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# Introduction to Fourier Optics

## Fourth EditionJoseph W. Goodman

©2017ISBN:9781319153045

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ISBN:9781319119164

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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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Learn More## 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