HOLOGRAPHY, RESEARCH AND TECHNOLOGIES Edited by Joseph Rosen Holography, Research and Technologies Edited by Joseph Rosen Published by InTech Janeza Trdine 9, 51000 Rijeka, Croatia Copyright © 2011 InTech All chapters are Open Access articles distributed under the Creative Commons Non Commercial Share Alike Attribution 3.0 license, which permits to copy, distribute, transmit, and adapt the work in any medium, so long as the original work is properly cited. After this work has been published by InTech, authors have the right to republish it, in whole or part, in any publication of which they are the author, and to make other personal use of the work. Any republication, referencing or personal use of the work must explicitly identify the original source. Statements and opinions expressed in the chapters are these of the individual contributors and not necessarily those of the editors or publisher. No responsibility is accepted for the accuracy of information contained in the published articles. The publisher assumes no responsibility for any damage or injury to persons or property arising out of the use of any materials, instructions, methods or ideas contained in the book. Publishing Process Manager Katarina Lovrecic Technical Editor Teodora Smiljanic Cover Designer Martina Sirotic Image Copyright Vlue, 2010. Used under license from Shutterstock.com First published February, 2011 Printed in India A free online edition of this book is available at www.intechopen.com Additional hard copies can be obtained from orders@intechweb.org Holography, Research and Technologies, Edited by Joseph Rosen p. cm. ISBN 978-953-307-227-2 free online editions of InTech Books and Journals can be found at www.intechopen.com Part 1 Chapter 1 Chapter 2 Part 2 Chapter 3 Chapter 4 Chapter 5 Part 3 Chapter 6 Chapter 7 Chapter 8 Preface IX Basic Theory of Optics and Holography 1 The Fourier Transform in Optics: Analogous Experiment and Digital Calculus 3 Petre Cătălin Logofătu, Victor Nascov and Dan Apostol The Holographic Principle and Emergence Phenomenon 27 Marina Shaduri Holographic Materials 55 Polymer Holography in Acrylamide-Based Recording Material 57 Milan Květoň, Pavel Fiala and Antonín Havránek Real-time, Multi-wavelength Holographic Recording in Photorefractive Volume Media: Theory and Applications 83 Eduardo Acedo Barbosa The Composite Structure of Hologram and Optical Waveguide 109 Renxi Gao and Wenjun Liu Holographic Techniques 133 FINCH: Fresnel Incoherent Correlation Hologram 135 Joseph Rosen, Barak Katz and Gary Brooker Programmable Point-source Digital In-line Holography Using Digital Micro-mirror Devices 155 Adekunle A. Adeyemi and Thomas E. Darcie Pulsed Full-Color Digital Holography with a Raman Shifter 173 Percival Almoro, Wilson Garcia and Caesar Saloma Contents Contents VI Optical Holography Reconstruction of Nano-objects 191 Cesar A. Sciammarella, Luciano Lamberti and Federico M. Sciammarella Holographic Applications 217 Quantitative Analysis of Biological Cells Using Digital Holographic Microscopy 219 Natan T. Shaked, Lisa L. Satterwhite, Matthew T. Rinehart and Adam Wax Digital Holography and Cell Studies 237 Kersti Alm, Helena Cirenajwis, Lennart Gisselsson, Anette Gjörloff Wingren, Birgit Janicke, Anna Mölder, Stina Oredsson and Johan Persson Fabrication of Two- and Three-Dimensional Photonic Crystals and Photonic Quasi-Crystals by Interference Technique 253 Ngoc Diep Lai, Jian Hung Lin, Danh Bich Do,Wen Ping Liang, Yu Di Huang, Tsao Shih Zheng, Yi Ya Huang, Chia Chen Hsu Achieving Wide Band Gaps and a Band Edge Laser Using Face-Centered Cubic Lattice by Holography 279 Tianrui Zhai and Dahe Liu Accurate Axial Location for Particles in Digital In-Line Holography 293 Zhi-Bin Li, Gang Zheng, Li-Xin Zhang, Gang Liu and Fei Xia Hybrid Numerical-Experimental Holographic Interferometry for Investigation of Nonlinearities in MEMS Dynamics 303 Minvydas Ragulskis, Arvydas Palevicius and Loreta Saunoriene Vibration Measurement by Speckle Interferometry between High Spatial and High Temporal Resolution 325 Dan Nicolae Borza Digital Algorithms in Holography 347 Reconstruction of Digital Hologram by use of the Wavelet Transform 349 Jingang Zhong and Jiawen Weng Iterative Noise Reduction in Digital Holographic Microscopy 371 Victor Arrizón, Ulises Ruiz and Maria Luisa Cruz Chapter 9 Part 4 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Part 5 Chapter 17 Chapter 18 Contents VII Image Quality Improvement of Digital Holography by Multiple Wavelengths or