Introduction to Digital Holography

Book Series: Digital Signal Processing in Experimental Research

Volume 1

by

Leonid Yaroslavsky , Jaakko Astola

DOI: 10.2174/97816080507961090101
eISBN: 978-1-60805-079-6, 2009
ISBN: 978-1-60805-026-0
ISSN: 1879-4432

  
  




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Table of Contents

Foreword (Survival of Holography provided by Signal Processing) , Pp. i

A. Lohmann
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Preface , Pp. ii-iv (3)

Leonid Yaroslavsky and Jaakko Astola
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Principles of Holography , Pp. 1-7 (7)

Leonid Yaroslavsky and Jaakko Astola
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Holographic Transforms in Digital Computers , Pp. 8-36 (29)

Leonid Yaroslavsky and Jaakko Astola
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Digital Recording and Numerical Reconstruction of Holograms , Pp. 37-58 (22)

Leonid Yaroslavsky and Jaakko Astola
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Computer Generated Holograms (CGH): Principles , Pp. 59-69 (11)

Leonid Yaroslavsky and Jaakko Astola
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Hologram Encoding for Recording on Physical Media , Pp. 70-88 (19)

Leonid Yaroslavsky and Jaakko Astola
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Optical Reconstruction of Computer-Generated Holograms , Pp. 89-109 (21)

Leonid Yaroslavsky and Jaakko Astola
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Computer-Generated Holograms and Optical Information Processing , Pp. 110-128 (19)

Leonid Yaroslavsky and Jaakko Astola
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Computer-Generated Holograms and 3D Visual Communication , Pp. 129-145 (17)

Leonid Yaroslavsky and Jaakko Astola
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Image Processing Methods , Pp. 146-187 (42)

Leonid Yaroslavsky and Jaakko Astola
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Index , Pp. 188-189 (2)

Leonid Yaroslavsky and Jaakko Astola
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Foreword

Survival of Holography provided by Signal Processing

Natural scientists belong to one of two categories: either they deal with matter and energy, or they are concerned with signals and systems. Sometimes collaboration of these two kinds of scientists is essential for solving problems at hand. The emergence of holography was a typical case, where systems people saved the physics people. Originally, holograms caused amusing displays. Now holograms are also used at industrial jobs. To do that the physical optics people had to adapt the working style of systems people to what is now often called "digital holography", the subject of this book.

Back in 1948 Dennis Gabor succeeded in producing holograms. The objects usually consisted of a few dark lines on a large transparent background. The method did not work properly with a negative as object, i.e. a few bright narrow lines. More annoying was the twin image that appeared at an undesirable location. Gabor attempted to solve this problem with the help of tools from physical optics: lenses, prisms, and beam-splitters in a Mach-Zehnder interferometer. No luck, he gave up. When appointed Professor at the Imperial College, London, in 1959, he presented, in his acceptance speech, his three most noticeable inventions. Holography was not a part of it.

Meanwhile, I had learned from a systems scientist what single side-band modulation can do. We tried it with a modest success, shortly before Emmett Leith solved the problems with his tilted reference method. Leith, in his memoirs, wrote that he was lucky to be a physicist surrounded by signal-processing experts. Systems theory is much richer in concepts beyond side-band processing. Another interesting concept is matched filtering. It was soon translated from electronic filtering to optical spatial filtering.

This new book is a tremendous collection of digital signal and image processing in general, and specifically on digital holography. It presents digital holography in one unified language called "algorithmics". The volume appears at an appropriate time, i.e. while optics is mutating from micro to nano with typical dimensions 10-3 and 10-6 microns.

I am amazed when I compared today's capabilities with what was available around 1950-1960. When will we have mobile-3D-in color impressions? The youth is so powerful. They will simply demand it, and get it because of the market. Good luck!

