 | Optical correlation: techniques and applications / ed. by Angelsky O.V. - Bellingham, Wash.: SPIE, 2007. - xi, 270 p.: ill., ports. - ISBN 978-0-819-46534-4
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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
С 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 В Fourier Image of Isotropic Vortex ........... 121
Appendix С 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.R 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
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