hypothetical targets is used, and the result in shown in Fig. 4.12. In this test, SA misses the targets of some angles, and SD detects some false positives in the axial and lateral directions but is capable of capturing all the targets. SH removes some false positives, but does not recover the missing ones. A more sophisticated hybrid approach needs to be further developed. Another test is performed with a simulated point targets phantom with the first two targets 10◦ laterally and 2 mm axially apart, and three bottom ones 10◦ laterally apart at z = 22 mm, as shown in Fig. 4.13. SD provides 126 Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (d) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (e) Figure 4.11: Imaging results for two columns of point targets, calculated with manifold matrices of 21 by 6 hypothetical targets. (a) Idealized B- mode image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. better estimation results, and SH gives the best image quality. As shown in Fig. 4.10, the full-width at half-maximum (FWHM) beam width at the focal point is 5 mm. All the above imaging results show that the proposed method is able to distinguish lateral targets within this beam width, which means our method can achieve super resolution. We measured the performance of the new method using the signal-to- noise-ratio (SNR) calculated as follows: the binary masks of the signal area 127 Lateral distance [mm] A xi al  d is ta nc e [m m ] -20 -15 -10 -5 0 5 10 15 20 10 15 20 25 (a) Lateral distance [mm] A xi al  d is ta nc e [m m ] -20 -15 -10 -5 0 5 10 15 20 10 15 20 25 (b) Lateral distance [mm] A xi al  d is ta nc e [m m ] -20 -15 -10 -5 0 5 10 15 20 10 15 20 25 (c) Lateral distance [mm] A xi al  d is ta nc e [m m ] -20 -15 -10 -5 0 5 10 15 20 10 15 20 25 (d) Lateral distance [mm] A xi al  d is ta nc e [m m ] -20 -15 -10 -5 0 5 10 15 20 10 15 20 25 (e) Figure 4.12: Imaging results for targets with high spatial sampling rate, calculated with manifold matrices of 21 by 6 hypothetical targets. (a) Ide- alized scan-converted image. (b) B-mode image result using phased array beamforming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. and the noise area are created using idealized B-mode images, and the SNR of a new B-mode image is computed as the mean grayscale level in the signal area versus the mean grayscale level in the noise area. The SNR of the B-mode images produced by the phased array, the SA method, the SD method, and the SH method of the simulated phantoms shown in Fig. 4.11 to Fig. 4.14 is listed in Table 4.1. The SNR results show that SH has the highest success rate at distin- 128 Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (d) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (e) Figure 4.13: Imaging results of a simulated point targets phantom, calcu- lated with manifold matrices of 21 by 6 hypothetical targets. (a) Idealized scan-converted image. (b) B-mode image result using phased array beam- forming. (c) B-mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. Table 4.1: B-mode image SNR comparison of different imaging methods (dB) for different target configurations shown in Fig. 4.11 to Fig. 4.14. Phased array SA SD SH Fig. 4.11 27.3135 31.2149 36.7075 38.8461 Fig. 4.12 30.0102 37.5658 31.7047 34.0847 Fig. 4.13 28.4123 40.1686 44.0710 61.6018 Fig. 4.14 30.3678 29.0679 31.4033 40.0093 guishing point targets among all methods, except for Fig. 4.12 where both SD and SH generate more false positives than SA. 129 Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (d) Lateral distance [mm] Ax ia l d ist an ce  [m m] −20 −15 −10 −5 0 5 10 15 20 10 15 20 25 (e) Figure 4.14: Imaging results calculated with manifold matrices of 9 by 6 hy- pothetical targets, same targets as in Fig. 4.11. (a) Idealized scan-converted image. (b) B-mode image result using phased array beamforming. (c) B- mode image result using SA. (d) B-mode image result using SD. (e) B-mode image result using SH. The SNR for the result with a coarse target grid (Fig. 4.14) listed on the last row of Table 4.1 is not meant to be directly compared with the other rows, since it was calculated against its own idealized image with fewer number of targets and larger interpolation effect. This row of SNR shows that with lower number of calibrated targets, SD and SH still produces higher SNR than the phased array while the SA is performing even worse than the phased array. This means that the proposed methods SD and SH 130 can improve image quality over the phased array with a coarse calibrating target grid and therefore should be considered as more computationally efficient but still feasible methods. 4.3.4 Discussion of Simulation Results The imaging results show that the inherent side lobes of a phased ring array result in considerable blur in the image, whereas the proposed imaging methods SA, SD and SH all give super resolution. The apparent estimation accuracy of the method improves when SD is used, and further increases when the false positives are removed by SH. The result also shows that the image quality improves for SA when the number of hypothetical grid points increases, i.e. the dimension of the manifold matrices increases. This means that the differential signal requires smaller manifold matrices to achieve a similar image resolution. Furthermore, the SH method improves on SD and SH while keeping the matrix dimension low, making the proposed method a relatively low computational complexity, super resolution imaging approach. SD and SH methods may generate more false positives when the spatial sampling rate of the test phantom is close to the highest spatial sampling rate of the hypothetical target grid. The pruning step may cause false negatives especially when the hypothetical target grid is dense and estimation error is relatively large. Using a weighted average of the values from neighboring angles may be a solution. 