Theoretical Statistical Optics

This monograph overviews classic and recent developments in theoretical statistical optics in connection with stationary and non-stationary (pulsed) optical source characterization and modeling, discusses various phenomena occurring with random light propagating in free space, on its interaction with optical systems, extended media and particulate collections. The text includes scalar, beam-like and general electromagnetic treatment of light. A brief statistical description of four fundamental experiments relating to random light: spatial and temporal field interference, intensity interferometry and phase conjugation, is also included in order to relate the analytical descriptions with practical observations.Rigorous mathematical methods for statistical manipulation of light sources useful for remote shaping of its various average properties, enhanced image resolution, optimized transmission in random media and for other applications are introduced. For illustration of efficient ways for manipulation of light polarization the generalized Stokes-Mueller calculus is applied for description of interaction of beam-like fields with classic and currently popular devices of polarization optics, including a spatial light modulator.Random light plays a special role in the image formation process. Three imaging modalities including the classic intensity-based system with structured source correlations, the polarization-based imaging system and the ghost interference approach are discussed in detail.Theoretical aspects of potential scattering of light from weakly scattering media are considered under a very broad range of assumptions: scalar/electromagnetic incident light, deterministic/random light/media, single/particulate media. Then, problems and methods in light characterization on interaction with extended, turbulent-like natural media, such as the Earth's atmosphere, oceans and soft bio-tissues that are currently widely used for communication, remote sensing and imaging purposes in these media, are provided.

This book discusses statistical methods that are useful for treating problems in modern optics, and the application of these methods to solving a variety of such problems This book covers a variety of statistical problems in optics, including both theory and applications. The text covers the necessary background in statistics, statistical properties of light waves of various types, the theory of partial coherence and its applications, imaging with partially coherent light, atmospheric degradations of images, and noise limitations in the detection of light. New topics have been introduced in the second edition, including: Analysis of the Vander Pol oscillator model of laser light Coverage on coherence tomography and coherence multiplexing of fiber sensors An expansion of the chapter on imaging with partially coherent light, including several new examples An expanded section on speckle and its properties New sections on the cross-spectrum and bispectrum techniques for obtaining images free from atmospheric distortions A new section on imaging through atmospheric turbulence using coherent light The addition of the effects of “read noise” to the discussions of limitations encountered in detecting very weak optical signals A number of new problems and many new references have been added Statistical Optics, Second Edition is written for researchers and engineering students interested in optics, physicists and chemists, as well as graduate level courses in a University Engineering or Physics Department.

Authoritative introduction covers the role of Green's function in mathematical physics, essential differences between spatial and time filters, fundamental relations of paraxial optics, and effects of aberration terms on image formation. "An excellent book; well-organized, and well-written." — Journal of the Optical Society of America. 80 illustrations. 1963 edition.

Scientists and engineers in optics are increasingly confronted with problems that are of a random nature and that require a working knowledge of probability and statistics for their solution. This book develops these subjects within the context of optics, using a problem-solving approach. All methods are explicitly derived and can be traced back to three simple axioms given at the outset. This third edition contains many new applications to optical and physical phenomena, including a method of exactly estimating probability laws.

This is the first of a two-volume presentation on current research problems in quantum optics, and will serve as a standard reference in the field for many years to come. The book provides an introduction to the methods of quantum statistical mechanics used in quantum optics and their application to the quantum theories of the single-mode laser and optical bistability. The generalized representations of Drummond and Gardiner are discussed together with the more standard methods for deriving Fokker-Planck equations.

This new edition incorporates corrections of all known typographical errors in the first edition, as well as some more substantive changes. Chief among the latter is the addition of Chap. 17, on methods of estimation. As with the rest of the text, most applications and examples cited in the new chapter are from the optical perspective. The intention behind this new chapter is to empower the optical researcher with a yet broader range of research tools. Certainly a basic knowledge of estimation methods should be among these. In particular, the sections on likelihood theory and Fisher information prepare readers for the problems of optical parameter estimation and probability law estimation. Physicists and optical scientists might find this material particularly useful, since the subject of Fisher information is generally not covered in standard physical science curricula. Since the words "statistical optics" are prominent in the title of this book, their meaning needs to be clarified. There is a general tendency to overly emphasize the statistics of photons as the sine qua non of statistical optics. In view is taken, which equally emphasizes the random medium this text a wider that surrounds the photon, be it a photographic emulsion, the turbulent atmo sphere, a vibrating lens holder, etc. Also included are random interpretations of ostensibly deterministic phenomena, such as the Hurter-Driffield (H and D) curve of photography. Such a "random interpretation" sometimes breaks new ground, as in Chap.

A basic skill in probability is practically demanded nowadays in many bran ches of optics, especially in image science. On the other hand, there is no text presently available that develops probability, and its companion fields stochastic processes and statistics, from the optical perspective. [Short of a book, a chapter was recently written for this purpose; see B. R. Frieden (ed. ): The Computer in Optical Research, Topics in Applied Physics, Vol. 41 (Springer, Berlin, Heidelberg, New York 1980) Chap. 3] Most standard texts either use illustrative examples and problems from electrical engineering or from the life sciences. The present book is meant to remedy this situation, by teaching probability with the specific needs of the optical researcher in mind. Virtually all the illustrative examples and applications of the theory are from image science and other fields of optics. One might say that photons have replaced electrons in nearly all considera tions here. We hope, in this manner, to make the learning of probability a pleasant and absorbing experience for optical workers. Some of the remaining applications are from information theory, a con cept which complements image science in particular. As will be seen, there are numerous tie-ins between the two concepts. Students will be adequately prepared for the material in this book if they have had a course in calculus, and know the basics of matrix manipulation.

New ideas on the mathematical foundations of quantum mechanics, related to the theory of quantum measurement, as well as the emergence of quantum optics, quantum electronics and optical communications have shown that the statistical structure of quantum mechanics deserves special investigation. In the meantime it has become a mature subject. In this book, the author, himself a leading researcher in this field, surveys the basic principles and results of the theory, concentrating on mathematically precise formulations. Special attention is given to the measurement dynamics. The presentation is pragmatic, concentrating on the ideas and their motivation. For detailed proofs, the readers, researchers and graduate students, are referred to the extensively documented literature.