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Spie Press Book

Coherent Fields and Images in Remote Sensing
Author(s): Valery I. Mandrosov
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Book Description

Coherent fields and images can provide significant information about remote objects in a variety of practical ways. This volume considers several coherent phenomena, including the use of coherent remote sensing to obtain information about the dynamic parameters of remote objects, the use of Fourier telescopy for exact imaging of remote objects in a turbulent atmosphere, and the use of time-background holography for remote sensing of moving objects. The book is intended for the broad community of researchers and engineers interested in coherent phenomena and their applications, plus senior and graduate students specializing in this field.

Book Details

Date Published: 8 April 2004
Pages: 244
ISBN: 9780819451903
Volume: PM130

Table of Contents
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Preface

Notation

Explanation of Terms

Chapter 1 Basic Concepts of the Statistical Theory of Light Scattering
1.1 Introduction
1.2 Random surfaces and fields scattered by them; the Kirchhoff method
1.3 Statistical characteristics of a field scattered by a stationary object of finite size
1.4 Statistical characteristics of fields scattered by a moving object
1.5 Conclusions

Chapter 2 Statistical Description of Coherent Images
2.1 Introduction
2.2 Statistical properties of fields in coherent images
2.3 Statistical characteristics of coherent image intensity in nonflat rough objects
2.4 Methods of estimating and improving the quality of coherent images
2.5 Statistical characteristics of images of an object illuminated by quasi-monochromatic and polychromatic light
2.6 Coherent images of small-scale surface roughness
2.7 Speckle structure of the time spectrum of a coherent field scattered by a moving rough object
2.8 Conclusions
2.9 to Chapter 2 General conclusions to Chapters 1 and 2

Chapter 3 Use of Coherent Fields and Images to Determine the Dynamic Parameters of Remote Objects
3.1 Introduction
3.2 Methods of determining the linear velocity of a remote rough object
3.3 Method of determining the angular velocity of a rotating object
3.4 Determining object surface deformation parameters
3.5 Combined method of determining the motion and deformation parameters of an object
3.6 Conclusions

Chapter 4 Fourier Telescopy
4.1 Introduction
4.2 Statistical model of the received signal in Fourier telescopy and the Fourier-telescopic image
4.3 Fourier-telescopic panoramic microscope
4.4 Integral and local measures of the relationship between a Fourier-telescopic image of an object and its averaged undistorted image
4.5 Conclusions

Chapter 5 Time Background Holography of Moving Objects
5.1 Introduction
5.2 General theory of time background holography
5.3 Using time background holography to detect a moving object
5.4 Application of time background holography to the fast detection of moving objects and determination of their parameters
5.5 Time background holography of moving objects placed close to the background surface; the principle of time averaging of coherent wavefields
5.6 Time background intensity holography
5.7 Conclusions

Appendix 1 Statistical Characteristics of the Intensity Distribution in a Coherent Image

Appendix 2 Statistical Characteristics of the Intensity Distribution in a Fourier-Telescopic Image and the Resolution of Fourier Telescopy

Appendix 3 Phase Closure Algorithm in Fourier Telescopy

Appendix 4 The Coherence of Fields Scattered by Sufficiently Large Rough Objects, and the Contrast of the Scattered Field Intensity Distribution

Appendix 5 Physics of Speckle Pattern Formation in the Images of Rough Objects


References

Index



PREFACE


This book is devoted to the problems connected with detailed analysis of
coherent fields and images and their application in remote sensing. Our
consideration is based on several coherent phenomena, such as the Doppler
effect, which is related to the phase variation of radiation reflected by a moving
object, and the effect of speckle pattern formation on the radiation scattered by
rough objects. Since the beginning of the twentieth century, coherent phenomena,
including interference, have been actively used in radio and acoustic
communication and in location techniques. At first, applications were concerned
with rather simple effects such as interference of two mutually coherent plane
waves leading to a sinusoidal pattern. However, in the second half of the century,
rapid development of laser technology brought more complicated problems
related to interference effects. Those who observed images of rough objects by
means of laser radiation noticed their strongly inhomogeneous structure. This
structure is called the speckle pattern. The speckle pattern also appears in laser
radiation scattered by a rough object or by a large number of randomly
distributed particles. A multicolor speckle pattern can be observed for white light
scattered by rough objects, randomly distributed particles, and diffraction
gratings a with random period. For instance, if one looks at the sun with blinking
eyes, light is scattered by one's eyelashes, which is a similar effect as a
diffraction grating with a random period, and a speckle pattern consisting of
colored spots can be seen.

