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Spie Press Book

Analog and Digital Holography with MATLAB
Author(s): Georges T. Nehmetallah; Rola Aylo; Logan Williams
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Book Description

Holography is the only truly three-dimensional imaging method available, and MATLAB has become the programming language of choice for engineering and physics students. Whereas most books solely address the theory behind these 3D imaging techniques, this monograph concentrates on the exact code needed to perform complex mathematical and physical operations. The text and the included CD-ROM spare students and researchers from the tedium of programming complex equations so that they can focus on their experiments instead. Topics include a brief introduction to the history, types, and materials of holography; the basic principles of analog and digital holography; a detailed explanation of famous fringe-deciphering techniques for holographic interferometry; holographic and non-holographic 3D display technologies; and cutting-edge concepts such as compressive, coherence, nonlinear, and polarization holography.

Book Details

Date Published: 6 August 2015
Pages: 528
ISBN: 9781628416923
Volume: PM256

Table of Contents
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Table of Contents


List of Acronyms and Abbreviations

1 Introduction and Preliminaries
1.1 History of Holography
     1.1.1 Introductionn
     1.1.2 Types of holograms
     1.1.3 Holographic recording media
1.2 Scalar Theory of Diffraction
     1.2.1 Maxwell's equations
     1.2.2 Spatial frequency transfer function and Fresnel diffraction
     1.2.3 Fraunhofer diffraction
     1.2.4 Fourier transform property of an ideal lens
     1.2.5 Gaussian beam optics
     1.2.6 q-transformation of Gaussian beams
     1.2.7 Focusing a Gaussian beam
1.3 Example 1: MATLAB Code for Calculating Diffraction with the Fast Fourier Transform
1.4 Example 2: MATLAB Code for Calculating Forward and Backward Gaussian Beam Propagation
1.5 Example 3: MATLAB Code for Gaussian Beam Propagation through a Lens
1.6 Generalized Diffraction Example via the Fresnel Transform

2 Analog Holography, Holographic Interferometry, and Phase-Shifting Holographic Interferometry
2.1 Fourier Optics Theory
2.2 Analog Holography Theory and Setups
2.3 Analog Holographic Interferometry Theory and Setups
2.4 Phase Unwrapping in 1D and 2D
2.5 Application of Phase Unwrapping in Holographic Interferometry
2.6 Phase-Shifting Holography through Dynamic Holography and Self-Diffraction

3 Fringe Deciphering Techniques Applied to Analog Holographic Interferometry
3.1 Introduction
3.2 Interferogram Processing Using Frequency Techniques
3.3 Interferogram Processing Using Fringe Orientation and Fringe Direction
     3.3.1 Definition of fringe orientation and fringe direction
     3.3.2 Orientation computation methods
     3.3.3 Phase unwrapping and fringe direction computation using regularized phase tracking
3.4 Phase Demodulation Using the Hilbert Transform Technique
3.5 Fringe Skeletonization and Normalization
     3.5.1 Reconstruction formula for equiangular sampling
     3.5.2 Reconstruction formula for equal-spaced sampling
     3.5.3 Fan-beam to parallel-beam rebinning
3.6 Contrast Enhancement of Fringe Patterns
3.7 Phase Unwrapping: Interferogram Analysis
     3.7.1 Path-dependent techniques
     3.7.2 Path-independent techniques

4 Digital Holography and Digital Holographic Microscopy
4.1 Basics of Digital Holography
4.2 Digital Holography Reconstruction Algorithms
     4.2.1 Numerical reconstruction by the discrete Fresnel transformation
     4.2.2 Numerical reconstruction by the convolution approach
     4.2.3 Numerical reconstruction by the angular spectrum approach
4.3 DC Suppression during Reconstruction
4.4 Digital Holography Example
4.5 Digital Holograms of Large Objects
4.6 Digital Holographic Microscopy
4.7 Digital Holographic Microscopy Example
4.8 Optimization of the Fresnel Transform
4.9 General Functions for Digital Holography Using MATLAB

