Library of Congress Cataloging-in-Publication Data

Blanche, Pierre-Alexandre, author.

Field guide to holography / Pierre-Alexandre Blanche.

pages cm. – (SPIE field guides ; FG31)

Includes bibliographical references and index.

ISBN 978-0-8194-9957-8

1. Holography. I. Title. II. Series: SPIE field guides; FG31.

QC449.B53 2014

621.36075–dc23

2013039089

Published by

SPIE

P.O. Box 10

Bellingham, Washington 98227-0010 USA

Phone: 360.676.3290

Fax: 360.647.1445

Email: books@spie.org

The content of this book reflects the thought of the author(s). Every effort has been made to publish reliable and accurate information herein, but the publisher is not responsible for the validity of the information or for any outcomes resulting from reliance thereon.

Printed in the United States of America.

First printing

## Introduction to the Series

Welcome to the * SPIE Field Guides—*a series of publications written directly for the practicing engineer or scientist. Many textbooks and professional reference books cover optical principles and techniques in depth. The aim of the

*is to distill this information, providing readers with a handy desk or briefcase reference that provides basic, essential information about optical principles, techniques, or phenomena, including definitions and descriptions, key equations, illustrations, application examples, design considerations, and additional resources. A significant effort will be made to provide a consistent notation and style between volumes in the series.*

**SPIE Field Guides**Each * SPIE Field Guide* addresses a major field of optical science and technology. The concept of these

*is a format-intensive presentation based on figures and equations supplemented by concise explanations. In most cases, this modular approach places a single topic on a page, and provides full coverage of that topic on that page. Highlights, insights, and rules of thumb are displayed in sidebars to the main text. The appendices at the end of each*

**Field Guides***provide additional information such as related material outside the main scope of the volume, key mathematical relationships, and alternative methods. While complete in their coverage, the concise presentation may not be appropriate for those new to the field.*

**Field Guide**The * SPIE Field Guides* are intended to be living documents. The modular page-based presentation format allows them to be updated and expanded. We are interested in your suggestions for new

*topics as well as what material should be added to an individual volume to make these*

**Field Guide***more useful to you. Please contact us at fieldguides@SPIE.org.*

**Field Guides**John E. Greivenkamp, **Series Editor**

College of Optical Sciences

The University of Arizona

## The Field Guide Series

, Second Edition, Robert Tyson & Benjamin Frazier**Adaptive Optics**, Larry Andrews**Atmospheric Optics**, Paul Yoder, Jr. & Daniel Vukobratovich**Binoculars and Scopes**, Yakov Soskind**Diffractive Optics**Jonathan D. Ellis**Displacement Measuring Interferometry,**, John Greivenkamp**Geometrical Optics**, Pierre-Alexandre Blanche**Holography**, Angelo Arecchi, Tahar Messadi, & John Koshel**Illumination**, Khan M. Iftekharuddin & Abdul Awwal**Image Processing**, Second Edition, Arnold Daniels**Infrared Systems, Detectors, and FPAs**, Eric Goodwin & Jim Wyant**Interferometric Optical Testing**, Rüdiger Paschotta**Laser Pulse Generation**, Rüdiger Paschotta**Lasers**, Julie Bentley & Craig Olson**Lens Design**, Tomasz Tkaczyk**Microscopy**, Peter Powers**Nonlinear Optics**, Ray Williamson**Optical Fabrication**, Rüdiger Paschotta**Optical Fiber Technology**, Chris Mack**Optical Lithography**, Ronald Willey**Optical Thin Films**, Katie Schwertz & James Burge**Optomechanical Design and Analysis**, Daniel Smith**Physical Optics**, Edward Collett**Polarization**, Larry Andrews**Probability, Random Processes, and Random Data Analysis**, Barbara Grant**Radiometry**, Larry Andrews**Special Functions for Engineers**, David Ball**Spectroscopy**, Créidhe O’Sullivan & J. Anthony Murphy**Terahertz Sources, Detectors, and Optics**, Jim Schwiegerling**Visual and Ophthalmic Optics**

## Field Guide to Holography

Few people can forget their first time seeing a hologram: the ghostlike image floating in space, changing its appearance in response to movement. Holograms have stirred childlike wonder in scientists and rapt curiosity in generations of schoolchildren. Abundantly depicted in science fiction novels and movies, holography is still imprinted with the dream of a better future through science and technology. Nowadays, holography plays a critical role in applications as diverse as credit card security, nondestructive testing of composite materials, and data storage and processing. Holography is one of the rare techniques that can transcend the realm of science into the magic of art.

The primary objective of this Field Guide is to present an overview of the various concepts of holography, including a theoretical foundation, a description of the different types of holograms (both optical- and computer-based), techniques used to produce them, and the most common recording materials. It is meant to provide the student, scholar, researcher, engineer, or professor with a broad panorama of the field and to help readers explore holography and understand its technical aspects and methodology.

Holography is not reserved solely for scientists with expensive equipment—it is a hobby and a passion that can be enjoyed by anyone with an interest in science who wants to make their own holograms. I hope that this Field Guide can demystify holography, but keep the wonder untouched and inspire you to discover the beauty of optical sciences.