Prof. Dr. A. Lohmann
University Erlangen-Nuernberg, Germany


Preface

The history of science is, to a considerable degree, the history of invention, development and perfection of imaging methods and devices. Modern science began with the invention and application of optical telescope and microscope in the beginning of 17-th century by Galileo Galilei (1564-1642), Anthony Leeuwenhoek (1632-1723) and Robert Hook (1635-1703).

The next decisive stage was invention of photography in the first half of the 19-th century. Photographic plates were the major means in the discoveries of X-rays by Wilhelm Conrad Roentgen (1845-1923, The Nobel Prize Laureate, 1901) and radioactivity by Antoine Henri Becquerel (1852-1908, The Nobel Prize Laureate, 1903) at the end of 19-th century. These discoveries, in their turn, almost immediately gave birth to new imaging techniques i.e. X-ray imaging and radiography.

X-rays were discovered by W.C. Roentgen in the experiments with cathode rays. Cathode rays were discovered in 1859 by Julius Plücker (1801-1868), who used vacuum tubes invented in 1855 by a German inventor Heinrich Geissler (1815-1879). These tubes, as modified by Sir William Crookes (1832-1919) led eventually to the discovery of electron and finally brought about the development of electronic television and electron microscopy in 30-th - 40-th of 20-th century. Designer of the first electron microscope E. Ruska (1906-1988) was awarded The Nobel Prize in Physics for 1986. This award was shared with G. Binning and H. Rohrer, who were awarded for their invention of the scanning tunneling microscope.

The discovery of diffraction of X-rays by Max von Laue (1889-1960, the Nobel Prize Laureate, 1914) in the beginning of 20-th century marked the advent of a new imaging technique, which we now call computational imaging. Although Von Laue’s motivation was not created a new imaging technique but rather proved the wave nature of X-rays, lauegrams had very soon become the main imaging tool in crystallography. Lauegrams are not conventional images for visual observation. However, by using “lauegrams”, one could numerically reconstruct the spatial structure of atoms in crystals. This shoot gave its crop in less than half a century. One of the most remarkable scientific achievements of 20-th century is based on X-ray crystallography. It is discovered by J. Watson and F. Crick of spiral structure of DNA (the Nobel Prize, 1953). And about at the same time a whole bunch of new computational imaging methods had appeared: holography, synthetic aperture radar, coded aperture imaging and tomography. Two of these inventions were awarded the Nobel Prize: D. Gabor for “his invention and developments of the holographic method” (the Nobel Prize in Physics, 1971) and A. M. Cormack and G. N. Hounsfield for “the development of computer assisted tomography” (the Nobel Prize in Physiology and Medicine, 1979).

Denis Gabor invented holography in 1948. This is what D. Gabor wrote in his Nobel Lecture about the development of holography: ” Around 1955 holography went into a long hibernation. The revival came suddenly and explosively in 1963, with the publication of first successful laser hologram by Emmett N. Leith and Juris Upatnieks of the University of Michigan, An Arbor. Their success was not only due to the laser, but also due to the long theoretical preparation of Emmett Leith (in the field of the “side looking radar”) started in 1955. Another important development in holography happened in 1962, just before the “holography explosion”. Russian physicist Yu. N. Denisyuk published an important paper in which he combined holography with the ingenious method of photography in natural colors, for which Gabriel Lippman received the Nobel Prize in 1908.

Denis Gabor received Nobel Prize in 1971. The same year, a paper “Digital holography” was published in Proceedings of IEEE by T. Huang. This paper marked the next step in the development of holography, the use of digital computers for reconstructing, generating and simulating wave fields, and reviewed pioneer accomplishments in this field. These accomplishments prompted a burst of research and publications in early and mid 70-th. At that time, most of the main ideas of digital holography were suggested and tested. Numerous potential applications of digital holography such as fabricating computer-generated diffractive optical elements and spatial filters for optical information processing, 3-D holographic displays and holographic television and computer vision stimulated a great enthusiasm among researchers.