131 4.4 Experimental Results Using a CMUT Probe The methods developed in the preceding section are summarized in Table 4.2 in terms of the signals to be obtained, and the type of CMUT array required. Since the multi-electrode CMUT array is still in the design and fabrication stage, we present ultrasound imaging test results with a generic CMUT probe on the SA method which does not require a multi-electrode CMUT probe. The goal is to show the feasibility of the series of methods using SA as a representing method. We also show the results of using element-wise difference signals as an intermediate step to using the differential signals from left and right electrodes. Table 4.2: Proposed super-resolution methods and their corresponding re- ceived signals and required transducer array type. Method Average signal Differential signal Single-electrode CMUT array Multi-electrode CMUT array SA x x SD x x SH x x x The SA super-resolution method was tested using a packaged CMUT probe (LA5/CMUT) from Vermon (Vermon SA, Tours Cedex, France). The CMUT probe has 128 elements with an element pitch of 305µm, and a cen- ter frequency of 4 MHz. The pull-in voltage of the CMUT cells is 110 V, and the front-end electronics are embedded in the probe. Unlike piezoelec- tric ultrasound probes, the particular CMUT probe requires multiple power supplies, including fixed voltages for the circuitry (two dual low-voltage power supplies of +/2.5 V and +/ 5V and a high-voltage supply for -100 V 132 CMUT probe Water tank Motion stage Figure 4.15: Experiment setup for super-resolution imaging. DC voltage), and a high-voltage supply for the bias voltage VDC . 4.4.1 Experiment Setup The CMUT probe was connected to a SonixRP ultrasound machine (Ultra- sonix Medical Corporation, Richmond, Canada). A bias voltage VDC = 80 V was applied to the CMUT elements, and an AC voltage Vac = 90 Vp−p specified by the Ultrasonix research interface was used to drive the CMUT elements to send out ultrasound pulses. The pre-beamformed per-channel received data was collected by the SonixDAQ board for further processing. The experiment setup is shown in Fig.4.15. The CMUT probe was fixed to a motion stage with a translation resolution of 0.002 mm. A nylon wire with the diameter of 0.54 mm was fixed in a water tank in the focal region of the CMUT probe. During the test, the probe was translated in lateral and axial directions to simulate the different positioning of the wire relative to the probe. 133 4.4.2 Experiment Procedure and Results The experiment conceptually consists of a calibration stage and a test stage. In the calibration stage, the probe is translated in a rectangular grid to simulate the translation of the nylon wire relative to the probe. For each grid position, the probe transmits a pulse with a fixed focus, and the per- channel received data is collected and processed offline to create the manifold matrices of multiple focal points. In the test stage, the probe is moved to an off-grid position, transmits a focused pulse, and the received data is collected for testing. In practice, the calibration and testing data can be collected in the same run following a rectangular grid shape. In the future, this setup can be improved to allow multiple test point targets at once by switching from a single-wire calibration setup to a multiple-wire test setup. Two sub-experiments were carried out to test the SA method: a linear array imaging test, and a phased array imaging test, in order to show the feasibility of the proposed method for different imaging schemes. Linear Array Imaging In a linear array imaging process, an active aperture made up of a group of the array elements is excited to transmit a focused pulse, and receives the echo to create a scan line. Then a second group in a translated position is excited and creates a second scan line, just like the process described in Subsection 3.1.1. In this test, an aperture of 32 elements moved across the center part of the probe to generate 10 scan lines for B-mode image reconstruction. A nylon wire was placed approximately 20 mm away from 134 the probe, and the probe was translated on a rectangular grid of 10 points in lateral direction, with a spacing of 0.25 mm, and 3 points in axial direction, with a spacing of 1 mm. The aperture had a beam width of 1.9 mm at 20 mm depth, which is approximately the entire lateral range of the 10 lateral points. The relative scales of the CMUT probe and active aperture, the beam width, and the ROI are shown in Fig. 4.16(a). Region of Interest      CMUT probe      active aperture Beam width (a) Region of Interest      CMUT probe      active aperture Beam width (b) Figure 4.16: Relative scales of the CMUT probe, the active aperture, the beam width, and the imaging ROI of the linear array and phased array imaging tests. (a) Relative scales of the linear array imaging tests. (b) Relative scales of the phased array imaging tests. The per-element received data was processed in two ways for compari- son. The first way was the conventional delay-and-sum method. For each scan line, the received signal of each element of the active aperture was tem- porally delayed based on its distance to the focal point, and then summed up to create a single signal trace for the scan line. The second way was the 135 SA method described in Section 4.2 where the active aperture was trans- lated across the probe the same way as the delay-and-sum imaging, and the manifold matrix construction and estimation was done for each scan line. A temporal sampling of 10 MHz was used to reduce the computational load. Fig.4.17 shows the reconstructed B-mode image results for two non- grid point targets (wires at non-grid locations) that are 0.25 mm apart. The idealized B-mode images were reconstructed the same way as that of the SA method (Eq. 4.3), assuming that the weight vector estimated at each scan line position was perfectly correct. Therefore, the idealized images have the same axial blurring as the ones reconstructed by delay-and-sum and SA, which result from the finite thickness of the wire (0.54 mm) and the acoustic reverberation around the wire. It is shown that the results using the conven- tional delay-and-sum method cannot distinguish the two points due to the beam width, while the SA method produces a good delineation between the two points. The lateral artifacts in the reconstructed images using SA are the results of estimation inaccuracy, as well as the difficulty in the weight vector pruning step due to the coarse physical alignment of the scan lines and the lateral target positions. Phased Array Imaging In a phased array imaging process, a fixed active aperture steers to (focused at) multiple angular positions to create multiple scan lines. In this test, we simulated a phased array using the central 32 elements of the probe that were electronically steered to 5 directions with an angular spacing of 2◦. The nylon wire was placed approximately 30 mm away from the probe, and the 136 Lateral distance [mm] Ax ia l d ist an ce  [m m] 17 18 19 1 2 3 4 5 6 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] 17 18 19 1 2 3 4 5 6 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] 17 18 19 1 2 3 4 5 6 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] 17 18 19 1 2 3 4 5 6 (d) Lateral distance [mm] Ax ia l d ist an ce  [m m] 17 18 