Pierre-Alexandre Blanche

College of Optical Sciences

The University of Arizona

December 2013

## Table of Contents

**Glossary ix**

**Introduction and Basic Concepts 1**

Historical Background 1

Optical Field: Plane Wave 2

Optical Field: Complex Notation and Spherical Waves 3

Interference 4

Coherent Waves 6

Diffraction 7

Holograms 8

Diffraction Grating and Orders 9

Holographic Optical Elements 10

Holography outside the Visible Spectrum 11

**Theory and Mathematical Formalism 12**

Grating Equation 12

Angular Dispersion 13

Bragg’s Law 14

Grating Vector 15

Classification of Holograms 16

Reflection Geometry 17

Transmission Geometry 18

Thin/Thick Criteria 19

Analytic Coupled-Wave Analysis of Thick, Unslanted Gratings 20

Rigorous Coupled-Wave Analysis 22

Dispersion of Thick-Volume Gratings 23

Remarkable Thin Gratings 24

Scalar Theory of Diffraction: Kirchhoff Diffraction Integral 26

Fresnel Diffraction Integral 27

Fraunhofer Diffraction Integral 28

Diffraction by Simple Apertures 29

Remarkable Interference Patterns 31

Interference Recording and Reconstruction Formalization 33

Aberrations in Holograms 35

Computer-Generated Holograms 37

Errors in Computer-Generated Holograms 39

Space–Bandwidth Product 41

**Holographic Setups 42**

Inline Transmission Hologram (Gabor) 42

Inline Reflection Hologram (Denisyuk) 43

Off-axis Transmission Hologram (Leith and Upatnieks) 44

Imaging Consideration of Transmission Holograms 45

Transfer Hologram (H2) 46

Rainbow Hologram (Benton) 47

Edge-Lit Holograms 48

Holographic Stereograms 49

Color Holograms 50

Lippmann Photography 52

Multiplexing 53

Holographic Interferometry 54

Phase Conjugate Mirror 55

Digital Holography 56

Holographic Television 57

3D Perception and Holograms 58

Phase Stabilization 60

**Holographic Recording Materials 62**

Silver Halide 62

Photopolymer 63

Dichromated Gelatin 64

Photochromic Materials 65

Photoresists and Embossed Holograms 66

Polarization-Sensitive Material 67

Photorefractive Materials 68

Inorganic and Organic Photorefractive Materials 69

Acousto-optic Modulator (Bragg Cell) 70

Spatial Light Modulators 71

**Equation Summary 73**

**Bibliography 77**

**Index 78**

#### Glossary

$\widehat{\mathbf{\text{a}}}$

Unit polarization vector: ${a}_{x}\widehat{\mathbf{x}}+{a}_{y}\widehat{\mathbf{y}}+{a}_{z}\widehat{\mathbf{z}}$

**A**

Complex vector electric field amplitude (containing the polarization information)

**A**

Scalar electric field amplitude

$\mathbf{a}\cdot \mathbf{b}$

**c**

Speed of light

**d**

Hologram thickness

**D**

Aperture diameter

DMD

Digital micromirror device

**ds**

Elemental surface element (2D)

**E**

Electric field (scalar)

**E**

Vector electric field

${\widehat{\mathbf{e}}}_{m}$

Unit basis vector

$\mathcal{F}$

Fourier transform

**F**

Fresnel number $F={\left(D/2\right)}^{2}/z\text{\lambda}$

**i**

Imaginary unit $i=\sqrt{-1}$

**I**

Intensity

**k**

Wave vector $\left|k\right|=2\text{\pi}/\lambda $

**K**

Grating vector $\left|K\right|=2\text{\pi}/\Lambda $

LCoS

Liquid crystal on silicon

**m**

Integer number

MOEMS

Micro-opto-electro-mechanical system

**n**

Index of refraction

**N**

Numbers of elements composing a computer-generated hologram

**N**_{
h
}

Number of holograms recorded within the media

**r**

Position vector $\sum _{m=1}^{3}{x}_{m}{\widehat{e}}_{m}$

$\Re $

Real part

SBP

Space–bandwidth product

SLM

Spatial light modulator

TE

Transverse electric polarization mode (* s*-polarization)

TM

Transverse magnetic polarization mode (* p*-polarization)

**U**

Scalar electric field in complex notation

**U**

Vector electric field in complex notation $\text{E}=\Re \left[\text{U}\right]$

* U**

Complex conjugate of the complex expression **U**

**V**

Interference pattern visibility

$\widehat{x},\widehat{y},\widehat{z}$

Unit Cartesian coordinate vectors

${x}_{z},{y}_{z}$

$x,y$ coordinates at position $z$

$z$

Optical axis

$\partial $

Partial derivative

$\alpha $

Absorption coefficient

$\text{\Delta}M$

Material dynamic range, either amplitude $\text{\Delta}\text{\alpha}$ or phase $\text{\Delta}\text{\phi}$

$\text{\Delta}n$

Refractive index modulation (half the amplitude)

$\text{\Delta}{s}_{m}$

Spatial extent in $m$ dimensions

$\text{\Delta}x$

Spatial extent in the $\widehat{x}$ direction

$\text{\Delta}\text{\alpha}$

Absorption coefficient modulation (half the amplitude)

$\text{\Delta}\text{\lambda}$

Light source spectral linewidth in the wavelength domain

$\text{\Delta}\text{\mathit{v}}$

Spatial frequency bandwidth

$\text{\Delta}\text{\phi}$

Phase difference

$\text{\Delta}\text{\omega}$

Light source spectral linewidth in the frequency domain

$\text{\eta}$

Diffraction efficiency

$\text{\theta}$

Beam angle (relative to the surface normal)

${\text{\theta}}_{B}$

Bragg angle

${\text{\theta}}_{d}$

Diffracted beam angle

${\text{\theta}}_{i}$

Incident beam angle

${\text{\theta}}_{r}$

Reflection beam angle

$\text{\lambda}$

Light wavelength

$\text{\Lambda}$

Grating spacing, distance between Bragg planes

$\text{\rho}$

Polarization vector angle

$\text{\phi}$

Phase angle

$\text{\Phi}$

Slant angle

$\text{\omega}$

Light-wave frequency