Multiple Holograms 397 Takanori Nomura Digital Holography and Phase Retrieval 407 Hamootal Duadi, Ofer Margalit, Vicente Mico, José A. Rodrigo, Tatiana Alieva, Javier Garcia and Zeev Zalevsky Non-optical Holography 421 In-line Hard X-ray Holography for Biomedical Imaging 423 Andrzej Krol Fundamentals and Applications of Electron Holography 441 Akira Tonomura Chapter 19 Chapter 20 Part 6 Chapter 21 Chapter 22 Pref ac e Holography has recently become a fi eld of much interest because of the many new applications implemented by various holographic techniques. This book is a collec- tion of 22 excellent chapters wri en by various experts, and it covers various aspects of holography. Naturally, one book by 22 researches cannot cover all the richness of the holography world. Nevertheless, the book gives an updated picture on the ho est topics that the scientifi c community deals with, in the fi eld of holography. The book contains recent outputs from researches belonging to diff erent research groups world- wide, providing a rich diversity of approaches to the topic of holography. The aim of the book is to present a cu ing edge research on holography to the reader. We are lucky that it is freely accessible on the internet and enables outstanding contributors to share their knowledge with every interested reader. The 22 chapters of the book are organized in six sections, starting with theory, continu- ing with materials, techniques, applications as well as digital algorithms, and fi nally ending with non-optical holograms. There are two chapters in the fi rst section of Basic Theory of Optics and Holography. The fi rst chapter is about optical Fourier transform which is an essential tool in many holographic schemes. The second chapter discusses philosophically the role of the holographic principle in nature. The sections subse- quent to the fi rst section deal with more practical aspects of holography. The section of holographic materials contains three chapters describing holograms recorded on the following mediums: 1. Acrylamide-based recording material 2. Photorefractive media, and 3. Optical waveguides The next section depicting holographic techniques also contains four chapters: 1. New technique of recording incoherent digital holograms, 2. Novel technique of recording in-line coherent digital holograms. 3. Original technique of recording pulsed color digital holograms. 4. The latest method of reconstructing nano-objects from optical holograms. The subsequent section detailing holographic applications, obviously contains the largest number of chapters. The applications described in this book are only a tiny sample of the use of holography in many scientifi c and industrial areas. Two chapters deal with the role of holography in research of biological cells. Then the next two chap- ters describe the creation of holographic la ice structures for manufacturing photonic X Preface crystals. The last three chapters in the applications section discuss the use of hologra- phy in the fi elds of particles tracking, MEMS, and vibration measurement, respectively. Following the extensive section of applications, a section consisting of four chapters is devoted to the growing link between holography and the world of digital computation. This link is best expressed by the digital holograms which are the type of holograms that are recorded optically and reconstructed digitally in the computer memory. Each of the four chapters in this section describes a specifi c digital algorithm of digital ho- logram reconstructions. This book rounds off with two interesting chapters on non- optical holograms: one discusses the x-ray holography for biomedical imaging, and the other introduces the topic of electron holography. Finally, I would like to thank all of the authors for their eff orts in writing these in- teresting chapters. Their contributions light up hidden corners in the broad topic of holography and extend the knowledge of the rapidly growing holographic community. I would also like here to cite a quote of a famous American novelist, Edith Wharton: “There are two ways of spreading light; to be the candle or the mirror that refl ects it,” and to say without a hesitation that this book defi nitely presents 22 glowing candles. Joseph Rosen Ben-Gurion University of the Negev, Israel [...]