19 1 2 3 4 5 6 (e) Lateral distance [mm] Ax ia l d ist an ce  [m m] 17 18 19 1 2 3 4 5 6 (f) Figure 4.17: Linear array imaging results using a CMUT probe. (a) Idealized B-mode image for target No.1. (b) B-mode image result using delay-and- sum for target No.1. (c) B-mode image result using SA for target No.1. (d) Idealized B-mode image for target No.2. (e) B-mode image result using delay-and-sum for target No.2. (f) B-mode image result using SA for target No.2. probe was translated on a rectangular grid of 5 points in lateral direction, with a spacing of 1 mm, and 3 points in axial direction, with a spacing of 137 1 mm. Due to the large imaging depth and small angles, the lateral grid positions and the steering lines can be considered as aligned. The relative scales of the CMUT probe and active aperture, the beam width, and the ROI are shown in Fig. 4.16(b). The per-element received data was processed in two ways for comparison. The first way was the conventional phased array method. For each scan line, the received signal of each element of the active aperture was temporally delayed based on its distance to the focal point, taking into account the steering angle, and then summed up to create a single signal trace for the scan line. The second way was the SA method described in Section 4.2 where the active aperture steered to multiple angles as the phased array method did, and the manifold matrix construction and estimation was done for each angle. The temporal sampling was also 10 MHz. Fig.4.18 show the reconstructed B-mode images for two non-grid point targets that were 1 mm apart. The phased array method gives smeared images across the field of view, while the proposed SA method distinguishes the targets by showing two lines with shifted centers. The lateral blur in the B-mode image is largely due to the interpolation of the few number (5) of scan lines. Use of Element-wise Differential Signals Since the structure of the current packaged CMUT probe does not allow receiving echoes from two electrodes on the same CMUT cell, and thus un- able to detect asymmetric modes as proposed, we carried out an experiment using a variation of SD that used the differential signals from two elements instead of from the two electrodes of the same cell. This is an exploratory 138 Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (d) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (e) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (f) Figure 4.18: Phased array imaging results using a CMUT probe. (a) Ideal- ized B-mode image for target No.1. (b) B-mode image result using phased array for target No.1. (c) B-mode image result using SA for target No.1. (d) Idealized B-mode image for target No.2. (e) B-mode image result using phased array for target No.2. (f) B-mode image result using SA for target No.2. study that serves an intermediate step toward the validation of SD and SH, as well as understanding of the connection between the signature in the manifold matrix and the estimation accuracy. In this test, the difference of the temporal signals received from neighbor- ing elements was used to construct the manifold matrices and the new data for the weight vector estimation process. The appearance of the manifold matrices constructed by the element-wise regular signals, and the element- wise differential signals are compared in Fig. 4.19. The manifold matrix of 139 the element-wise differential data shows a more distinctive amplitude pat- tern for different targets. However, the B-mode imaging results using the differential data for the two point targets show comparable quality with the regular data (Fig.4.20). To achieve better estimation results, the unique amplitude feature of the differential manifold matrix needs to be further analyzed and exploited. 0 500 1000 1500 2000 2500 3000 3500 4000 Concatenated temporal received samples from 32 channels H yp ot he tic al  ta rg et  lo ca tio ns   (a) 0 500 1000 1500 2000 2500 3000 3500 4000 H yp ot he tic al  ta rg et  lo ca tio ns Concatenated temporal received samples from 32 channels (b) Figure 4.19: Visualization of manifold matrices using element-wise regular and differential signals. (a) Manifold matrix constructed from element-wise regular echo data. (b) Manifold matrix constructed from element-wise dif- ferential echo data. 4.4.3 Discussion of Experimental Results The proposed SA method was applied to acoustic experiments where the calibration, weight vector estimation and B-mode image reconstruction were done on real ultrasound data obtained by a CMUT probe. The results show that the focused super-resolution method SA can generate super-resolution image results, i.e. distinguishing targets that fall within the beam width. The manifold matrix constructed by element-wise differential signals shows a 140 Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (d) Figure 4.20: Phased array imaging results using element-wise differential sig- nals. (a) Idealized B-mode image for target No.1. (b) B-mode image result using element-wise differential signals in SA for target No.1. (c) Idealized B-mode image for target No.2. (d) B-mode image result using element-wise differential signals in SA for target No.2. distinctive amplitude pattern similar to the pattern expected to be generated by the asymmetric mode and produces comparable image quality, which suggests the harmonic behavior from the asymmetric mode may further improve the estimation performance. The artifacts shown in the current results come from several major sources: 1. the multiple echoes in the axial 141 direction may have come from the reverberation signals due to the finite thickness of the nylon wire; 2. lateral artifacts are the combined effects of estimation inaccuracy, and the way of weighting the RF data, which can be further improved; 3. interpolation effects are the results from the limited number of scan lines acquired. 