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.
Author(s): Toyohiko Yatagai
Series: Multidisciplinary and Applied Optics
Publisher: CRC Press
Year: 2022
Language: English
Pages: 247
City: Boca Raton
Cover
Half Title
Series Page
Title Page
Copyright Page
Contents
Preface
Chapter 1: Light and Waves
1.1. Waves and the Wave Equation
1.2. Plane Wave
1.3. Spherical Wave
1.4. Complex Representation of Wave
1.5. Principle of Superposition
1.6. Scalar Wave and Vector Wave
Chapter 2: Interference and Diffraction
2.1. Interference
2.2. Fringe Visibility
2.3. Young’s Experiment
2.4. Interferometer
2.5. Diffraction
2.6. Fresnel Diffraction
2.7. Fraunhofer Diffraction
2.7.1. Rectangular Aperture
2.7.2. Circular Aperture
2.7.3. Diffraction Grating
Chapter 3: Fourier Transform and Convolution
3.1. Fourier Series
3.2. Optimum Polynomial Approximation
3.3. Normalized Orthogonal Polynomials
3.4. Fourier Transform
3.5. Some Representations of Fourier Transform
3.6. Properties of the Fourier Transform
3.7. Delta Function
3.8. Convolution Integral and Correlation Function
3.9. Some Functions and Their Fourier Transforms
3.10. Sampling Theory
Chapter 4: Linear System
4.1. System and Operator
4.2. Linear System and Shift-Invariant System
4.2.1. Linear System
4.2.2. Shift-Invariant System
4.2.3. Impulse Response
4.3. Frequency Response Function
4.4. Eigenfunction and Eigenvalue
Chapter 5: Discrete Fourier Transform and Fast Fourier Transform
5.1. Discrete Fourier Transform
5.2. Window Functions
5.3. Principle of Fast Fourier Transform (FFT)
5.4. Numerical Calculation Using FFT
5.5. Interpolation in DFT
5.5.1. Zero Padding
5.5.2. Some Other Interpolation Techniques
Chapter 6: Fourier Optics
6.1. Fresnel Diffraction
6.2. Fourier Transform Operation of Lens
6.3. Coherent Imaging
6.4. Incoherent Imaging
6.5. Frequency Response of Optical System
6.5.1. Coherent Imaging
6.5.2. Incoherent Imaging
6.6. Resolving Power
6.7. Angular Spectrum Method
6.8. Diffraction Based on 3-D Fourier Spectrum
Chapter 7: Holography
7.1. Conventional Optical Holography
7.2. Computer Generated Holography
7.2.1. Cell-Oriented CGH
7.2.2. Point-Oriented CGH
7.2.3. Kinoform
7.3. Digital Holography
Chapter 8: Optical Computing
8.1. Spatial Frequency Filtering
8.1.1. Low-Pass and High-Pass Filters
8.1.2. Differentiation and Laplacian Filters
8.1.3. Phase-Contrast Filter
8.1.4. Super Resolution and Apodization
8.2. Matched Filter
8.3. Optimum Filter for Additive Noise
8.4. Optimum Filter for Multiplicative Noise
8.5. Spectrum Analyzer
8.6. Optical Correlator
8.6.1. Space-Integral Type
8.6.2. Time-Integral Type
8.7. Joint Transform Correlator
8.8. Optical Addition and Optical Subtraction
8.9. Coordinate Transform
8.9.1. Equal Magnification Imaging
8.9.2. Logarithmic Coordinate Transform
8.10. Mellin Transform
8.11. Wavelet Transform
8.12. X-Ray Computer Tomography
8.12.1. Two-Dimensional Fourier Transform Method
8.12.2. Filtered Back Projection Method
Chapter 9: Analytic Signal and Hilbert Transform
9.1. Complex Representation and Negative Frequency
9.2. Analytic Signal
9.3. Hilbert Transform
Chapter 10: Coherence, Spectroscopy and Fringe Analysis
10.1. Coherence
10.1.1. Temporal Coherence
10.1.2. Spatial Coherence
10.2. Fourier Transform Spectroscopy
10.3. Phase Shift in Interferometry
10.4. Fourier Transform Fringe Analysis
10.5. Fringe Analysis by Hilbert Transform
Chapter 11: Spatio-Temporal Signal Processing
11.1. FemtoSecond Pulse Shaper
11.1.1. Function of Grating
11.1.2. Diffracted Beam
11.2. Spatial Frequency Filtering for Ultra-Short Pulse
11.3. Spatio-Temporal Joint Fourier Transform Correlator
11.4. Optical Coherence Tomography
11.5. Spectral Holography
Chapter 12: Wigner Distribution Function
12.1. WDF for Spatial Signal
12.1.1. Definition and Its Properties
12.1.2. WDF in Optical System
12.1.2.1. Lens Effect
12.1.2.2. Space Propagation
12.2. WDF for Spatio-Temporal Signal
12.2.1. Extension to Spatio-Temporal Signals
12.2.2. Lens Effect in Spatio-Temporal WDF
12.2.3. Temporal Phase Modulator (Time Lens)
12.2.4. Propagation and Dispersion
12.2.5. Diffraction Grating
12.2.6. Matrix Representation of WDF Transformation
12.2.6.1. Lens
12.2.6.2. Temporal Phase Modulation (Time Lens)
12.2.6.3. Propagation and Dispersion
12.2.6.4. Grating
Chapter 13: Fractional Fourier Transform
13.1. Definition of Fractional Fourier Transform
13.2. Some Representations of Fractional Fourier Transform
13.3. Applications to Optical Computing
13.3.1. Wiener Filtering
13.3.2. Correlator and Matched Filter
13.3.3. Joint Fractional Fourier Transform Correlator
Appendix A: Numerical Calculation of Discrete Fresnel Diffraction
Appendix B: Numerical Calculation of Fresnel Hologram
Solutions to Selected Problems
Index
