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Spie Press Book

Use of Optical Correlation Techniques for Characterizing Scattering Objects and Media
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Book Description

This monograph examines the possibilities for diagnostics of light-scattering objects and media by utilizing the properties of coherent optical radiation. Special emphasis is placed on diagnostics of rough surfaces. Ideas formulated in classical work on statistical radiophysics and optics have been adapted to diagnostic applications. The text includes unique techniques and unconventional methods aimed at obtaining the maximum information available.

Book Details

Date Published: 2 November 1999
Pages: 204
ISBN: 9780819434906
Volume: PM71

Table of Contents
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ACKNOWLEDGMENTS
FOREWORD
INTRODUCTION 1
Chapter 1. RANDOM NON-UNIFORM MEDIA AND FIELDS 7
1.1 Determinate Objects and Random Non-uniform Media 7
1.1.1 Random fields 7
1.1.2 Continuous random non-uniform media 12
1.1.3 Characterization of rough surfaces 17
1.1.4 Dispersive media 21
1.2 Propagation of Random Waves in an Unbounded Uniform Medium 22
1.3 Transmission of a Plane Wave Through a Random Phase Screen 24
1.4 Scattering of Optical Radiation by Dispersive Media 30
1.4.1 Conventional light scattering 31
1.4.1.1 Rayleigh (point) scatterer, 31
1.4.1.2 Rayleigh-Gans-Debye (RGD) scatterer 32
1.4.1.3 Mie scatterer 33
1.4.1.4 Dilute suspension of identical RGD particles 33
1.4.1.5 The effects of polydispersity 34
1.4.2 Dynamic light scattering 34
1.4.2.1 Dilute suspension of identical spheres 35
1.4.2.2 Polydispersity 36
References 37
Chapter 2. ROUGH SURFACES USING LIGHT-SCATTERING METHODS 40
2.1 Scattering by a Rough Surface 41
2.1.1 The Kirchhoff approximation (scalar theory) 43
2.1.2 Small perturbation method 46
2.1.2.1 Scalar theory 46
2.1.2.2 Vector theory 47
2.2 Determining Roughness from Scattering Measurements 48
2.2.1 Total Integrated Scattering 49
2.2.2 Angle-resolved scattering 51
2.2.3 Limits of applicability of light-scattering methods (ARS, TIS) for measuring surface roughness 55
2.2.4 Bidirectional reflectance distribution function 65
2.2.5 Heterodyne techniques for surface roughness diagnostics 66
References 68
Chapter 3. STRUCTURE DIAGNOSTICS OF PHASE OBJECTS WITH SMALL PHASE VARIANCE 72
3.1 Infinitely Extended Screen Approximation 73
3.2 Correlation Methods for Structure Diagnostics of RPO 75
3.3 Measurement of the roughness element height distribution function of slightly rough surfaces 85
3.4 Studies of Optical Crystals with Refractive Index Inhomogeneities 89
3.5 Diagnostics of Slightly Rough Surfaces 93
3.5.1 Low-reflectance surfaces 93
3.5.2 Measurement of arbitrarily shaped surfaces 96
3.5.3 Surfaces with roughness scales comparable to 98
3.5.4 Roughness measurements on plane-parallel plates 100
3.5.5 Optical correlation studies of turbulence in a liquid 102
REFERENCES 107
Chapter 4. STOCHASTIC APPROACH TO DIAGNOSTICS OF SCATTERING OBJECTS 111
4.1 Stochastic Characteristics of Objects and Fields 113
4.2 Diffraction on Simple 1D Phase Structures 115
4.3 Fractal Classification 118
4.4 The Possibility for Remote Diagnostics of Koch Fractals 121
4.4.1 Angle-averaged intensity 122
4.4.2 Band-averaged intensity 123
4.4.3 The applicability of autocorrelation for measuring a field's dimension 128
4.4.4 Error sources connected with optical measurement of the fractal dimension 135
4.5 Diagnostics of Random Phase Inhomogeneous Objects 136
4.5.1 Diagnostics of slightly rough surfaces 137
4.5.2 Diagnostics of large-scale roughness 142
REFERENCES 150
Chapter 5. STRUCTURE AND DYNAMICAL DIAGNOSTICS OF DISPERSE MEDIA 155
5.1 Optical Correlation Methods for Sizing and Measuring Concentration of Light-Scattering Particles 155
5.2 Optical correlation systems for Reducing diagnostic Response Time in Disperse Media 164
5.3 Transformation of the Longitudinal Coherence Function of a Field Propagating in a Light-Scattering Medium 169
5.4 Holographic Methods for Dynamic and Structure Diagnostics of Light-Scattering Particles 177
References 185
Index 189

Foreword

Optical methods are known to provide some of the most important information obtained in studying the surrounding world. The amplitude, phase, polarization, spectral, angular, and correlation characteristics of optical fields may carry vital information on the objects of interest. Modern fast-acting optical processing systems are capable of collecting information on diagnostically important parameters with high efficiency. This is primarily achieved by means of parallel processing of large amounts of data and by taking advantage of analog optical computing devices. The problem of metrology of random optical fields, such as speckle fields resulting from the interaction of laser beams with a random phase object, has a significant place in optical diagnostics and optical recognition studies. These problems range from astronomy to industrial quality control.

In the present monograph, consideration is given to interference, polarization interference, and holographic correlometry of amplitude and phase parameters of random optical fields for the purpose of subsequent diagnostics of the appropriate objects and media. An attempt is made to show the possibilities for a diagnostics of light-scattering objects and media provided by utilization of the properties of coherent optical radiation. The diagnostics of rough surfaces, being of great importance for many branches of industry, is particularly emphasized throughout the monograph.

An important feature of this monograph is the adaptation of the ideas formulated in classical work on statistical radiophysics and optics to diagnostic applications. At the same time, the proposed diagnostic techniques are aimed at obtaining the maximum information on objects, such as the roughness height (or phase increment) distribution functions for random phase objects, size distribution functions for dispersive systems, or root-mean-square velocity distribution functions for Brownian particles. Some of the diagnostic methods considered are unconventional. The proposed group of unique techniques for interference measurement of statistical moments of the field amplitude and phase up to the third and fourth orders constitutes a particular class of statistical methods for interference correlometry of optical fields. Most of the methods discussed result from physical modeling.


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