5 Digital Holographic Interferometry and Phase-Shifting Digital Holography
5.1 Digital Holographic Interferometry: Basic Principles
5.2 Two-Illumination-Point Technique
5.3 3D Stress and Strain Sensors from Three Digital Hologram Recordings
5.4 Phase-Shifting Digital Holography
5.5 Techniques to Perform Phase-Shifting Digital Holography
5.6 One-Shot Phase-Shifting Digital Holography Using Wave Plates
5.7 General Functions for Digital Holographic Interferometry and Phase-Shifting Digital Holography Using MATLAB

6 Digital Holographic Tomography
6.1 Introduction
6.2 Single-Shot Optical Tomography Using the Multiplicative Technique (SHOT-MT)
6.3 Single-Shot Optical Tomography Using the Radon Transform Technique
6.4 Recording Considerations for Holographic Tomography
     6.4.1 Numerical reconstruction by the discrete Fresnel transformation
     6.4.2 Multiple-angle, multiple-exposure methods
     6.4.3 Microscopic tomography methods
     6.4.4 Angular sampling considerations
6.5 Examples of Digital Holographic Tomography Using MATLAB

7 Multiwavelength Digital Holography
7.1 Holographic Contouring
7.2 Principle of Multiwavelength Digital Holography
7.3 Hierarchical Phase Unwrapping
7.4 Multiwavelength Digital Holography
7.5 Multiwavelength Digital Holography with Spatial Heterodyning
7.6 Multiwavelength Digital Holographic Microscopy
7.7 Multiwavelength Digital Holographic Microscopy with Spatial Heterodyning
7.8 Holographic Volume-Displacement Calculations via Multiwavelength Digital Holography
7.9 Multiwavelength Digital Holography: Image-Type Setup and Results

8 Computer-Generated Holography
8.1 A Brief History
8.2 Fourier Transform Holograms: Detour Method
8.3 Phase-Only CG Hologram
8.4 Gerchberg–Saxton Algorithm for Recording a CG Hologram
8.5 Point-Source Holograms and the Wavefront Recording Plane Method
8.6 A Brief History
     8.6.1 Fourier ping-pong algorithm
     8.6.2 Interference-based algorithms
     8.6.3 Diffraction-specific algorithm
     8.6.4 Binarization algorithms
8.7 CGH-based Display Systems
     8.7.1 Advantages
     8.7.2 Challenges
     8.7.3 Computational loads

9 Compressive Sensing and Compressive Holography
9.1 Compressive Sensing: Background
9.2 Compressive Holography
9.3 Experimental Setups and MATLAB Examples

10 Contemporary Topics in Holography
10.1 Transport-of-Intensity Imaging
10.2 Nonlinear Holography
10.3 Coherence Holography
10.4 Polarization Imaging Using Digital Holography

11 Progress in Stereoscopic, Head-Mounted, Multiview, Depth-Fused, Volumetric, and Holographic 3D Displays
11.1 Introduction to 3D Displays
     11.1.1 Characteristics of an optimal 3D display
     11.1.2 Display-technology depth cues related to the human visual system
11.2 Stereoscopic 3D Displays
     11.2.1 Spectral-based stereoscopic display (anaglyph)
     11.2.2 Polarization-based stereoscopic display
     11.2.3 Alternate-frame stereoscopic display
11.3 Head-Mounted Displays (HMDs)
11.4 Autostereoscopic 3D Displays
     11.4.1 Multiview 3D display technology
     11.4.2 Depth-fused 3D display technology
     11.4.3 Volumetric 3D display technology
     11.4.4 Holographic 3D display technology
11.5 Comparison of the Different 3D Display Techniques
11.6 Commonly Misunderstood Nonholographic, Non-3D Displays
     11.6.1 Pepper's ghost illusion
     11.6.2 Heliodisplay




