Diagnostic ultrasound imaging : inside out

1.1 Introduction 1 1.1.1 Early Beginnings 2 1.1.2 Sonar 3 1.2 Echo Ranging of the Body 4 1.3 Ultrasound Portrait Photographers 6 1.4 Ultrasound Cinematographers 12 1.5 Modern Ultrasound Imaging Developments 16 1.6 Enabling Technologies for Ultrasound Imaging 19 1.7 Ultrasound Imaging Safety 20 1.8 Ultrasound and Other Diagnostic Imaging Modalities 22 1.8.1 Imaging Modalities Compared 22 1.8.2 Ultrasound 22 1.8.3 X-rays 24 1.8.4 Computed Tomography Imaging 24 1.8.5 Magnetic Resonance Imaging 25 1.9 Conclusion 26 Bibliography 26 References 27 2.1 Introduction 29 2.2 Fourier Transform 30 2.2.1 Introduction to the Fourier Transform 30 2.2.2 Fourier Transform Relationships 31 2.3 Building Blocks 34 2.3.1 Time and Frequency Building Blocks 34 2.3.2 Space Wave Number Building Block 36 2.4 Central Diagram 43 References 45 3 ACOUSTIC WAVE PROPAGATION 47 3.1 Introduction to Waves 47 3.2 Plane Waves in Liquids and Solids 48 3.2.1 Introduction 48 3.2.2 Wave Equations for Fluids 49 3.2.3 One-Dimensional Wave Hitting a Boundary 52 3.2.4 ABCD Matrices 53 3.2.5 Oblique Waves at a Liquid–Liquid Boundary 57 3.3 Elastic Waves in Solids 59 3.3.1 Types of Waves 59 3.3.2 Equivalent Networks for Waves 64 3.3.3 Waves at a Fluid–Solid Boundary 66 3.4 Conclusion 70 Bibliography 70 References 70 4 ATTENUATION 71 4.1 Losses in Tissues 72 4.1.1 Losses in Exponential Terms and in Decibels 72 4.1.2 Tissue Data 73 4.2 Losses in Both Frequency and Time Domains 75 4.2.1 The Material Transfer Function 75 4.2.2 The Material Impulse Response Function 76 4.3 Tissue Models 77 4.3.1 Introduction 77 4.3.2 Thermoviscous Model 78 4.3.3 Multiple Relaxation Model 79 4.3.4 The Time Causal Model 5.8 Comparison of Piezoelectric Materials 127 5.9 Transducer Advanced Topics 128 Bibligraphy 131 References 132 6 BEAMFORMING 137 6.1 What is Diffraction? 137 6.2 Fresnel Approximation of Spatial Diffraction Integral 140 6.3 Rectangular Aperture 142 6.4 Apodization 148 6.5 Circular Apertures 149 6.5.1 Near and Far Fields for Circular Apertures 149 6.5.2 Universal Relations for Circular Apertures 153 6.6 Focusing 154 6.6.1 Derivation of Focusing Relations 154 6.6.2 Zones for Focusing Transducers 158 6.7 Angular Spectrum of Waves 163 6.8 Diffraction Loss 164 6.9 Limited Diffraction Beams 168 Bibliography 168 References 168 7 ARRAY BEAMFORMING 171 7.1 Why Arrays? 172 7.2 Diffraction in the Time Domain 172 7.3 Circular Radiators in the Time Domain 173 7.4 Arrays 177 7.4.1 The Array Element 178 7.4.2 Pulsed Excitation of an Element 181 7.4.3 Array Sampling and Grating Lobes 182 7.4.4 Element Factors 185 7.4.5 Beam Steering 186 7.4.6 Focusing and Steering 188 7.5 Pulse-Echo Beamforming 190 7.5.1 Introduction 190 7.5.2 Beam-Shaping 192 7.5.3 Pulse-Echo Focusing 194 7.6 Two-Dimensional Arrays 196 7.7 Baffled 199 7.8 General Approaches 203 7.9 Nonideal Array Performance 203