### Spie Press Book

Optical Correlation Techniques and ApplicationsFormat | Member Price | Non-Member Price |
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Pages: 286

ISBN: 9780819465344

Volume: PM168

- Preface ix
- References x
- 1 Introduction to Linear Singular Optics 1
- I.I. Mokhun
- 1.1 Introduction 1
- 1.2 Basics of Scalar Singular Optics 2
- 1.2.1 Phase vortices 2
- 1.2.2 Topological charge and index of singular points: elementary topological reactions 4
- 1.2.3 Experimental observation and identification of vortices in scalar fields 7
- 1.2.4 Generation of vortices using computer-generated holograms 8
- 1.3 Vortices and the Phase Structure of a Scalar Field 8
- 1.3.1 Sign principle 8
- 1.3.2 "Breathing" of phase speckles 10
- 1.3.3 Birth of vortices 11
- 1.3.4 Appearance of wavefront dislocations as a result of interference of waves with simple phase surfaces 13
- 1.3.5 Topological indices of the field of intensity: extrema and "correlation" of phase and intensity 18
- 1.3.6 Vortex nets: phase skeleton of a scalar field 23
- 1.4 Singularities of a Vector Field 31
- 1.4.1 Disclinations: polarization singularities 31
- 1.4.2 Vortices of phase difference: sign principle for a vector field 36
- 1.4.3 "Correlation" of intensity and polarization of the vector field 49
- 1.4.4 Interconnection of the component vortices and C points 51
- 1.4.5 Elementary polarization structures and elementary polarization singularities of vector fields 57
- 1.4.6 Fine structure and averaged polarization characteristics of inhomogeneous vector fields 66
- 1.4.7 "Stokes formalism" for polarization singularites: "Stokes vortices" 83
- 1.5 Singularities of the Poynting Vector and the Structure of Optical Fields 85
- 1.5.1 General Assumptions: components of the Poynting vector 87
- 1.5.2 Singularities of the Poynting vector in scalar fields 88
- 1.5.3 Singularities of the Poynting vector at vector fields 94
- Appendix A Wavefront Approximation 115
- Appendix B Fourier Image of Isotropic Vortex 121
- Appendix C Poynting Vector The Paraxial Approximation 122
- References 125
- 2 Optical Correlation Diagnostics of Phase Singularities in Polychromatic Fields 133
- P.V. Polyanskii
- 2.1 Introduction 133
- 2.2 Manifestations of Phase Singularities on the Strength of Scattering in White Light 134
- 2.2.1 Structural interference coloring 134
- 2.2.2 Interference coloring as a peculiar effect of singular optics 135
- 2.2.3 Experiment: the blue moon is tamed 142
- 2.3 Phase Singularities in Polychromatic Laguerre-Gaussian Modes (Rainbow Vortices) and the Young's Diagnostics of Them 144
- 2.4 Optical Correlation Diagnostics of Phase Singularities in Polychromatic Speckle Fields 151
- 2.4.1 Interferometric diagnostics of spectral phase singularities in polychromatic speckle fields 151
- 2.4.2 Chromascopic processing of polychromatic speckle fields 155
- References 163
- 3 Optical Correlation Approaches in Rough Surface Characterization 167
- O.V. Angelsky and P.P. Maksimyak
- 3.1 Introduction 167
- 3.2 Random Surfaces 170
- 3.2.1 Random phase screen model 170
- 3.2.2 Computer simulation 171
- 3.2.3 Experimental study 177
- 3.2.4 Optical correlation technique for characterizing of rough surfaces 181
- 3.3 Fractal Surfaces 189
- 3.3.1 Fractal approach 189
- 3.3.2 Simulation of rough surfaces 190
- 3.4 Interferometric Study of Phase Singularities in a Field Scattered by Rough Surfaces 194
- 3.4.1 Diffraction of optical radiation on cylindrical and spherical surfaces 194
- 3.4.2 Interferometric study of phase singularities in a field scattered by rough surfaces 200
- 3.5 Conclusions 207
- References 208
- 4 Statistical and Fractal Structure of Biological Tissue Mueller Matrix Images 213
- O.V. Angelsky, V.P. Pishak, A.G. Ushenko and Yu.A. Ushenko
- 4.1 Techniques for Diagnostics of Phase-Inhomogeneous Layer Structure 213
- 4.2 Stokes Parametric Description of Light Polarization 219
- 4.3 Statistical Analysis of Biological Tissue Polarization Properties 223
- 4.4 Self-Similarity Degree of Biological Tissue Polarization Properties 226
- 4.5 Mueller Matrix Method in Diagnostics of Pathological Changes of Biological Tissue 232
- 4.6 First- Through Fourth-Order Statistics of Biological Tissue Mueller Matrix Images 238
- 4.7 Diagnostic Possibilities of Statistic Analysis of Biological Tissue Mueller Matrix Images 247
- 4.8 Self-Similar (Fractal) 2D Mueller Matrix Structure of Biological Tissue 249
- 4.9 Reconstruction of the Orientation Structure of Biological Tissue Birefringent Architectonics Using their Mueller Matrix Images 257
- 4.10 Summary 262
- References 263
- Index 267

#### Preface

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 "optics of observable quantities." The essence of this methodology, which is accepted by the authors of this book, follows:

- 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;
- 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;
- 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 "from fundamentals to applications."

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

March 2007

**References**

1. Born, M., and Wolf, E., Principles of Optics, 7th ed., Pergamon, New York (1999).

2. Rytov, S.M., Kravtsov, Yu.A., and Tatarsky, V.I., Principles of Statistical Radiophysics, Springer, Berlin (1989).

3. Angelsky, O.V., Hanson, S.G., and Maksimyak, P.P., Use of the Optical Correlation Techniques for Characterizing Scattering Objects and Media, SPIE Press, Bellingham (1999).

4. Swartzlander, Jr., G.S., Singular Optics/Optical Vortex References, www.u.arizona.edu/~grovers/SO/so.html.

5. Nye, J.F., Natural Focusing and Fine Structure of Light: Caustics and Wave Dislocations, Institute of Physics Publishing, Bristol (1999).

6. Soskin, M.S., and Vasnetsov, M.V., "Singular optics," Prog. Opt., 42, pp. 219-276 (2001).

7. Handbook of Coherent Domain Optical Methods, Vols. 1 and 2, Tuchin, V.V., Ed., Kluwer Academic Publishers, Boston (2004).

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