Although the concept of holography has been known for decades, the field has seen significant development due to the availability of moderately priced lasers in the market for holographic applications. Also due to the advances in computer technology and computational processes, gathering and processing the experimental data has become much more tangible. Holography is a useful technique because it is the only truly three-dimensional imaging method available. It is used in a plethora of fields, such as 3D nonintrusive testing of cracks and fatigue in equipment, high-axial and lateral-resolution 3D topography of surfaces, 3D particle image velocimetry, 3D stress and deformation measurement, 3D microscopy of transparent phase objects for biomedical imaging, and holographic displays for the entertainment industry, just to name a few. For these reasons, digital and analog holography, along with their many variations (i.e., holographic interferometry, holographic microscopy, holographic tomography, multiwavelength digital holography, phase-shifting holography, compressive holography, coherence holography, computer-generated holography, etc.) have become the methods of choice for various metrological applications in 3D imaging.

This book begins with a brief introduction of the history of holography, types of holograms, and materials used for hologram recording, followed by a discussion of the basic principles of analog and digital holography and an indepth explanation of some of the most famous fringe-deciphering techniques for holographic interferometry. Besides the traditional topics already mentioned, other related topics are discussed—dynamic holography, non-Bragg orders, and compressive holographic tomography—as well as a nonholographic technique for 3D visualization, i.e., transportation of intensity imaging. Furthermore, the latest topics in the field of holography are discussed for the first time here: compressive holography, coherence holography, nonlinear holography, and polarization holography. The last chapter is dedicated to the progress in holographic and nonholographic 3D display technologies.

Multiple holographic techniques are presented, and readers may master their basic concepts through in-depth theory and applications. This book is a comprehensive study in the sense that traditional and up-to-date topics concerning holographic imaging and displays are presented. The focus is not so much the theory of these 3D imaging techniques, which exists in many references and will be briefly mentioned in this book, but rather the programming side, namely, the exact code that is needed to perform complex mathematical and physical operations. The code associated with each section help the reader grasp the mathematical concepts better through changing and adapting the parameters. Programming these complex equations is tedious and not straightforward; supplying the code with the text makes it easier for students and experienced researchers to concentrate on performing the experiment and simply changing the parameters in the code to get their results.

Because MATLAB® has become the programming language of choice for engineering and physics students, we decided to use this fantastic tool for our code examples. A few authors suggest the use of MATLAB for optics-oriented books, but none is adequate for use in practical situations. There are many books about analog and digital holography, but this book is more practical in terms of MATLAB code and examples because it includes all of the different techniques and codes in a single volume. A supplemental CD-ROM is included, which has a detailed version of the code and functions, as well as typical test images, so that readers do not need to perform the experiment to use the code in the book.

Special thanks to Dr. Partha Banerjee, Dr. Joe Haus, and Dr. Andrew Sarangan, Dr. John Loomis, and Dr. Russel Hardie from the University of Dayton. Also, special thanks to those who contributed to some of the original code in this book, namely, Mr. Thanh Nguyen (CUA), Dr. D. J. Brady (Duke University), Dr. J. Antonio Quiroga (The University of Madrid), Drs. J. Bioucas-Dias and G. Valadão (the Instituto Superior Técnico, Lisboa, Portugal), Dr. Munther Gdeisat [the General Engineering Research Institute (GERI) at Liverpool John Moores University], Dr. Miguel Arevallilo Herraez (the Mediterranean University of Science and Technology, Valencia, Spain), Dr. Justin Romberg (Georgia Tech.), Mr. Peyman Soltani (University of Zanjan, Iran), Dr. Jeny Rajan (the National Institute of Technology, Karnataka Surathkal, Mangalore, India), Dr. Wei Wang (the Heriot–Watt University, Edinburgh), Dr. Laura Waller (UC Berkeley), and Drs. Lei Tian and George Barbastathis (the Department of Mechanical Engineering at MIT). We offer special thanks to our parents, for without them this work would not have been possible.

Georges Nehmetallah
Rola Aylo
Logan Williams
June 2015

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