ACOUSTICAL IMAGING -- Contents -- About the Author -- Foreword -- 1 Introduction -- References -- 2 Physics of Acoustics and Acoustical Imaging -- 2.1 Introduction -- 2.2 Sound Propagation in Solids -- 2.2.1 Derivation of Linear Wave Equation of Motion and its Solutions -- 2.2.2 Symmetries in Linear Acoustic Wave Equations and the New Stress Field Equation -- 2.3 Use of Gauge Potential Theory to Solve Acoustic Wave Equations -- 2.4 Propagation of Finite Wave Amplitude Sound Wave in Solids -- 2.4.1 Higher-Order Elasticity Theory -- 2.4.2 Nonlinear Effects -- 2.4.3 Derivation of the Nonlinear Acoustic Equation of Motion -- 2.4.4 Solutions of the Higher-Order Acoustics Equations of Motion -- 2.5 Nonlinear Effects Due to Energy Absorption -- 2.5.1 Energy Absorption Due to Thermal Conductivity -- 2.5.2 Energy Absorption Due to Dislocation -- 2.6 Gauge Theory Formulation of Sound Propagation in Solids -- 2.6.1 Introduction of a Covariant Derivative in the Infinitesimal Amplitude Sound Wave Equation -- 2.6.2 Introduction of Covariant Derivative to the Large Amplitude Sound Wave Equation -- References -- 3 Signal Processing -- 3.1 Mathematical Tools in Signal Processing and Image Processing -- 3.1.1 Matrix Theory -- 3.1.2 Some Properties of Matrices -- 3.1.3 Fourier Transformation -- 3.1.4 The Z-Transform -- 3.2 Image Enhancement -- 3.2.1 Spatial Low-Pass, High-Pass and Band-Pass Filtering -- 3.2.2 Magnification and Interpolation (Zooming) -- 3.2.3 Replication -- 3.2.4 Linear Interpolation -- 3.2.5 Transform Operation -- 3.3 Image Sampling and Quantization -- 3.3.1 Sampling versus Replication -- 3.3.2 Reconstruction of the Image from its Samples -- 3.3.3 Nyquist Rate -- 3.3.4 Sampling Theorem -- 3.3.5 Examples of Application of Two-Dimensional Sampling Theory -- 3.3.6 Sampling Theorem for Radom Fields.

3.3.7 Practical Limitation in Sampling and Reconstruction -- 3.3.8 Image Quantization -- 3.4 Stochastic Modelling of Images -- 3.4.1 Autoregressive Models -- 3.4.2 Properties of AR Models -- 3.4.3 Moving Average Model -- 3.5 Beamforming -- 3.5.1 Principles of Beamforming -- 3.5.2 Sonar Beamforming Requirements -- 3.6 Finite-Element Method -- 3.6.1 Introduction -- 3.6.2 Applications -- 3.7 Boundary Element Method -- 3.7.1 Comparison to Other Methods -- References -- 4 Common Methodologies of Acoustical Imaging -- 4.1 Introduction -- 4.2 Tomography -- 4.2.1 The Born Approximation -- 4.2.2 The Rytov Approximation -- 4.2.3 The Fourier Diffraction Theorem -- 4.2.4 Reconstruction and Backpropagation Algorithm -- 4.3 Holography -- 4.3.1 Liquid Surface Method -- 4.4 Pulse-Echo and Transmission Modes -- 4.4.1 C-Scan Method -- 4.4.2 B-Scan Method -- 4.5 Acoustic Microscopy -- References -- 5 Time-Reversal Acoustics and Superresolution -- 5.1 Introduction -- 5.2 Theory of Time-Reversal Acoustics -- 5.2.1 Time-Reversal Acoustics and Superresolution -- 5.3 Application of TR to Medical Ultrasound Imaging -- 5.4 Application of Time-Reversal Acoustics to Ultrasonic Nondestructive Testing -- 5.4.1 Theory of Time-Reversal Acoustics for Liquid-Solid Interface -- 5.4.2 Experimental Implementation of the TRM for Nondestructive Testing Works -- 5.4.3 Incoherent Summation -- 5.4.4 Time Record of Signals Coming from a Speckle Noise Zone -- 5.4.5 The Iterative Technique -- 5.4.6 Iterative Process for a Zone Containing a Hard-Alpha -- 5.4.7 Iterative Process as a Pure Speckle Noise Zone -- 5.5 Application of TRA to Landmine or Buried Object Detection -- 5.5.1 Introduction -- 5.5.2 Theory -- 5.5.3 Experimental Procedure -- 5.5.4 Experimental Setup -- 5.5.5 Wiener Filter -- 5.5.6 Experimental Results -- 5.6 Application of Time-Reversal Acoustics to Underwater Acoustics.