4.5 Conclusion and Discussion In this work, we first proposed a series of novel focused super-resolution imaging methods that takes advantage of the focusing process and the dif- ferential received signal of multi-electrode CMUTs. The proposed method uses focused transmit and beamforming at receive. Manifold matrices of multiple steering angles were constructed, and a pruning step was added to minimize the side lobe artifact. A hybrid step was then proposed to reduce false positive estimation from average and differential signals. Ultrasound imaging simulation was performed with a revised Field II program using the impulse responses from FEM simulation. Imaging simulation results showed that the unique signature of the differential received signal resulted in higher estimation accuracy, and thus higher resolution than the classic phased array beam forming method, and lower computational cost than the first super-resolution method using average received signals. The SD and SH methods can be readily extended to linear arrays, and can be applied to plane wave fast imaging by constructing and solving weight vectors using only one manifold matrix and omitting the weight vector pruning step. The image quality can be traded off for higher frame rate, and the differential 142 received signals still outperforms the average received signals. More simu- lations are needed to identify the optimal operating zone of the differential signals, i.e. the maximum angles, the distances from the focal zone, and the optimum operation frequencies. Simulations with a large number of point targets, e.g. a diffuse speckle generating cyst, will be an interesting next step to fully test the SA method and to analyze the advantages of the SD and SH methods. Preliminary B-mode imaging results using a CMUT probe are shown to demonstrate the effectiveness of the proposed super-resolution method. Although only the SA method was tested on the experimental data due to the limitation of the facilities, the proposed focused method is promising for obtaining super-resolution images, and the results from element-wise differ- ential data point provides useful indication for SD and SH methods. An ongoing research direction is to use parameters extracted from the temporal echo data for estimation. The detail of this direction is described in the Future Work Section in Chapter 5. Future directions include experiments with more grid points and better alignment with focal directions, imaging and estimating multiple point targets simultaneously, and ultimately, test- ing SD and SH methods using the asymmetric responses when the devices are ready. 143 Chapter 5 Conclusion and Future Work 5.1 Summary of the Thesis Capacitive Micromachined Ultrasonic Transducers (CMUTs) have attracted a wide interest in the medical ultrasound imaging community as an alterna- tive to piezoelectric transducers because of their inherent wide bandwidth, as well as the ease of integration with the electronics and low cost thanks to microfabrication technology. CMUTs are especially useful for making high-frequency, miniaturized probes for intravascular and intracardiac ap- plications. Considerable previous research has been performed on modeling the CMUT operation, fabricating CMUTs of various structures in order to achieve stability, uniformity, power efficiency, and integration with front-end electronics. Several types of CMUT probes (e.g., catheters, 2D arrays) have been built and integrated with commercial or custom ultrasound imaging systems, and optical, acoustical measurements were carried out to character- ize their performance. B-mode as well as 3D image results show comparable quality with those from the commercial piezoelectric probes with advantages in resolution but often inferiority in output power, receiving sensitivity, and depth penetration. Improvements in these aspects, such as modeling and fabrication of deep-collapsed CMUT cells, understanding the crosstalk be- 144 tween cells are ongoing directions in the CMUT research field. Despite the thorough studies on improving the capabilities of CMUTs to rival and surpass those of piezoelectric transducers, little work has been done to explore the unique structure of CMUTs for improving imaging ap- plications. Unlike a piezoelectric element that typically vibrates in a single mode, i.e. the bulk vibration like a piston, a CMUT cell has a suspended- plate structure that allows many more modes of vibration under different types of actuation. Many previous works perceive the drum-like structure of CMUT cell as a disadvantage as it provides maximum pressure output or receiving sensitivity in a limited area around its center, and is likely to cause acoustic crosstalk. A few works even attempt to modify the cell structure to approximate the piston-like operation. In this thesis, a multi-modal op- eration concept with a novel structure for the CMUTs is proposed, and the imaging applications offered by the concept are investigated. The summary of the thesis is as below, organized by chapters. Chapter 2 proposes to analyze the CMUT operation from a mode su- perposition perspective. While most current literature focuses on modeling CMUTs as a vibrating piston with uniform vibration profile, or a drum whose cross-sectional vibration profile is described by a fourth-order poly- nomial, we model a CMUT’s position-dependent vibration profile using the characteristic functions of different modes. Through judicious design of the locations and frequencies of the electrostatic force on the cell membrane, multiple vibration modes can be excited simultaneously. In the simplest case, by applying different voltages on two halves of membrane, the first symmetric mode ((0,1) mode) and the first asymmetric mode ((1,1) mode) 145 can be both excited, producing a vibration with a shifted center. The mode-superposition based analytical model also includes the model- ing of electromechanical and mechano-acoustical interaction. The mechani- cal vibration profile, and the output pressure calculated from the analytical model for in-air and in-water operations are compared with the results from a finite element model (FEM) of a CMUT cell in an infinite acoustic medium. The error that mainly comes from the simplification of the electromechan- ical interaction has then been investigated. The far-field acoustic pressure profile is compared with that of the piston, suggesting that the piston model leads to much larger errors in far-field beam profile calculation. The vibra- tion profile of an asymmetrically excited CMUT cell is also compared with that from the FEM simulation with good accuracy. An equivalent circuit model with multiple sub-circuits for multiple modes is also developed for fast and accurate simulation of the multi-modal oper- ation. To capture the CMUT behavior in an array, a different medium loading condition than the previous analytical model is considered, and the corresponding FEM simulation is carried out. The comparison between the simulation result from the equivalent circuit model and from the FEM model indicates that the equivalent circuit is not only able to capture the electromechanical interaction and the mechano-acoustic interaction, but also the multi-modal behavior both in air and in water. To show the viability of the multi-modal operation of