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Computational Fourier Optics: A MATLAB Tutorial
Author(s): David G. Voelz
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Book Description

Computational Fourier Optics is a text that shows the reader in a tutorial form how to implement Fourier optical theory and analytic methods on the computer. A primary objective is to give students of Fourier optics the capability of programming their own basic wave optic beam propagations and imaging simulations. The book will also be of interest to professional engineers and physicists learning Fourier optics simulation techniques-either as a self-study text or a text for a short course. For more advanced study, the latter chapters and appendices provide methods and examples for modeling beams and pupil functions with more complicated structure, aberrations, and partial coherence.

For a student in a course on Fourier optics, this book is a concise, accessible, and practical companion to any of several excellent textbooks on Fourier optical theory.

Book Details

Date Published: 4 January 2011
Pages: 250
ISBN: 9780819482044
Volume: TT89

Table of Contents
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Author's Book Page
Analytic Fourier Theory Review
1.1 A Little History and Purpose
1.2 The Realm of Computational Fourier Optics
1.3 Fourier Transform Definitions and Existence
1.4 Theorems and Separability
1.5 Basic Functions and Transforms
1.6 Linear and Space-Invariant Systems
1.7 Exercises
1.8 References
Sampled Functions and the Discrete Fourier Transform
2.1 Sampling and the Shannon–Nyquist Sampling Theorem
2.2 Effective Bandwidth
2.3 Discrete Fourier Transform from the Continuous Transform
2.4 Coordinates, Indexing, Centering, and Shifting
2.5 Periodic Extension
2.6 Periodic Convolution
2.7 Exercises
2.8 References
MATLAB Programming of Functions, Vectors, Arrays, and Fourier Transforms
3.1 Defining Functions
3.2 Creating Vectors
3.3 Shift for FFT
3.4 Computing the FFT and Displaying Results
3.5 Comparison with Analytic Results
3.6 Convolution Example
3.7 Two Dimensions
3.8 Miscellaneous Hints
3.9 Exercises
Scalar Diffraction and Propagation Solutions
4.1 Scalar Diffraction
4.2 Monochromatic Fields and Irradiance
4.3 Optical Path Length and Field Phase Representation
4.4 Analytic Diffraction Solutions
    4.4.1 Rayleigh–Sommerfeld solution I
    4.4.2 Fresnel approximation
    4.4.3 Fraunhofer approximation
4.5 Fraunhofer Diffraction Example
4.6 Exercises
4.7 References
Propagation Simulation
5.1 Fresnel Transfer Function (TF) Propagator
5.2 Fresnel Impulse Response (IR) Propagator
5.3 Square Beam Example
5.4 Fresnel Propagation Sampling
    5.4.1 Square beam example results and artifacts
    5.4.2 Sampling regimes and criteria
    5.4.3 Criteria applied to square beam example
    5.4.4 Propagator accuracy
    5.4.5 Sampling decisions
    5.4.6 Split-step simulation, windowing, and expanding grids
5.5 Fraunhofer Propagation
5.6 Coding Efficiency
5.7 Exercises
5.8 References
Transmittance Functions, Lenses, and Gratings
6.1 Tilt
6.2 Focus
6.3 Lens
6.4 Gratings and Periodic Functions
    6.4.1 Cosine magnitude example
    6.4.2 Square-wave magnitude example
    6.4.3 One-dimensional model
    6.4.4 Periodic model
6.5 Exercises
6.6 References
Imaging and Diffraction-Limited Imaging Simulation
7.1 Geometrical Imaging Concepts
7.2 Coherent Imaging
    7.2.1 Coherent imaging theory
    7.2.2 Coherent transfer function examples
    7.2.3 Diffraction-limited incoherent imaging simulation
    7.2.4 Rough object
7.3 Incoherent Imaging
    7.3.1 Incoherent imaging theory
    7.3.2 Optical transfer function examples
    7.3.3 Diffraction-limited incoherent imaging simulation
7.4 Exercises
7.5 Problems
Wavefront Aberrations
8.1 Wavefront Optical Path Difference
8.2 Seidel Polynomials
    8.2.1 Definition and primary aberrations
    8.2.2 MATLAB function
8.3 Pupil and Transfer Functions
    8.3.1 Pupil function
    8.3.2 Imaging transfer functions
8.4 Image Quality
    8.4.1 Point spread function
    8.4.2 Modulation transfer function
8.5 Lens Example—PSF and MTF
8.6 Wavefront Sampling
8.7 Superposition Imaging Example
    8.7.1 Image plane PSF map
    8.7.2 Image simulation
    8.7.3 Practical image simulation
8.8 Exercises
8.9 References
Partial Coherence Simulation
9.1 Partial Temporal Coherence
    9.1.1 Quasi-monochromatic light
    9.1.2 Partial temporal coherence simulation approach
    9.1.3 Partial temporal coherence example
9.2 Partial Spatial Coherence
    9.2.1 Stochastic transmission screen
    9.2.2 Partial spatial coherence simulation approach
    9.2.3 Partial spatial coherence example
9.3 Reducibility, Number of Spectral Components, and Phase Screens
9.4 Exercises
9.5 References
Appendix A Fresnel Propagator Chirp Sampling
Appendix B Fresnel Two-Step Propagator
Appendix C MATLAB Function Listings
Appendix D Exercise Answers and Results

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