References -- 6 Nonlinear Acoustical Imaging -- 6.1 Application of Chaos Theory to Acoustical Imaging -- 6.1.1 Nonlinear Problem Encountered in Diffraction Tomography -- 6.1.2 Definition and History of Chaos -- 6.1.3 Definition of Fractal -- 6.1.4 The Link between Chaos and Fractals -- 6.1.5 The Fractal Nature of Breast Cancer -- 6.1.6 Types of Fractals -- 6.1.7 Fractal Approximation -- 6.1.8 Diffusion Limited Aggregation -- 6.1.9 Growth Site Probability Distribution -- 6.1.10 Approximating the Scattered Field Using GSPD -- 6.1.11 Discrete Helmholtz Wave Equation -- 6.1.12 Kaczmarz Algorithm -- 6.1.13 Hounsfield Method -- 6.1.14 Applying GSPD into Kaczmarz Algorithm -- 6.1.15 Fractal Algorithm Using Frequency Domain Interpolation -- 6.1.16 Derivation of Fractal Algorithm's Final Equation Using Frequency Domain Interpolation -- 6.1.17 Simulation Results -- 6.1.18 Comparison between Born and Fractal Approximations -- 6.2 Nonclassical Nonlinear Acoustical Imaging -- 6.2.1 Introduction -- 6.2.2 Mechanisms of Harmonic Generation via CAN -- 6.2.3 Nonlinear Resonance Modes -- 6.2.4 Experimental Studies on Nonclassical CAN Spectra -- 6.2.5 CAN Application for Nonlinear Acoustical Imaging and NDE -- 6.2.6 Conclusion -- 6.3 Modulation Method of Nonlinear Acoustical Imaging -- 6.3.1 Introduction -- 6.3.2 Principles of Modulation Acoustic Method -- 6.3.3 The Modulation Mode Method of Crack Location -- 6.3.4 Experimental Procedure of the Modulation Method for NDT -- 6.3.5 Experimental Procedures for the Modulation Mode System -- 6.3.6 Conclusions -- 6.4 Harmonic Imaging -- References -- 7 High-Frequencies Acoustical Imaging -- 7.1 Introduction -- 7.2 Transducers -- 7.3 Electronic Circuitry -- 7.4 Software -- 7.5 Applications of High-Frequencies In Vivo Ultrasound Imaging System -- 7.6 System of 150 MHz Ultrasound Imaging of the Skin and the Eye.