CMUTs, fabricated CMUT chips with regular CMUT arrays and standalone CMUT cells with multiple electrodes were experimentally characterized. The optical, acousti- cal and electrical test results agree with the FEM and analytical simulation 146 in terms of resonant frequencies of the symmetric and asymmetric modes in air, and the vibration profile with a shifted center is optically captured. Due to a lack of complete hermetic sealing, the immersion operation in oil is heavily damped, but still shows asymmetric vibration under asymmetric excitation. The symmetric and asymmetric mode resonances in air are ob- served electrically, but the resonance for the asymmetric mode in immersion is difficult to observe due to the heavy damping and high parasitics of a single test cell. Two novel imaging applications are developed that take advantage of the multi-modal vibration capability of CMUTs. Chapter 3 investigates the concept of tiltable transducers for reducing side lobes and grating lobes while preserving main lobe energy for B-mode ultrasound imaging. The conventional transducer array focuses and steers the ultrasonic beam en- ergy through inter-element time delays so that the beams from different elements arrive at a location in the region of interest at the same time. That approach of focusing does not physically direct the largest portion of the energy (the main lobe) to the focal point, especially when focusing at targets at large angles with the center line of the element. Transducer ar- rays of certain geometries, such as small footprint intracardiac transducers and curvilinear arrays, thus have degraded imaging quality when steered to large angles because the elements are physically directed at a fixed direction. Grating lobes resulting from the periodic layout of the transducer array, are reduced amplitude acoustic energy peaks at different directions other than the intended ones, and produce false images of the real targets. As a solution to these problems, new methods of physical focusing and physical steering 147 are proposed where the transducer elements are tilted toward the focal point or the beam steering direction to better direct the acoustic energy and break the periodicity of the array. Ultrasound imaging simulations are carried out to compare the physical focusing and steering with conventional electronic focusing and steering using time delays. The grating lobes can be reduced by up to 24 dB when using physical steering or physical focusing while the main lobe energy is preserved. Physical focusing and steering can be flex- ibly combined with each other, or with electronic focusing and steering to produce more desired results. Since physical tilting is difficult to imple- ment using the piezoelectric technology, CMUTs can be a candidate in the embodiment of the tiltable transducers. When excited by an asymmetric voltage, CMUTs are able to vibrate with a shifted center, an approximation of “tilting”. FEM simulations show the CMUT cell is able to emit the beam 7◦ from its center line. An element consisting of multiple CMUT cells can be considered to be tilted as a whole when each cell is tilted. Imaging simula- tions with the feasible (small) tilting angle show that physical focusing and steering even with small angles reduce the grating lobes and maintain the main lobe energy for a larger range of frequencies than electronic focusing the steering. While the FEM simulation of the tilted beam is based on a single CMUT cell vibrating in an infinite spherical medium, in practice, the CMUT dimension and the central frequency need to be designed so that the tilting effect of the transmitted acoustic waves can propagate to the far-field. In Chapter 4, several super-resolution imaging methods are studied that leverages the focused transmission, and the unique resonant behavior of CMUTs in response to off-axis acoustic sources. CMUTs have been suc- 148 cessfully used for ring array catheters, yet the small aperture of the ring array geometry tends to produce a wide beam and high side lobes that com- promise the imaging resolution. The super-resolution imaging approaches use the differential signal received from the left and right electrodes of the multi-electrode CMUTs. When the acoustic pressure from an off-axis source strikes the CMUT membrane, the asymmetric mode can be excited by the pressure difference on both sides of the membrane. The pressure difference cannot be captured in the conventional received signal averaged on the whole electrode, but shows as a ringing at the resonant frequency of the asymmet- ric mode in the differential signal. The ringing depends on the angle of the acoustic target, and the differential signals across different elements form less correlated signature than the signals averaged on the whole electrode. The new method starts with a manifold matrix building process similar to one used in [33] but with multiple focal angles. The transmit pulses are steered to multiple angles, and the received signals of all receiving elements are recorded at each focal angle for each point target in a calibration grid. During the imaging process, for each focal angle, an iterative Maximum a Posteriori (MAP) process is carried out to estimate the weights of each cal- ibration target, and an angular pruning process is performed to eliminate signals from angles different from the current focal direction (side lobes). The B-mode image is reconstructed by weighting the calibrated RF data of each target. Due to the ringing signature of the received signal, the es- timation results using the differential signals are more accurate than using the average signals even with sparse calibration grid points. The estimated weight factors using average and differential signals can be further com- 149 bined into a hybrid method to remove false positives. An FEM simulation is performed to verify the ringing behavior of the receiving CMUTs. Then imaging simulations are carried out with different layouts of test point tar- gets, and the SNRs for the reconstructed images are calculated. The hybrid approach is up to 33 dB higher in SNR than the conventional phased ar- ray approach and up to 21 dB higher than the same method using average signals. This method can achieve super-resolution at relative lower compu- tational cost than using average signals, and can be applied with any CMUT dimension, although the configuration for optimal performance, such as the maximum steering angles, needs to identified. Preliminary experimental data is shown to demonstrate that super-resolution can be obtained within the lateral width of the beam, and an exploratory study was performed us- ing element-wise differential signals to provide useful information for using differential signals from a single cell. In summary, this thesis explores the multi-modal vibration behavior of CMUTs through modeling, experimental characterization of fabricated multi-electrode CMUTs, and design, simulation and experimental studies of two imaging applications. As one of the first few attempts on this topic, this work shows that exciting multiple modes of CMUTs can benefit a wide range of ultrasound imaging applications, and the multi-modal perspective is a useful tool for modeling and design. 