Although effects of this kind are well known to everyone, it was M. Von
Laue1,2 who first described this phenomenon and studied it for the case of
scattering by multiple particles. In the beginning of the twentieth century, he
pointed out for the first time that a speckle pattern is built by many interfering
waves diffracted by the elements of the scattering medium. However, up until the
mid-1960s, effects related to speckle pattern formation did not attract much
attention. This is evident, for instance, from the fact that such phenomena were
not considered in the monumental book of Born and Wolf.3 One of the first
works that used speckle pattern formation analysis for light scattered by rough
surfaces was by Rigden and Gordon.4 One of the first works to analyze the
dynamic speckle pattern was by Anisimov et al.5

In the 1970s and beginning of the 1980s, many authors suggested using
speckle pattern formation to determine the shape, velocity parameters, and
dynamic parameters of deformations for various objects. These proposals are
summarized in Refs. [6]�[9]. In the 1980s, a consistent statistical description of
coherent phenomena was developed,10 and the statistical characteristics of
coherent fields scattered by rough objects as well as coherent images of those
objects were studied in detail.11, 12 Due to further development of this subject, the
terms "coherent field" and "coherent image" (meaning, respectively, a field
scattered by a rough object and by its image11, 12) became widely used. In this
book, a scattered field is coherent if its value at each point is given by a sum of
amplitudes (interference) of all waves scattered by the object surface and
reaching this point. A coherent image of a rough object is defined as an image
that satisfies the following condition: at each point, there is interference of all
waves coming from the smallest area of the object surface that is resolvable by
the imaging system. In particular, coherent fields and images are formed when an
object is illuminated by monochromatic light. Conditions under which coherent
fields and images are formed will be considered in detail in Appendix 4 and in
Sec. 2.5.

Finally, beginning in the 1990s there appeared a number of works analyzing
phenomena connected with coherent light scattering by moving rough objects. In
such phenomena, both the Doppler effect and the speckle effects are manifested,
and they can be used for determining the parameters of an object's motion.
Among these works, one of the most important is that by Asakura and
Okomato.13

At present, the use of coherent fields and images in remote sensing is
drawing increasingly more attention from the scientific community. This is due
to a growing understanding of the fact that coherent fields and images can
provide significant information about remote objects in a variety of practical
situations.12 For example, coherent remote sensing can be very helpful when
either the scattered radiation is seriously distorted because of propagation
through inhomogeneous (turbulent) medium or remote objects with low
reflection, or the resolution of the imaging system is too low. Development of
fast computers, sensitive detectors, and high-power sources of coherent radiation
increased the feasibility of coherent remote sensing.

A bright example of the progress in coherent remote sensing is Fourier
telescopy.14-18 This technique, which enables exact imaging of remote objects in a
turbulent atmosphere, is proposed for the ambitious project GLINT,15 which aims
to image objects that are 40,000 km away from Earth. Most alternative methods
for achieving this goal use adaptive elements to compensate for the phase
distortions accumulated while the scattered radiation propagates to the observer.
This approach requires a large number of highly sensitive detectors and a lot of
computations. Fourier telescopy uses a matrix of coherent sources controlled in
such a way that sinusoidal interference patterns formed by radiation from
particular source pair on the object's surface have different periods and
directions. Selecting portions of the scattered radiation corresponding to a given
interference pattern, one can compensate for the phase distortions using a special
(phase-closure) algorithm and build the Fourier components of the object's true
image. The image itself is formed by applying the inverse Fourier transform to
these components. This imaging technique does not require powerful computers
or sensitive detectors.

Another example of a successful application of coherent fields and images is
a radically new kind of holography that was developed by the author, i.e., time
background holography of moving objects. This technique enables remote
sensing of transparent or weakly reflecting objects that are moving against a
relatively bright, inhomogeneous background. Although there had been several
earlier attempts to solve this problem,19,20 only time background holography
provides a practical solution.21-23 The approach involves obtaining information
about the moving object from the time spectrum of the coherent fields scattered
by an object and its background. Two papers report the results of experiments
performed in the microwave and ultrasonic ranges.21,23

A special part of time background holography is the time averaging method.
The method implies that the time-averaged amplitude of the scattered field, i.e.,
the point of the spectrum corresponding to the frequency of the illuminating
radiation, contains information about the object. The time averaging method
enables one to detect moving objects and to determine their shapes even when
they are either transparent, weakly reflecting, or indistinguishable from the
background. One of the most important advantages of the method is that it allows
a completely absorbing object to be detected with the same probability as an
object whose reflection does not differ from that of the background. Akapov and
Mandrosov proposed a conceptual schematic of a device that use the time
averaging method in environmental monitoring, specifically for detecting clusters
of pollution particles�including completely absorbing particles�and
determining their concentration, average size, and average velocity. 22

Naturally, applications of coherent remote sensing are not limited to the
above two examples. However, since they are both illustrative and promising,
they will be given detailed consideration in this book.

