Fourier Theory in Optics and Optical Information Processing (Multidisciplinary and Applied Optics)

Fourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Written by a world renowned author, this book looks to unify the readers understanding of principles of optics, information processing and measurement. This book describes optical imaging systems through a linear system theory. The book also provides an easy understanding of Fourier transform and system theory in optics. It also provides background of optical measurement and signal processing. Finally, the author also provides a systematic approach to learning many signal processing techniques in optics. The book is intended for researchers, industry professionals, and graduate level students in optics and information processing. Fourier analysis is one of the most important concepts when you apply physical ideas to engineering issues. This book provides a comprehensive understanding of Fourier transform and spectral analysis in optics, image processing, and signal processing. Cover 1 Half Title 2 Series Page 3 Title Page 4 Copyright Page 5 Contents 6 Preface 10 Chapter 1: Light and Waves 12 1.1. Waves and the Wave Equation 12 1.2. Plane Wave 14 1.3. Spherical Wave 17 1.4. Complex Representation of Wave 18 1.5. Principle of Superposition 19 1.6. Scalar Wave and Vector Wave 20 Chapter 2: Interference and Diffraction 24 2.1. Interference 24 2.2. Fringe Visibility 26 2.3. Young’s Experiment 27 2.4. Interferometer 29 2.5. Diffraction 29 2.6. Fresnel Diffraction 34 2.7. Fraunhofer Diffraction 36 2.7.1. Rectangular Aperture 38 2.7.2. Circular Aperture 39 2.7.3. Diffraction Grating 40 Chapter 3: Fourier Transform and Convolution 44 3.1. Fourier Series 44 3.2. Optimum Polynomial Approximation 50 3.3. Normalized Orthogonal Polynomials 51 3.4. Fourier Transform 52 3.5. Some Representations of Fourier Transform 53 3.6. Properties of the Fourier Transform 55 3.7. Delta Function 58 3.8. Convolution Integral and Correlation Function 60 3.9. Some Functions and Their Fourier Transforms 63 3.10. Sampling Theory 67 Chapter 4: Linear System 74 4.1. System and Operator 74 4.2. Linear System and Shift-Invariant System 75 4.2.1. Linear System 75 4.2.2. Shift-Invariant System 75 4.2.3. Impulse Response 76 4.3. Frequency Response Function 77 4.4. Eigenfunction and Eigenvalue 78 Chapter 5: Discrete Fourier Transform and Fast Fourier Transform 82 5.1. Discrete Fourier Transform 82 5.2. Window Functions 84 5.3. Principle of Fast Fourier Transform (FFT) 86 5.4. Numerical Calculation Using FFT 89 5.5. Interpolation in DFT 91 5.5.1. Zero Padding 91 5.5.2. Some Other Interpolation Techniques 93 Chapter 6: Fourier Optics 96 6.1. Fresnel Diffraction 96 6.2. Fourier Transform Operation of Lens 97 6.3. Coherent Imaging 100 6.4. Incoherent Imaging 104 6.5. Frequency Response of Optical System 104 6.5.1. Coherent Imaging 104 6.5.2. Incoherent Imaging 105 6.6. Resolving Power 106 6.7. Angular Spectrum Method 107 6.8. Diffraction Based on 3-D Fourier Spectrum 109 Chapter 7: Holography 116 7.1. Conventional Optical Holography 116 7.2. Computer Generated Holography 118 7.2.1. Cell-Oriented CGH 118 7.2.2. Point-Oriented CGH 120 7.2.3. Kinoform 122 7.3. Digital Holography 122 Chapter 8: Optical Computing 126 8.1. Spatial Frequency Filtering 126 8.1.1. Low-Pass and High-Pass Filters 127 8.1.2. Differentiation and Laplacian Filters 128 8.1.3. Phase-Contrast Filter 129 8.1.4. Super Resolution and Apodization 130 8.2. Matched Filter 131 8.3. Optimum Filter for Additive Noise 134 8.4. Optimum Filter for Multiplicative Noise 136 8.5. Spectrum Analyzer 137 8.6. Optical Correlator 139 8.6.1. Space-Integral Type 140 8.6.2. Time-Integral Type 140 8.7. Joint Transform Correlator 141 8.8. Optical Addition and Optical Subtraction 142 8.9. Coordinate Transform 145 8.9.1. Equal Magnification Imaging 146 8.9.2. Logarithmic Coordinate Transform 147 8.10. Mellin Transform 147 8.11. Wavelet Transform 149 8.12. X-Ray Computer Tomography 151 8.12.1. Two-Dimensional Fourier Transform Method 153 8.12.2. Filtered Back Projection Method 153 Chapter 9: Analytic Signal and Hilbert Transform 158 9.1. Complex Representation and Negative Frequency 158 9.2. Analytic Signal 160 9.3. Hilbert Transform 161 Chapter 10: Coherence, Spectroscopy and Fringe Analysis 166 10.1. Coherence 166 10.1.1. Temporal Coherence 168 10.1.2. Spatial Coherence 170 10.2. Fourier Transform Spectroscopy 171 10.3. Phase Shift in Interferometry 174 10.4. Fourier Transform Fringe Analysis 178 10.5. Fringe Analysis by Hilbert Transform 179 Chapter 11: Spatio-Temporal Signal Processing 182 11.1. FemtoSecond Pulse Shaper 182 11.1.1. Function of Grating 182 11.1.2. Diffracted Beam 183 11.2. Spatial Frequency Filtering for Ultra-Short Pulse 185 11.3. Spatio-Temporal Joint Fourier Transform Correlator 187 11.4. Optical Coherence Tomography 190 11.5. Spectral Holography 193 Chapter 12: Wigner Distribution Function 196 12.1. WDF for Spatial Signal 196 12.1.1. Definition and Its Properties 196 12.1.2. WDF in Optical System 198 12.1.2.1. Lens Effect 198 12.1.2.2. Space Propagation 198 12.2. WDF for Spatio-Temporal Signal 199 12.2.1. Extension to Spatio-Temporal Signals 199 12.2.2. Lens Effect in Spatio-Temporal WDF 201 12.2.3. Temporal Phase Modulator (Time Lens) 202 12.2.4. Propagation and Dispersion 202 12.2.5. Diffraction Grating 203 12.2.6. Matrix Representation of WDF Transformation 204 12.2.6.1. Lens 204 12.2.6.2. Temporal Phase Modulation (Time Lens) 204 12.2.6.3. Propagation and Dispersion 205 12.2.6.4. Grating 205 Chapter 13: Fractional Fourier Transform 208 13.1. Definition of Fractional Fourier Transform 208 13.2. Some Representations of Fractional Fourier Transform 208 13.3. Applications to Optical Computing 212 13.3.1. Wiener Filtering 212 13.3.2. Correlator and Matched Filter 213 13.3.3. Joint Fractional Fourier Transform Correlator 215 Appendix A: Numerical Calculation of Discrete Fresnel Diffraction 222 Appendix B: Numerical Calculation of Fresnel Hologram 226 Solutions to Selected Problems 230 Index 246 Fourier,optics;,Coherence;,fringe,analysis,and,super,resolution;,optical,computing;,optical,imaging;,Information,processing;,Spectrscopy;,Fourier,transform Fourier optics,Coherence,fringe analysis and super resolution,optical computing,optical imaging,Information processing,Spectrscopy,Fourier transform