150 5.2 Future Directions The multi-modal concept and applications proposed in this thesis may be experimentally tested, and extended to other aspects of ultrasound imaging. The current and future research directions include: 5.2.1 Experimental Characterization of CMUTs in Immersion Hermetically sealed CMUT arrays need to be fabricated using existing in- house methods in literature (e.g. [63]) or alternative methods such as Electro- discharge Machining (EDM) which is being collaboratively developed at UBC, or ink jet printing. Then, fabrication methods for arrays of multi- electrode CMUTs need to developed and implemented, and the multi-electrode CMUT chips will be experimentally characterized in air and in immersion. The characterization includes the pull-in voltage and resonant frequency measurement using the Laser Doppler Vibrometer (LDV) and the impedance analyzer, output pressure measurement in immersion using a hydrophone, and pulse-echo measurement. The CMUT chip may be tested in integration with the CMOS circuit for transmission and receiving, which is currently being developed by another student. 5.2.2 Experimental Study of the Asymmetrically Actuated CMUTs After characterizing the chip, experimental studies regarding the adaptive CMUT concept may be carried out. The beam profile of asymmetrically 151 driven single CMUT cell as well as CMUT array in immersion need to be measured and compared with the theoretical and FEM results. The beam angle versus the distance from the surface of the CMUTs may be recorded to provide guidance for designing CMUT structures whose transmit beam need be tilted by a practically significant angle. The analytical model for estimating the far-field beam profile for array operation (instead of single cell operation in the thesis) can be developed and compared with the exper- imental result. 5.2.3 Experimental Study of the Super-resolution Imaging Method The proposed super-resolution imaging method has been preliminarily tested with a generic single-electrode CMUT probe, and has shown promising re- sults. An ongoing research direction is to reduce the matrix dimension using parameter extraction. Matrix Dimension Reduction Using Parameter Extraction To reduce the computational complexity of the target weight vector esti- mation process, the temporal data collected in the experiments was down- sampled to tightly satisfy the Nyquist sampling limit, yet the process still involves operating matrices of 4000 rows. We are currently exploring the approach of reconstructing the temporal data with a much coarser sampling rate using the parameters extracted from a signal model of the original data. The computation time for weight vector estimation can be greatly reduced. Fig. 5.1 (blue curve) shows the original temporal trace of an acoustic 152 echo collected by a CMUT element. We model this echo using a decaying complex exponential model: s(n) = A0U(n− n0)eα(n−n0)ejω0(n−n1) (5.1) where s(n) is the discrete model signal, A0 is the maximum amplitude of the echo, U is the step function, n0 is the discrete delay, α is the decay rate, ω0 is the central frequency of the transmit pulse, and n1 is the phase of the harmonic part of the signal. The model can be simplified to a decaying exponential assuming insignificant change of the harmonic frequency and phase. Then a set of three parameters (A0, n0, α) can be extracted from the envelope of each temporal trace at each receiving element, and a decaying exponential trace can be reconstructed using the parameter set (Fig. 5.1, green curve): s′(n) = A0U(n− n0)eα(n−n0) (5.2) 0 100 200 300 400 500 600 −1000 −800 −600 −400 −200 0 200 400 600 800 1000 sample points e ch o am pl itu de   original data reconstructed data Figure 5.1: Illustration of reconstructing the temporal echo data from an element as a decaying exponential function. 153 Since the estimation algorithm relies primarily on matching the delay, relative amplitude and envelope of the temporal signals across the elements, s′(n) can be coarsely sampled without losing significant information. Fig.5.2 shows the examples of manifold matrices of both element-wise regular data and element-wise differential data in their reconstructed form. The param- eter extraction and reconstruction was applied to both the construction of the manifold matrices and the new data for the weight vector estimation process. Fig.5.3 shows the B-mode image results where the estimation of the hypothetical target weights of the SA method were done on the recon- structed element-wise regular and differential data. The largest dimension of the manifold matrix was reduced from 4000 to 400, and the image quality is marginally reduced compared to the B-mode imaging results using the original temporal data in Fig. 4.18 and Fig. 4.20. Note that the B-mode image reconstruction step was still performed using the original RF data, multiplied by the estimated weights. The parameter extraction method can be further explored to reduce the redundancy of the manifold matrix and simplify the estimation process, which is part of the ongoing research of the author. Once a CMUT probe capable of receiving signals from multiple elec- trodes is ready, the differential received signal of the multi-electrode CMUT array in response to off-axis acoustic sources can be obtained, and compared with the FEM results. Then the super-resolution imaging method using the differential and average received signals can be tested with a similar setup to that of the current experiment, and the performance will be compared with the phased array result. Refined super-resolution algorithm to compensate 154 0 50 100 150 200 250 300 350 400 Concatenated temporal received samples from 32 channels H yp ot he tic al  ta rg et  lo ca tio ns (a) 0 50 100 150 200 250 300 350 400 Concatenated temporal received samples from 32 channels H yp ot he tic al  ta rg et  lo ca tio ns (b) Figure 5.2: Examples of manifold matrices using reconstructed signals. (a) Manifold matrix constructed from reconstructed element-wise regular echo data. (b) Manifold matrix constructed from reconstructed element-wise dif- ferential echo data. the speed-of-sound difference in the human body may be developed for the method to be used in-vivo. 5.2.4 Imaging Application Using the Multi-modal Vibration Concept The acoustic crosstalk between CMUT cells may cause multiple vibration modes to be excited, especially when the CMUT array steers to a large angle [8], resulting in dips in the frequency response. Actively exciting multiple modes in the CMUTs may counteract this effect and potentially reduce the artifacts caused by crosstalk. 