7.7 Signal Processing for the 150 MHz System -- 7.8 Electronic Circuits of Acoustical Microscope -- 7.8.1 Gated Signal and Its Use in Acoustical Microscope -- 7.8.2 Quasi-Monochromatic Systems -- 7.8.3 Very Short Pulse Technique -- References -- 8 Statistical Treatment of Acoustical Imaging -- 8.1 Introduction -- 8.2 Scattering by Inhomogeneities -- 8.3 Study of the Statistical Properties of the Wavefield -- 8.3.1 Fresnal Approximation or Near-Field Approximation -- 8.3.2 Farfield Imaging Condition (Fraunhofer Approximation) -- 8.3.3 Correlation of Fluctuations -- 8.3.4 Quasi-static Condition -- 8.3.5 The Time Autocorrelation of the Amplitude Fluctuations -- 8.3.6 Experimental Verification -- 8.3.7 Application of Fluctuation Theory to the Diffraction Image of a Focusing System -- 8.3.8 Conclusion -- 8.4 Continuum Medium Approach of Statistical Treatment -- 8.4.1 Introduction -- 8.4.2 Parabolic Equation Theory -- 8.4.3 Assumption for the Refractive Index Fluctuation -- 8.4.4 Equation for the Average Field and General Solution -- References -- 9 Nondestructive Testing -- 9.1 Defects Characterization -- 9.2 Automated Ultrasonic Testing -- 9.2.1 Introduction -- 9.2.2 Testing Procedure -- 9.2.3 Example of an AUT System -- 9.2.4 Signal Processing and Automatic Defects and Features Clarification in AUT -- 9.3 Guided Waves Used in Acoustical Imaging for NDT -- 9.4 Ultrasonic Technologies for Stress Measurement and Material Studies -- 9.4.1 Introduction -- 9.4.2 Internal Stress Measurements -- 9.4.3 V(z) Curve Technique in the Characterization of Kissing Bond -- 9.5 Dry Contact or Noncontact Transducers -- 9.5.1 Defect Depth, Sizing and Characterization -- 9.5.2 Pitch/Catch Swept Method -- 9.5.3 Pitch/Catch Impulse Method -- 9.5.4 MIA Test Method -- 9.6 Phased Array Transducers -- 9.6.1 Introduction -- 9.6.2 Meaning of Phased Array.

9.6.3 Principle of Phased Array Ultrasonic Technology -- 9.6.4 Focal Laws -- 9.6.5 Basic Scanning and Imaging -- 9.6.6 Advantages of Phased Array Testing as Compared with Conventional UT -- References -- 10 Medical Ultrasound Imaging -- 10.1 Introduction -- 10.2 Physical Principles of Sound Propagation -- 10.2.1 Propagation of Sound Wave in Solids -- 10.2.2 Contrast -- 10.3 Imaging Modes -- 10.3.1 B-Scan -- 10.3.2 C-Scan -- 10.4 B-scan Instrumentation -- 10.4.1 Manual Systems -- 10.4.2 Real-Time System -- 10.4.3 Mechanical Scan -- 10.4.4 Electronic Scan -- 10.5 C-scan Instrumentation -- 10.5.1 Sokolov Tube -- 10.5.2 Ultrasonic Holography -- 10.6 Tissue Harmonic Imaging -- 10.6.1 Introduction -- 10.6.2 Principles of Tissue Harmonic Imaging -- 10.6.3 Image Formation in Tissue Harmonics -- 10.6.4 Tissue Harmonic Image Characteristics -- 10.6.5 Some Examples of Commercial Systems -- 10.7 Elasticity Imaging -- 10.7.1 Introduction -- 10.7.2 Comparison of Human Palpation and Elasticity Imaging -- 10.7.3 Choice of Force Stimulus and Imaging Modality -- 10.7.4 Physics of Elasticity Imaging -- 10.7.5 Image Formation Algorithm -- 10.7.6 Some Examples of Commercial Systems -- 10.8 Colour Doppler Imaging -- 10.8.1 Doppler Ultrasound -- 10.8.2 Pulsed (Gated) and Spectral Doppler -- 10.8.3 Quantitative Doppler Techniques -- 10.8.4 Velocity Measurements -- 10.8.5 Spectral Doppler Waveform Measurements -- 10.8.6 Volume Blood Flow Measurements -- 10.8.7 Colour Doppler -- 10.8.8 Newer Techniques -- 10.9 Contrast-Enhanced Ultrasound -- 10.9.1 Introduction -- 10.9.2 Bubble Echocardiogram -- 10.9.3 Microbubble Contrast Agents -- 10.9.4 How it Works -- 10.9.5 Applications -- 10.10 3D Ultrasound Medical Imaging -- 10.10.1 Introduction -- 10.10.2 Elective 3D Ultrasound -- 10.10.3 Risk Reduction of 3D Ultrasounds -- 10.10.4 Future Developments -- 10.10.5 Regional Anaesthesia.

10.11 Development Trends.