... are hybrid in nature, digital and analogous in the same time For such devices as CCDs and SLMs one has to switch back and forth between CFT and DFT and think sometimes in terms of one of the formalisms and some other times in terms of the other Here we should The Fourier Transform in Optics: Analogous Experiment and Digital Calculus 5 mention the pioneer work of Lohmann and Paris for the compensation... discretely, and such functions do not exist in reality, and one may wonder what is the usefulness of it all There is usefulness inasmuch as gsp relates to g and Gsp to G, and they are related because we built gsp starting from g But constructing gsp we adapted g for the purpose of discrete computing and we departed from the original g and consequently from G Now we have to find how close are the CFT and the... “naturally” sampled input of mask B (see Fig 7 below) The abscissa and the ordinate are the spatial frequencies and the light intensity of the spectrum is coded as levels of grey 24 Holography, Research and Technologies Fig 7 The discrete Fourier spectrum of the “natural” sampling of mask B The abscissa and the ordinate are the spatial frequencies, and the light intensity is codes as levels of grey, just as... −Δ∫ 2 t (2) and (III) the purely discrete Fourier transform where a list of numbers is transformed into another list of numbers by a summation procedure and not by integration Gq = N 2 −1 ∑ p =− N 2 g p exp ( −i 2 π q p / N ) , q = − N 2 , ,N 2 − 1 (3) (For clarity purposes, in this chapter we use consistently m and n to indicate the periodicity, and p and q to indicate the sampling of g and G respectively.)... and they are hampered by the gap between DFT and CFT, discrete mathematics, digital computers on the one hand and real physical experiments on the other hand With the above rich justification we did not exhaust by far the uses of DFT and the need to rigorously connect it to CFT Apart from all virtual computation, which also requires the connection between DFT and CFT to be worked out, digital holography... neglected and the transposition or rotation operations mentioned above have to be performed In the 2D case the transpositions do not have to be a double series of wing transpositions for rows and columns One can make just two diagonal transpositions of the quadrants of the input and output matrices The division of the input and output matrices depends on the parity of M and N For even M and N things... looks like (37) Let the integer indexes p and q be so that p = m + N 2 or m = p − N 2 , p = 0,1,… ,N − 1 q = n + N 2 or n = q − N 2 , q = 0,1,… ,N − 1 (40) which means we can introduce two similar sets of samples g’ and G’, having the indexes shifted by N/2 g′ = g p − N 2 = g m , G′ = Gq − N 2 = G n p q (41) 18 Holography, Research and Technologies Introducing (40) and (41) in (39) we obtain G n = G′ =... improving the similarity of DFT to CFT described above and illustrated in Figs 3 and 4 may be combined and the result is shown in Fig 5 The sampling array used for the calculation of DFT is now both “swollen” and extended, having 100 times more elements than the “natural” sampling Now DFT is both closer to CFT and richer in information Now DFT is both accurate and able to provide enough information for a correct... 1 Basic Theory of Optics and Holography 1 The Fourier Transform in Optics: Analogous Experiment and Digital Calculus Petre Cătălin Logofătu1, Victor Nascov2 and Dan Apostol1 1National Institute for Laser, Plasma and Radiation Physics 2Universitatea Transilvania Braşov Romania 1 Introduction Discrete optics and digital optics are fast becoming a classical chapter in optics and physics in general, despite... discrete and periodic, we have to combine the forms (9) and (10) of g together, and, taking into account (11), we obtain g sp ( t ) = δt ∞ N 2 −1 ∑ ∑ m =−∞ p =− N 2 g pδ ( t + m Δt − p δt ) (12) Here the superscript “sp” means that the function gsp is both sampled (discrete) and periodic We know from the general properties of CFT of its reciprocal character (Bracewell, 1965; Goodman, 1996) and that . Microscopy 3 71 Victor Arrizón, Ulises Ruiz and Maria Luisa Cruz Chapter 9 Part 4 Chapter 10 Chapter 11 Chapter 12 Chapter 13 Chapter 14 Chapter 15 Chapter 16 Part 5 Chapter 17 Chapter 18 Contents VII Image. HOLOGRAPHY, RESEARCH AND TECHNOLOGIES Edited by Joseph Rosen Holography, Research and Technologies Edited by Joseph Rosen Published by InTech Janeza Trdine 9, 510 00 Rijeka, Croatia Copyright. Israel Part 1 Basic Theory of Optics and Holography 1 The Fourier Transform in Optics: Analogous Experiment and Digital Calculus Petre Cătălin Logofătu 1 , Victor Nascov 2 and Dan Apostol 1 1 National