The above considerations were taken into account when the framework for
this book was formulated. Therefore, in the first and second chapters, statistical
characteristics of speckle patterns in coherent fields scattered by rough objects
and in the coherent images of such objects are studied. These chapters will help
the reader to understand the relationship between speckle patterns and a surface's
geometric and roughness parameters. The third chapter describes methods that
use coherent images to determine the dynamic parameters of an object, such as
linear velocity, rotation rate, and the angle of rotation. A distinguishing feature of
these coherent remote sensing methods is that they require no reference beam and
therefore do not need highly coherent sources. In particular, one can use laser
sources with a coherence length not exceeding 1 m.

The fourth and the fifth chapters are devoted to issues closely connected with
the above two examples. The fourth chapter presents the basics of Fourier-
telescopic imaging. Theoretical consideration shows that the images obtained by
means of Fourier telescopy are similar to conventional coherent images; in
particular, they are speckle patterns. For this reason, the images can be
successfully used in the methods to determine the geometric and dynamic
parameters of various objects, considered in the third chapter. In the fourth
chapter, we analyze how the dimensions of the receiving and transmitting
apertures affect the resolving power of Fourier telescopy systems, and how noise
factors and surface roughness influence image quality. In the same chapter, it is
shown that Fourier telescopy can be used to construct a panoramic laser
microscope, an instrument that provides broad-angle high-resolution imaging in
medicine and biology.18 Such a microscope can be applied for imaging extended
(~10 cm) objects with a resolution of about 1 �m.

In the fifth chapter, it is shown how one can use time background holography
for the detection and determination of parameters of moving objects that are
indistinguishable against the background, transparent, or weakly reflecting. A
fast algorithm is proposed for the detection of objects with reflectance
considerably lower than that of the surrounding background.

This book is addressed to a broad community of researchers interested in
coherent phenomena and their applications. For one's first reading, I recommend
that the reader pay attention to the numbered equations and ignore the algebra.
The reader should concentrate on the physical essence of coherent phenomena,
the description of the arrangements based on those phenomena, the figures�
which play an important role in this book�and on the enumerated conclusions to
each chapter. The introductions to each chapter and several other sections will
expose the reader to the history of the problems posed in a variety of applicable
fields. In subsequent readings, one may give special attention to the study of
particular devices or to the derivation of particular formulas. The relatively large
number of formulas is not surprising: while deriving rather simple engineering
equations for the devices based on coherent fields and images in remote sensing,
one cannot bypass the mathematical analysis of the statistical structure of fields
scattered by objects and their images.

At the same time, the mathematics used here is within the framework of
courses taught in technical institutes. Therefore, this book can be helpful not only
for researchers and engineers working in the field where coherent fields and
images in remote sensing can be used, but also for senior university and graduate
students specializing in this field. The most complicated consideration of the
statistical structure of coherent fields and images, which is presented in
Appendixes 1�3, would be interesting for the reader who wishes to understand
the particular details of the mathematical analysis of this structure.

In Appendix 4, problems connected with the coherence of fields scattered by
rough objects and with contrast of the scattered field intensity distribution are
considered. In particular, a detailed answer is given to the question, what is a
coherent field. Appendix 5 contains a semi-qualitative explanation of the physics
of speckle pattern formation in the images of rough objects. Appendix 6 contains
the most frequently used terms and comments to them.

The basic results included in this text were published previously in
proceedings and journals. However, some of the results were obtained during the
preparation of this manuscript. For this reason, not all ideas presented in the book
can be considered as equally conventional; some of them need further discussion
and development. The author is grateful to anyone who wishes to discuss them or
suggests any comments.

I would like to express special gratitude to Prof. P. Bakut, an outstanding
scientist in the field of the statistical methods of obtaining and processing
information about remote objects from the scattered radiation in the radio and
visible frequency ranges. It is our long and fruitful collaboration that stimulated
the idea of this book. I am also indebted to Prof. I. Troitsky for valuable and
fruitful discussions on the statistics of coherent fields and images, especially
about the mathematical methods of their processing.

I am grateful to V. Barinov and R. Poliakov, who carried out high-quality
experiments on the registration and processing of radiation scattered by both
stable and moving rough objects as well as on the registration of their images.
The results of their experiments are presented in the book.
I would like to thank Dr. V. Gamiz for his support of this work and valuable
discussions of the results, and Dr. M. Chekhova for help with the manuscript
preparation and valuable remarks on the statistics of coherent fields. I feel special
gratitude to Dr. E. Akopov, whose help provided the crucial condition for the
launch of the book project.

I also express my sincere gratitude to Dr. Boris Ginzburg, whose invaluable
support was a great help for overcoming obstacles in my scientific career in the
field of coherent remote sensing.
Finally, I feel especially grateful to my wife Maria, whose constant support
made this work possible.

Valery Mandrosov
January 2004
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