INTRODUCTION TO MODERN DIGITAL HOLOGRAPHY

Transcription

1 INTRODUCTION TO MODERN DIGITAL HOLOGRAPHY With MATLAB Get up to speed with digital holography with this concise and straightforward introduction to modern techniques and conventions. Building up from the basic principles of optics, this book describes key techniques in digital holography, such as phase-shifting holography, low-coherence holography, diffraction tomographic holography, and optical scanning holography. Practical applications are discussed, and accompanied by all the theory necessary to understand the underlying principles at work. A further chapter covers advanced techniques for producing computer-generated holograms. Extensive MATLAB code is integrated with the text throughout and is available for download online, illustrating both theoretical results and practical considerations such as aliasing, zero padding, and sampling. Accompanied by end-of-chapter problems, and an online solutions manual for instructors, this is an indispensable resource for students, researchers, and engineers in the fields of optical image processing and digital holography. ting-chung poon is a Professor of Electrical and Computer Engineering at Virginia Tech, and a Visiting Professor at the Shanghai Institute of Optics and Fine Mechanics, Chinese Academy of Sciences. He is a Fellow of the OSA and SPIE. jung-ping liu is a Professor in the Department of Photonics at Feng Chia University, Taiwan.

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3 INTRODUCTION TO MODERN DIGITAL HOLOGRAPHY With MATLAB TING-CHUNG POON Virginia Tech, USA JUNG-PING LIU Feng Chia University, Taiwan

4 University Printing House, Cambridge CB2 8BS, United Kingdom Cambridge University Press is part of the University of Cambridge. It furthers the University s mission by disseminating knowledge in the pursuit of education, learning and research at the highest international levels of excellence. Information on this title: / T-C. Poon & J-P. Liu 2014 This publication is in copyright. Subject to statutory exception and to the provisions of relevant collective licensing agreements, no reproduction of any part may take place without the written permission of Cambridge University Press. First published 2014 Reprinted with corrections 2014 Printed in the United Kingdom by TJ International Ltd. Padstow Cornwall A catalog record for this publication is available from the British Library Library of Congress Cataloging in Publication data Poon, Ting-Chung. Introduction to modern digital holography : with MATLAB / Ting-Chung Poon, Jung-Ping Liu. pages cm ISBN (Hardback) 1. Holography Data processing. 2. Image processing Digital techniques. I. Liu, Jung-Ping. II. Title. TA1542.P dc ISBN Hardback Additional resources for this publication at /digitalholography Cambridge University Press has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.

5 Contents Preface page ix 1 Wave optics Maxwell s equations and the wave equation Plane waves and spherical waves Scalar diffraction theory Fresnel diffraction Fraunhofer diffraction Ideal thin lens as an optical Fourier transformer Optical image processing 15 Problems 24 References 26 2 Fundamentals of holography Photography and holography Hologram as a collection of Fresnel zone plates Three-dimensional holographic imaging Holographic magnifications Translational distortion Chromatic aberration Temporal and spatial coherence Temporal coherence Coherence time and coherence length Some general temporal coherence considerations Fourier transform spectroscopy Spatial coherence Some general spatial coherence considerations 53 Problems 56 References 58 v

6 vi Contents 3 Types of holograms Gabor hologram and on-axis (in-line) holography Off-axis holography Image hologram Fresnel and Fourier holograms Fresnel hologram and Fourier hologram Lensless Fourier hologram Rainbow hologram 73 Problems 78 References 78 4 Conventional digital holography Sampled signal and discrete Fourier transform Recording and limitations of the image sensor Imager size Pixel pitch Modulation transfer function Digital calculations of scalar diffraction Angular spectrum method (ASM) Validity of the angular spectrum method Fresnel diffraction method (FDM) Validation of the Fresnel diffraction method Backward propagation Optical recording of digital holograms Recording geometry Removal of the twin image and the zeroth-order light Simulations of holographic recording and reconstruction 111 Problems 116 References Digital holography: special techniques Phase-shifting digital holography Four-step phase-shifting holography Three-step phase-shifting holography Two-step phase-shifting holography Phase step and phase error Parallel phase-shifting holography Low-coherence digital holography Diffraction tomographic holography Optical scanning holography 137

7 Contents vii Fundamental principles Hologram construction and reconstruction Intuition on optical scanning holography 144 Problems 147 References Applications in digital holography Holographic microscopy Microscope-based digital holographic microscopy Fourier-based digital holographic microscopy Spherical-reference-based digital holographic microscopy Sectioning in holography Phase extraction Optical contouring and deformation measurement Two-wavelength contouring Two-illumination contouring Deformation measurement 175 Problems 175 References Computer-generated holography The detour-phase hologram The kinoform hologram Iterative Fourier transform algorithm Modern approach for fast calculations and holographic information processing Modern approach for fast calculations Holographic information processing Three-dimensional holographic display using spatial light modulators Resolution Digital mask programmable hologram Real-time display Lack of SLMs capable of displaying a complex function 206 Problems 210 References 211 Index 214

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9 Preface Owing to the advance in faster electronics and digital processing power, the past decade has seen an impressive re-emergence of digital holography. Digital holography is a topic of growing interest and it finds applications in threedimensional imaging, three-dimensional displays and systems, as well as biomedical imaging and metrology. While research in digital holography continues to be vibrant and digital holography is maturing, we find that there is a lack of textbooks in the area. The present book tries to serve this need: to promote and teach the foundations of digital holography. In addition to presenting traditional digital holography and applications in Chapters 1 4, we also discuss modern applications and techniques in digital holography such as phase-shifting holography, low-coherence holography, diffraction tomographic holography, optical scanning holography, sectioning in holography, digital holographic microscopy as well as computer-generated holography in Chapters 5 7. This book is geared towards undergraduate seniors or first-year graduate-level students in engineering and physics. The material covered is suitable for a one-semester course in Fourier optics and digital holography. The book is also useful for scientists and engineers, and for those who simply want to learn about optical image processing and digital holography. We believe in the inclusion of MATLAB in the textbook because digital holography relies heavily on digital computations to process holographic data. MATLAB will help the reader grasp and visualize some of the important concepts in digital holography. The use of MATLAB not only helps to illustrate the theoretical results, but also makes us aware of computational issues such as aliasing, zero padding, sampling, etc. that we face in implementing them. Nevertheless, this text is not about teaching MATLAB, and some familiarity with MATLAB is required to understand the codes. The MATLAB codes included in this book are all available to download from the publisher at /digitalholography. ix

10 x Preface Ting-Chung Poon would like to thank his wife, Eliza, and his children, Christina and Justine, for their love. This year is particularly special to him as Christina gave birth to a precious little one Gussie. Jung-Ping Liu would like to thank his wife, Hui-Chu, and his parents for their understanding and encouragement.