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Spie Press Book

Numerical Simulation of Optical Wave Propagation with Examples in MATLAB
Author(s): Jason D. Schmidt
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Book Description

Wave-optics simulation is an immensely useful tool for many applications. The simulation techniques in this book are directly applicable to atmospheric imaging, astronomy, adaptive optics, free-space optical communications, and LADAR. In addition, many of the basic techniques are applicable to integrated optics and nonlinear, anisotropic, and optically active media.

Numerical Simulation of Optical Wave Propagation is solely dedicated to wave-optics simulations. The book discusses digital Fourier transforms (FT), FT-based operations, multiple methods of wave-optics simulations, sampling requirements, and simulations in atmospheric turbulence.

This book will benefit optical scientists and engineers at all levels as a guide for FT-based data analysis, imaging system analysis, and wave-optics simulations. Professors can use this book to augment their Fourier optics courses and for independent studies with students. Problem sets are given at the end of each chapter. Students will learn principles and techniques from this book that can be utilized throughout their careers in optics. All readers will also benefit from the use of the MATLAB® scripting language and the code provided for the basic tools and examples used throughout the book.


Book Details

Date Published: 21 July 2010
Pages: 212
ISBN: 9780819483263
Volume: PM199

Table of Contents
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1 Foundations of Scalar Diffraction Theory
1.1 Basics of Classical Electrodynamics
    1.1.1 Sources of electric and magnetic fields
    1.1.2 Electric and magnetic fields
1.2 Simple Traveling Wave Solutions to Maxwell's Equations
    1.2.1 Obtaining a wave equation
    1.2.2 Simple traveling-wave fields
1.3 Scalar Diffraction Theory
1.4 Problems
2 Digital Fourier Transforms
2.1 Basics of Digital Fourier Transforms
    2.1.1 Fourier transforms: from analytic to numerical
    2.1.2 Inverse Fourier transforms: from analytic to numerical
    2.1.3 Performing discrete Fourier transforms in software
2.2 Sampling Pure-Frequency Functions
2.3 Discrete vs Continuous Fourier Transforms
2.4 Alleviating Effects of Discretization
2.5 Three Case Studies in Transforming Signals
    2.5.1 Sinc signals
    2.5.2 Gaussian signals
    2.5.3 Gaussian signals with quadratic phase
2.6 Two-Dimensional Discrete Fourier Transforms
2.7 Problems
3 Simple Computations Using Fourier Transforms
3.1 Convolution
3.2 Correlation
3.3 Structure Functions
3.4 Derivatives
3.5 Problems
4 Fraunhofer Diffraction and Lenses
4.1 Fraunhofer Diffraction
4.2 Fourier-Transforming Properties of Lenses
    4.2.1 Object against the lens
    4.2.2 Object before the lens
    4.2.3 Object behind the lens
4.3 Problems
5 Imaging Systems and Aberrations
5.1 Aberrations
    5.1.1 Seidel aberrations
    5.1.2 Zernike circle polynomials Decomposition and mode removal RMS wavefront aberration
5.2 Impulse Response and Transfer Function of Imaging Systems
    5.2.1 Coherent imaging
    5.2.2 Incoherent imaging
    5.2.3 Strehl ratio
5.3 Problems
6 Fresnel Diffraction in Vacuum
6.1 Different Forms of the Fresnel Diffraction Integral
6.2 Operator Notation
6.3 Fresnel-Integral Computation
    6.3.1 One-step propagation
    6.3.2 Two-step propagation
6.4 Angular-Spectrum Propagation
6.5 Simple Optical Systems
6.6 Point Sources
6.7 Problems
7 Sampling Requirements for Fresnel Diffraction
7.1 Imposing a Band Limit
7.2 Propagation Geometry
7.3 Validity of Propagation Methods
    7.3.1 Fresnel-integral propagation One step, fixed observation-plane grid spacing Avoiding aliasing
    7.3.2 Angular-spectrum propagation
    7.3.3 General guidelines
7.4 Problems
8 Relaxed Sampling Constraints with Partial Propagations
8.1 Absorbing Boundaries
8.2 Two Partial Propagations
8.3 Arbitrary Number of Partial Propagations
8.4 Sampling for Multiple Partial Propagations
8.5 Problems
9 Propagation Through Atmospheric Turbulence
9.1 Split-Step Beam Propagation Method
9.2 Refractive Properties of Atmospheric Turbulence
    9.2.1 Kolmogorov Theory of turbulence
    9.2.2 Optical propagation through turbulence
    9.2.3 Optical parameters of the atmosphere
    9.2.4 Layered atmosphere model
    9.2.5 Theory
9.3 Monte-Carlo Phase Screens
9.4 Sampling Constraints
9.5 Executing Properly Sampled Simulation
    9.5.1 Determine propagation geometry and turbulence conditions
    9.5.2 Analyze the sampling constraints
    9.5.3 Perform a vacuum simulation
    9.5.4 Perform the turbulent simulations
    9.5.5 Verify the output
9.6 Conclusion
9.7 Problems
Appendix A Function Definitions
Appendix B MATLAB Code Listings

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