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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

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

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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