This monograph is devoted to the selected applications of the optical correlation approaches and techniques in diverse problems of modern optics. We use the term correlation optics to designate a (nonquantum) wave statistical optics of partially coherent and partially (nonuniformly) polarized random light fields based on correlation functions and the higher-order statistical moments of the parameters used for describing optical fields. The conceptual background of the optical correlation approach correlates with the Wolf's methodology of the âoptics of observable quantities.â The essence of this methodology, which is accepted by the authors of this book, follows: â correlation functions and other statistical moments of the field directly characterize the interconnection of light oscillations in two spatial-temporal points, and this interconnection can be evaluated in a quantitative manner (can be measured) using observable quantities; â statistical moments of the field are governed by the wave equations that elaborate the peculiarities of their transformation under the propagation of radiation, and gives reliable ground for the solution for the inverse problem of optics, including diagnostics of the statistical parameters of random objects; â the mathematical apparatus used in the theory of partial coherence is well adopted to the theory of partial polarization, where interconnection between the orthogonal components of the vector electromagnetic field in different spatial points and in different instants can be characterized in terms of correlations, i.e., in terms of the corresponding statistical moments. Among observable quantities, which are used throughout the book, one meets visibility and the phase of interference fringes, Stokes parameters, Poynting vector, etc.
Note, that the road from the fundamental concepts and theories to the practical applications is not straightforward. The interconnection of the methodology and the technology is often mediated by sophisticated computer simulation and experimental techniques, now undergoing impressive progress in the study of correlation and polarization structures of the field into near zone (near-field optics), looking for the mechanisms of formation of randomly inhomogeneous speckle fields (both monochromatic and polychromatic) that follow from the presence of phase singularities, and elaborating the feasibilities for manipulating microobjects using optical radiation, etc. The gap between theory and practice is partly filled in studies reported at seven International Conferences on Correlation Optics, which have been held biannually in Chernivtsi since 1993 (see SPIE Proc. Volumes 2108, 2647, 3317, 3904, 4607, 5477, and 6254).
This monograph develops, to a certain extent, the experimental optical correlation approaches used for diagnostics of rough surfaces and random media represented in an earlier monograph. However, this book is not an updated issue of Ref. 3, being enriched with quite novel concepts and techniques rooted first in singular optics. Of course, statistical and fractal approaches, which lie as the basis of consideration in Ref. 3, are also developed in the present book. The general structure of the book is âfrom fundamentals to applications.â
Chapter 1 is devoted to linear singular optics of monochromatic, fully spatially coherent light fields. The originality of this consideration (with respect to the well-known book by J. Nye and its seminal review) is defined by the results of investigations in the field of singular optics that are integrated and highlighted using a single general concept. This concept can be formulated as the nets of singularities with various parameters of the electromagnetic field that are interconnected and comprehensively determine the behaviour of the field, at least qualitatively, at each point of the field. This basic concept is substantiated both for the conventional singularities, such as optical vortices and polarization singularities, and for less investigated singularities inherent the Poynting Vector.
Chapter 2 contains the results of recent investigations of phase singularities in polychromatic (white-light) optical fields. The key original concept of this chapter is that the phase singularities are intrinsic to not only the common complex amplitude of monochromatic and fully spatially coherent light fields, but also to any complex parameter of the field, some of which are unconventional (to say, the strength of scattering). The modern experimental techniques for detecting and diagnosing phase singularities at a partially coherent optical field are represented and compared for the first time in the literature on the basis of general criteria for solving technical problems.
Chapter 3 deals with optical correlation techniques for diagnostics of rough surfaces. In addition to the review of early results based on the classical model of a random phase screen, we discuss in detail new approaches that follow from the fractal model of surface roughness and account for the phase singularities in the field scattered by rough surfaces. The relevancy of these results is that they provide important extension of the optical correlation diagnostic techniques for the case of surfaces with large inhomogeneities as well as give new diagnostic criteria.
Chapter 4 represents the results of a study on Mueller-matrix images of biological tissues for finding out the statistical and fractal structures of such images. This approach develops earlier achievements in this field summarized in Ref. 7. It serves the important practical goal of using the optical correlation techniques for early (preclinical) detection and diagnostics of pathological changes of diverse biological tissues. We demonstrate the ways in which some widespread diseases can be optically diagnosed at early stages.
Oleg V. Angelsky
© 2007 Society of Photo-Optical Instrumentation Engineers