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 with a 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 Laue who first described this phenomenon and studied it for the case of scattering by multiple particles. A bibliography of his fundamental papers on the theory of coherence, including speckle optics, can be found in the books by Mandel and Wolf and Goodman. 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. One of the first works that used speckle pattern formation analysis for light scattered by rough surfaces was by Rigden and Gordon. One of the first works to analyze the dynamic speckle pattern was by Anisimov et al.

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. 6â9. In the 1980s, a consistent statistical description of coherent phenomena was developed, and the statistical characteristics of coherent fields scattered by rough objects as well as coherent images of those objects were studied in detail. Due to further development of this subject, the terms âcoherent fieldâ and âcoherent imageâ (meaning, respectively, a field scattered by a rough object and by its image) 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.

At present, the use of coherent fields and images in remote sensing is increasingly drawing 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. For example, coherent remote sensing can be very helpful when either the scattered radiation is seriously distorted because of propagation through an inhomogeneous (turbulent) medium or remote objects with low reflection, or when 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*. This technique, which enables exact imaging of remote objects in a turbulent atmosphere, is proposed for the ambitious project GLINT, 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 pairs 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, only time background holography provides a practical solution. 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.

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 uses the time averaging method in environmental monitoring, specifically for detecting clusters of pollution particlesâincluding completely absorbing particlesâand determining their concentration, average size, and average velocity.

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, which are 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. Such a microscope can be applied for imaging extended (Ì 10 cm) objects with a resolution of about 1 Î¼m.

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 figuresâwhich play an important role in this bookâand 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 1â3, 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.

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*

© 2004 Society of Photo-Optical Instrumentation Engineers