Introduction to Fourier Optics
Fourth Edition ©2017
Fourier analysis is a ubiquitous tool that has found application to diverse areas of physics and engineering. Goodman focuses on applications in optics, and in particular with applications to diffraction, imaging, optical information processing, holography, and optical communications.
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Fourier analysis is a ubiquitous tool that has found application to diverse areas of physics and engineering. Goodman focuses on applications in optics, and in particular with applications to diffraction, imaging, optical information processing, holography, and optical communications.
Goodman, Introduction to Fourier Optics satisfies the needs of several different types of Physics and Engineering courses. Directed towards both physicists and engineers this text is suitable for audiences focusing on applications of optics. A clear presentation makes this text work well as both a teaching resource and a reference book.
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Table of Contents
1 Introduction
1.1 Optics, Information, and Communication
1.2 The Book
2 Analysis of Two-Dimensional Signals and Systems
2.1 Fourier Analysis in Two Dimensions
2.2 Spatial Frequency and Space-Frequency Localization
2.3 Linear Systems
2.4 Two-Dimensional Sampling Theory
2.5 The Discrete Fourier Transform
2.6 The Projection-Slice Theorem
2.7 Phase Retrieval from Fourier Magnitude
3 Foundations of Scalar Diffraction Theory
3.1 Historical Introduction
3.2 From a Vector to a Scalar Theory
3.3 Some Mathematical Preliminaries
3.4 The Kirchhoff Formulation of Diffraction by a Planar Screen
3.5 The Rayleigh-Sommerfeld Formulation of Diffraction
3.6 Kirchhoff and Rayleigh-Sommerfeld Theories Compared
3.7 Further Discussion of the Huygens-Fresnel Principle
3.8 Generalization to Nonmonochromatic Waves
3.9 Diffraction at Boundaries
3.10 The Angular Spectrum of Plane Waves
4 Fresnel and Fraunhofer Diffraction
4.1 Background
4.2 The Fresnel Approximation
4.3 The Fraunhofer Approximation
4.4 Examples of Fraunhofer Diffraction Patterns
4.5 Examples of Fresnel Diffraction Calculations
4.6 Beam Optics
5 Computational Diffraction and Propagation
5.1 Approaches to Computational Diffraction
5.2 Sampling a Space-Limited Quadratic-Phase Exponential
5.3 The Convolution Approach
5.4 The Fresnel Transform Approach
5.5 The Fresnel Transfer Function Approach
5.6 The Exact Transfer Function Approach
5.7 Comparison of Computational Complexities
5.8 Extension to More Complex Apertures
5.9 Concluding Comments
6 Wave-Optics Analysis of Coherent Optical Systems
6.1 A Thin Lens as a Phase Transformation
6.2 Fourier Transforming Properties of Lenses
6.3 Image Formation: Monochromatic Illumination
6.4 Analysis of Complex Coherent Optical Systems
7 Frequency Analysis of Optical Imaging Systems
7.1 Generalized Treatment of Imaging Systems
7.2 Frequency Response for Diffraction-Limited Coherent Imaging
7.3 Frequency Response for Diffraction-Limited Incoherent Imaging
7.4 Aberrations and Their Effects on Frequency Response
7.5 Comparison of Coherent and Incoherent Imaging
7.6 Confocal Microscopy
8 Point-Spread Function and Transfer Function Engineering
8.1 Cubic Phase Mask for Increased Depth of Field
8.2 Rotating Point-Spread Functions for Depth Resolution
8.3 Point-Spread Function Engineering for Exoplanet Discovery
8.4 Resolution beyond the Classical Diffraction Limit
8.5 Light Field Photography
9 Wavefront Modulation
9.1 Wavefront Modulation with Photographic Film
9.2 Wavefront Modulation with Diffractive Optical Elements
9.3 Liquid Crystal Spatial Light Modulators
9.4 Deformable Mirror Spatial Light Modulators
9.5 Acousto-Optic Spatial Light Modulators
9.6 Other Methods of Wavefront Modulation
10 Analog Optical Information Processing
10.1 Historical Background
10.2 Coherent Optical Information Processing Systems
10.3 The VanderLugt Filter
10.4 The Joint Transform Correlator
10.5 Application to Character Recognition
10.6 Image Restoration
10.7 Acousto-Optic Signal Processing Systems
10.8 Discrete Analog Optical Processors
11 Holography
11.1 Historical Introduction
11.2 The Wavefront Reconstruction Problem
11.3 The Gabor Hologram
11.4 The Leith-Upatnieks Hologram
11.5 Image Locations and Magnification
11.6 Some Different Types of Holograms
11.7 Thick Holograms
11.8 Recording Materials
11.9 Computer-Generated Holograms
11.10 Degradations of Holographic Images
11.11 Digital Holography
11.12 Holography with Spatially Incoherent Light
11.13 Applications of Holography
12 Fourier Optics in Optical Communications
12.1 Introduction
12.2 Fiber Bragg Gratings
12.3 Ultrashort Pulse Shaping and Processing
12.4 Spectral Holography
12.5 Arrayed Waveguide Gratings
Appendix A Delta Functions and Fourier Transform Theorems
A.1 Delta Functions
A.2 Derivation of Fourier Transform Theorems
Appendix B Introduction to Paraxial Geometrical Optics
B.1 The Domain of Geometrical Optics
B.2 Refraction, Snell’s Law, and the Paraxial Approximation
B.3 The Ray-Transfer Matrix
B.4 Conjugate Planes, Focal Planes, and Principal Planes
B.5 Entrance and Exit Pupils
Appendix C Polarization and Jones Matrices
C.1 Definition of the Jones Matrix
C.2 Examples of Simple Polarization Transformations
C.3 Reflective Polarization Devices
Appendix D The Grating Equation
Bibliography
Index
Authors
Joseph W. Goodman
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