However, limited speed and memory capacity of computers available at that time, absence of electronic means and media for sensing and recording optical holograms hampered implementation of these potentials. In 1980-th digital holography went into a sort of hibernation, similarly to what happened to holography in 1950-th - 1960-th. With an advent, in the end of 1990-th,the new generation of high speed microprocessors, high resolution electronic optical sensors and liquid crystal displays, technology for fabricating micro lens and mirror arrays digital holography got a new wind. Digital holography tasks that required hours and days of computer time in 1970-th can now be solved in almost “real” time for tiny fractions of seconds. Optical holograms can now be directly sensed by high-resolution photo electronic sensors and fed into computers in “real” time without any need of any wet photo-chemical processing. Micro lens and mirror arrays promise a breakthrough in the means for recording computer-generated holograms and creating holographic displays. Recent flow of publications in digital holographic metrology and microscopy indicate revival of digital holography from hibernation.

The development of optical holography, one of the most remarkable inventions of the XX-th century, was driven by clear understanding of information nature of optics and holography. The information nature of optics and holography is especially distinctly seen in digital holography. Wave field recorded in the form of a hologram in optical, radio frequency or acoustic holography, is represented in digital holography by a digital signal that carries the wave field information deprived of its physical casing. With digital holography and with incorporating digital computers into optical information systems, information optics has reached its maturity.

This is not a coincidence that digital holography appeared in the end of 60-th, the same period of time, which digital image processing can be dated back to. In the same way, in a certain sense, as invention by Ch. Towns, G. Basov and A. Prokhorov lasers in mid 1950-th (the Nobel Prize in Physics, 1964) stimulated development of holography, two events stimulated digital holography and digital image processing: beginning of industrial production of computers in 1960-th and introducing Fast Fourier Transform algorithm made by J. W. Cooley and J. M. Tukey in 1965.

In this book, we will adhere meanings of digital holography as a branch of the imaging science that deals with numerical reconstruction of digitally recorded holograms and with computer synthesis of holograms and diffractive optical elements.

We started, in Ch. 1, with basic principles of physical holography and its mathematical models and introduce diffraction integrals that are used to describe wave propagation from objects to holograms. The fundamental issue of digital holography is discrete representation of optical signals and diffraction integrals. This problem, which has a direct relation to both numerical reconstruction of holograms and to synthesis of computer generated holograms, is addressed in Ch. 2. Then we proceed to methods of digital holography proper.

Methods and algorithms for digital recording and numerical reconstruction of holograms, their applicability and appropriate metrological characterization are presented in Ch. 3.

Chs. 4 to 6 are devoted to principles of computer-generated holography and mathematical models, to methods of encoding numerical holograms for recording them on spatial light modulators as hologram recording devices and to the analysis of how the results of optical reconstruction of computer-generated holograms depend on the encoding method and on physical parameters of hologram recording devices.

Chs. 7 and 8 review applications of computer-generated holograms in optical information processing and for information display and 3D visual communications. In the latter, especial emphasis is made on using limitations of human 3D vision for reducing the computational complexity of the hologram synthesis and for easing requirements to hologram recording and reconstruction devices.

In its methods and applications, digital holography is closely connected with digital image processing. Digital image processing is nowadays a well-established field of information technology covered in many books and educational courses. However, some of its aspects that have direct relation to digital holography and its applications deserve discussion and reviewing in the context of the book on digital holography. Therefore, in Ch. 9 we reviewed image processing methods in digital holography: mathematical models of imaging and holographic systems, statistical models of stochastic transformations of optical signals, measuring parameters of random interferences in sensors and imaging and holographic systems; principles of Mean Square Error (MSE)-optimal scalar Wiener filtering for image denoising and deblurring, methods for correcting image gray scale nonlinear distortions and methods for accurate image resampling.

Leonid Yaroslavsky
Author

List of Contributors

Editor(s):
Leonid Yaroslavsky
Tel Aviv University
Israel


Jaakko Astola
Tampere University of Technology
Finland




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