155 Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (a) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (b) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (c) Lateral distance [mm] Ax ia l d ist an ce  [m m] −4 −2 0 2 4 21 22 23 24 25 26 27 28 29 30 (d) Figure 5.3: B-mode image results where reconstructed signals are used for weights estimation. (a) B-mode image result using reconstructed element- wise regular signals for target No.1. (b) B-mode image result using recon- structed element-wise differential signals for target No.1. (c) B-mode image result using reconstructed element-wise regular signals for target No.2. 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Ultrasonics, Fer- roelectrics and Frequency Control, IEEE Transactions on, 54(6):1217– 1228, June 2007. 179 Appendix A Field II Implementation of a Tiltable Array This appendix shows a piece of Field II Matlab code implementing an ar- ray where the position, width, height, and tilting angle of each individual element are adjustable. %% Generate an array of arbitrarily placed elements % [Th] = arbitrary_array(N_ele , pos , wid , hei , ang , focus) % N_ele: number of elements % pos: array of element positions (x,y,z) % wid: vector of element widths % hei: vector of element heights % ang: vector of element tilting angles % focus: focus of this aperture function [Th] = arbitrary_array(N_ele , pos , wid , hei , ang , focus) c_apo = ones(N_ele)’; rect =[]; center = []’; for i=1: N_ele new_center = pos(i,:); new_1 = new_center +[-wid(i)/2*cos(ang(i)) -hei(i)/2 -wid(i)/2* sin(ang(i))]; new_2 = new_center +[wid(i)/2*cos(ang(i)) -hei(i)/2 wid(i)/2* sin(ang(i))]; new_3 = new_center +[wid(i)/2*cos(ang(i)) hei(i)/2 wid(i)/2* sin(ang(i))]; new_4 = new_center +[-wid(i)/2*cos(ang(i)) hei(i)/2 -wid(i)/2* sin(ang(i))]; 180 new_rect = [i new_1 new_2 new_3 new_4 c_apo(1,i) wid(i) hei(i) new_center ]; rect=[rect; new_rect ]; center = [center; new_center ]; end % Generate the array using rectangular elements Th = xdc_rectangles (rect , center , focus); 181 Appendix B Construction and Signal Processing of CMUTs in Field II This appendix provides the details of constructing the physical structure of CMUT cells and arrays capable of symmetric and asymmetric vibrations, as well as receiving average and differential signals. Due to copyright agreement of Field II source code, only the roadmap, the function prototypes of the C code, and part of the Matlab code as examples of usage will be provided. B.1 Construction of CMUT Cells Capable of Symmetric and Asymmetric Vibrations Different from the implementation in [3] where the CMUT cells are ap- proximated as part of a spherical surface, the model used in this thesis is constructed using the displacement profile extracted from FEM simula- tion or analytical calculation. As an example, Fig. B.1(a) is an asymmetric displacement profile input, and the CMUT cell is approximated by connect- 182 ing a 2D array of rectangles (Mathematical Elements offered in Field II) whose corresponding corner positions are determined by the profile input (Fig. B.1(b)). Several of such cells can be placed in space to form an array (aperture) (Fig. B.1(c)). All relevant array parameters required in Field II, such as excitation, electromechanical impulse response, apodization values can be used in the same fashion as regular arrays. -5 -4 -3 -2 -1 0 1 2 3 4 5 x 10 -5 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 x 10 -6 radial distance [m] D C  d is p la c e m e n t [m ] -0.04 -0.02 0 0.02 0.04 -0.04 -0.02 0 0.02 0.04 -8 -6 -4 -2 x 10 -3  x [mm]y [mm]  0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 -0.08 -0.06 -0.04 -0.02 0 0.02 0.04 0.06 0.08 -8-6 -4-2 x 10 -3  x [mm]  z  [ m m ] 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 (a) Cross-section displacement profile from FEM or analytical model (b) Construction of CMUT cells with the displacement profile (c) Multiple cells made into a transducer -0.1 0 0.1 -0.1 0 0.1  x [mm]y [mm]  z  [ m m ] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Figure B.1: Illustration of constructing CMUT cells in Field II. The function prototypes involved in the construction of the CMUT cells are listed below. /* *************************************************************** @function name xdc_cmut_array_ring_quarter @description construct a CMUT ring array with multiple elements. Each element contains multiple CMUT cells , and each cell is constructed quarter by quarter using rectangles by iteratively calling define_cmut_element_by_quarter () @return type transducer aperture @parameters 183 no_ele: number of transducer elements ele_centers: coordinates of the element centers width: width of the element height: height of the element no_cmut_cells: number of CMUT cells in each element cmut_radius: radius of each CMUT cell cmut_defl_0: CMUT deflection profile of the symmetric mode cmut_defl_1: CMUT deflection profile of the asymmetric mode dx: lateral sampling of the deflection profile cmut_centers: CMUT cell center coordinates no_sub_cmut: number of mathematical elements/rectangles in each CMUT cell focus: focal point of the array impulse_response: impulse response of the array no_impulse_response_samples: number of samples in the impulse response excitation_left: excitation signal of the left part of the cell excitation_right: excitation signal of the right part of the cell no_excitaion_samples: number of samples in the excitation apodization: apodization values for all elements asymmetry_vector: the asymmetry factor (0-1) of each CMUT cell mode_factor_dc: DC displacement factor mode_factor_ac: AC displacement factor *************************************************************** */ aperture *xdc_cmut_array_ring_quarter(int no_ele , point *ele_centers , float width , float height , int no_cmut_cells , float cmut_radius , float *cmut_defl_0 , float *cmut_defl_1 , float dx , point *cmut_centers , int no_sub_cmut , point focus , signal *impulse_response , int no_impulse_response_samples , float *excitation_left , float *excitation_right , int no_excitaion_samples , float apodization , int *asymmetry_vector , float mode_factor_dc , float mode_factor_ac); 184 /* *************************************************************** @function name define_cmut_element_by_quarter @description Determine the corner positions of the rectangular mathematical elements that make up each quarter of a CMUT cell @return value list of mathematical elements/rectangles @parameters xc: x coordinate of the CMUT cell center yc: y coordinate of the CMUT cell center radius: radius of the CMUT cell defl_0: CMUT deflection profile of the symmetric mode defl_1: CMUT deflection profile of the symmetric mode quarter_index: index of the quarter (0-3) asymmetry: asymmetry factor of the cell (0-1) dx: lateral sampling for the deflection profile ele_size: size of the mathematical element/rectangle mode_factor_dc: DC displacement factor mode_factor_ac: AC displacement factor tilt_factor: asymmetry factor reserved for physical focusing/steering *************************************************************** */ rectangles *define_cmut_element_by_quarter(float xc , float yc , float radius , float *defl_0 , float *defl_1 , int quarter_index , int asymmetry , float dx, float ele_size , float mode_factor_dc , float mode_factor_ac , float tilt_factor); 185 B.2 Signal Processing Procedure to Obtain the Average and Differential Signals of the CMUTs In order to obtain the average (regular) and differential received signals for the CMUTs, each CMUT cell is logically divided into four quarter units (Fig. B.2(a)). The procedure starts from extracting an intermediate pressure signal P , which is a convolution of the transmit electrical excitation signal, the symmetric electromechanical impulse response in transmit (IRsym), the amplitude of the acoustic target (Atar), and the transmit/receive Spatial Impulse Response (SIPtx and SIPrx) [51]. Then the average and differ- ential pressure signal Pavg and Pdiff are calculated in X and Y directions, and then convolved with the symmetric and asymmetric impulse responses (IRsym and IRasym) extracted from FEM simulation. The resulting average and differential received signals, Savg and Sdiff in two dimensions are then synthesized again to produce the received signals at each quarter or half unit (Fig. B.2(b)). The function prototypes for the signal processing procedure of receiving average and differential signals are listed as below. 186 0 2 1 3 X Y (a) Each cell divided into quarter-units for transmit and receive + - Excitation * IRsym* SIPtx *Atar * SIPrx Pavg Pdiff *IRsym (b) Signal processing procedure to get the receiving signals at all quarter units, and average and differential signals in x and y directions *IRasym Savg Sdiff S0+S1, S2+S3 S0+S2, S1+S3 X-direction Y-direction Figure B.2: Illustration of signal processing procedure of receiving average and differential signals. ∗ denotes convolution. /* *************************************************************** @function name calc_scat_multi_cmut_2d_quarter @description Calculate SIP_tx*SIP_rx of 2d quarter based CMUTs , need to convolve with excitation*IR_tx*IR_rx_sym/asym in the Matlab code @return value pressure signal @parameters tx_aperture: transmit array rx_aperture: receive array no_points: number of point targets in the phantom points: coordinates of the point targets amplitudes: amplitudes of the point targets *************************************************************** */ signal ** calc_scat_multi_cmut_2d_quarter(aperture *tx_aperture , aperture *rx_aperture , int no_points , point *points , float *amplitudes); 187 %% Matlab function to do further convolution of excitation*IR_tx*IR_rx_sym/asym and calculation of receiving signals on the four quarters function [v1]= compute_resp_by_quarter(v,excitation , impulse_resp_sym ,impulse_resp_asym , no_ele) % convolve with excitation p1=fconv(excitation , impulse_resp_sym); % convolve with IR_sym and IR_asym p2_sym = fconv(p1,impulse_resp_sym); p2_asym = fconv(p1 , impulse_resp_asym); % obtain receiving signals v1 = []; for i=1: no_ele cell_resp = v(:,(i-1) *4+1:(i-1) *4+4); xy_sym = fconv(sum(cell_resp ,2)/4,p2_sym ’); x_resp = [cell_resp (:,1) + cell_resp (:,2) cell_resp (:,3) + cell_resp (:,4)]; y_resp = [cell_resp (:,1) + cell_resp (:,3) cell_resp (:,2) + cell_resp (:,4)]; x_asym = fconv(( x_resp (:,1)-x_resp (:,2))/4, p2_asym ’); y_asym = fconv(( y_resp (:,1)-y_resp (:,2))/4, p2_asym ’); v1 = [v1 (xy_sym+x_asym+y_asym) (xy_sym+x_asym -y_asym) (xy_sym -x_asym+y_asym) (xy_sym -x_asym -y_asym)]; end 188 %% Matlab example code of constructing the transmit/receive aperture and obtaining differential receiving signals % construct transmit/receive CMUT ring array aperture Th_ring_asym_tx = xdc_ring_cmut_array_quarter (ele_centers , width , height ,cmut_radius , disp_l , disp_r , dx, cmut_centers , no_sub_cmut , focus , impulse_response_sym_tx , excitation , excitation , zeros(1,no_ele_x), 0, 0); Th_ring_asym_rx = xdc_ring_cmut_array_quarter (ele_centers , width , height ,cmut_radius , disp_l , disp_r , dx, cmut_centers , no_sub_cmut , focus , impulse_response_sym , excitation , excitation , zeros(1,no_ele_x), 0, 0); emit_aperture = Th_ring_asym_tx; receive_aperture = Th_ring_asym_rx; % construct a phantom made up of point targets [phantom_positions , phantom_amplitudes] = points_phantom(lateral_dis , z_dis , amplitudes); % calculate receiving signals [v,t]= calc_scat_multi_cmut_2d_quarter(emit_aperture , receive_aperture , phantom_positions , phantom_amplitudes); [v_temp ]= compute_resp_by_quarter(v, excitation , impulse_response_sym ,impulse_response_asym , no_ele); % concatenate differential responses from every other CMUT cell , averaging responses of CMUT cells at the same x position diff_ele = []; for i=[1:2: no_ele /4 no_ele /2+1:2: no_ele /4*3] % calculate differential receiving signal temp1 = v_temp (:,(i-1) *4+1) + v_temp (:,(i-1) *4+2) - (v_temp (:,(i-1) *4+3) + v_temp (:,(i-1) *4+4)); if i <= no_ele /2 j = no_ele/2-i+1; else j = no_ele /2*3-i+1; end temp2 = v_temp (:,(j-1) *4+1) + v_temp (:,(j-1) *4+2) - (v_temp (:,(j-1) *4+3) + v_temp (:,(j-1) *4+4)); temp_dim = min([ length(temp1) length(temp2)]); % averaging signals from CMUTs at same x positions temp = temp1 (1: temp_dim) + temp2 (1: temp_dim); temp = [zeros(round(t*fs/D) ,1); temp (1:D:end)]; if dim == 0 dim = length(temp); 189 elseif length(temp) >= dim temp = temp (1: dim); else temp = [temp; zeros(dim -length(temp) ,1)]; end % concatenate signals diff_ele = [diff_ele; temp]; end 190

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