Preface ................................................... XIII
List of Contributors ...................................... XVII
1 Radial Speckle Interferometry and Applications ............... 1
Armando Albertazzi Conçalves Jr. and Matias R. Viotti
1.1 Introduction ............................................ 1
1.2 Out-of-Plane Radial Measurement ......................... 2
1.2.1 Radial Deformation Measurement of Short
Internal Cylinders ............................... 3
1.2.2 Radial Deformation Measurement of Long Internal
Cylinders ........................................ 7
1.2.3 Radial Deformation Measurement of External
Cylinders ....................................... 11
1.3 In-Plane Measurement ................................... 13
1.3.1 Configuration Using Conical Mirrors ............. 17
1.3.2 Configuration Using a Diffractive Optical
Element ......................................... 19
1.4 Applications ........................................... 24
1.4.1 Translation and Mechanical Stress
Measurements .................................... 24
1.4.2 Residual Stress Measurement ..................... 27
1.5 Conclusions ............................................ 33
References .................................................. 34
2 Depth-Resolved Displacement Field Measurement ............... 37
Jonathan M. Huntley and Pablo D. Ruiz
2.1 Introduction ........................................... 37
2.2 Low-Coherence Electronic Speckle Pattern
Interferometry ......................................... 39
2.3 Wavelength Scanning Interferometry ..................... 43
2.3.1 WSI with a Single Scattering Surface ............ 44
2.3.1.1 Fourier Transform for Measurement of
Optical Path Length .................... 46
2.3.1.2 Fourier Transform for Calculation of
Interference Phase ..................... 47
2.3.1.3 Range and Resolution of Optical Path
Difference Measurement
2.3.1.4 Determination of Scattering Point
Location ............................... 49
2.3.1.5 Gauge Volume and Displacement
Sensitivity ............................ 52
2.3.2 WSI with Volume Scatterers ...................... 54
2.3.2.1 Proof-of-Principle Experiments: Two
Scattering Layers ...................... 57
2.3.3 Comparison of WSI with LCSI ..................... 59
2.4 Spectral Optical Coherence Tomography .................. 60
2.4.1 Phase Contrast SOCT for 2D Out-of-Plane
Displacement Field Measurement .................. 61
2.4.2 PC-SOCT for 2D In-Plane and Out-of-Plane
Displacement Field Measurement .................. 66
2.4.3 Hyperspectral Interferometry for 3D Surface
Profilometry .................................... 69
2.5 Tilt Scanning Interferometry ........................... 71
2.5.1 Depth-Dependent Phase Shift Introduced by
a Tilting Wavefront ............................. 72
2.5.2 Extraction of the Scattered Amplitude
Distribution .................................... 75
2.5.3 Depth-Resolved Displacements .................... 77
2.5.4 Gauge Volume, Depth Range, and Displacement
Sensitivity ..................................... 79
2.5.5 Experimental Implementation ..................... 80
2.6 Depth-Resolved Techniques Viewed as Linear Filtering
Operations ............................................. 83
2.6.1 Methods Viewed as Linear Filtering Operations ... 84
2.6.2 Relationship Between W(K) and Spatial
Resolution ...................................... 85
2.6.3 Relationship Between W(K) and Displacement
Sensitivity ..................................... 86
2.6.4 Ewald Sphere for a Wavelength Scanning
Interferometer .................................. 87
2.6.5 Ewald Sphere for a Tilt Scanning
Interferometer .................................. 89
2.6.6 Comparison of Spatial Resolution for WSI and
TSI ............................................. 89
2.7 Phase Unwrapping in Three Dimensions ................... 91
2.7.1 Phase Singularities in Two-Dimensional Phase
Data ............................................ 91
2.7.2 Phase Singularity Loops in Three-Dimensional
Phase Data ...................................... 93
2.7.3 3D Phase Unwrapping Algorithm ................... 95
2.7.4 Remaining Ambiguities ........................... 96
2.7.5 Example: Dynamic Deformation of Carbon-Fiber
Composite Panel ................................. 96
2.8 Concluding Remarks ..................................... 98
References .................................................. 99
3 Single-Image Interferogram Demodulation .................... 105
Manuel Servin, Julio Estrada, and Antonio Quiroga
3.1 Introduction .......................................... 105
3.1.1 Spatial Carrier Frequency Techniques ........... 105
3.1.2 Spatial Demodulation Without Carrier ........... 106
3.2 The Fourier Spatial Demodulating Method ............... 106
3.3 Linear Spatial Phase Shifting ......................... 109
3.4 Nonlinear Spatial Phase Shifting ...................... 113
3.5 Regularized Phase Tracking ............................ 115
3.6 Local Adaptive Robust Quadrature Filters .............. 118
3.7 Single Interferogram Demodulation Using Fringe
Orientation ........................................... 122
3.7.1 Orientation in Interferogram Processing ........ 122
3.7.2 Fringe Orientation and Fringe Direction ........ 124
3.7.3 Orientation Computation ........................ 126
3.7.3.1 Gradient-Based Orientation
Computation ........................... 127
3.7.3.2 Plane Fit Orientation Calculation ..... 129
3.7.3.3 Minimum Directional Derivative ........ 131
3.7.4 Direction Computation .......................... 132
3.7.4.1 Regularized Phase Tracking Direction
Estimation ............................ 132
3.7.4.2 Vector Field-Regularized Direction
Estimation ............................ 134
3.8 Quadrature Operators .................................. 135
3.8.1 Phase Demodulation of ID Interferograms ........ 135
3.8.2 Phase Demodulation from a Single
Interferogram: the Vortex Transform ............ 136
3.8.3 Vortex Transform-Based Orientation
Computation .................................... 138
3.8.4 The General n-Dimensional Quadrature
Transform ...................................... 139
3.9 2D Steering of ID Phase Shifting Algorithms ........... 142
3.10 Conclusions 143 References ............................ 144
4 Phase Evaluation in Temporal Speckle Pattern
Interferometry Using Time-Frequency Methods ................ 147
Alejandro Federico and Guillermo H. Kaufmann
4.1 Introduction .......................................... 147
4.2 The Temporal Speckle Pattern Interferometry Signal .... 148
4.3 The Temporal Fourier Transform Method ................. 151
4.4 Time-Frequency Representations of the TSPI Signals .... 153
4.4.1 Preliminaries .................................. 154
4.4.1.1 The Asymptotic Signal and the
Exponential Model ..................... 154
4.4.1.2 Fidelity Measures ..................... 155
4.4.2 The Windowed Fourier Transform ................. 156
4.4.3 The Wavelet Transform .......................... 160
4.4.3.1 Evaluation of the Ridge of
a Wavelet Transform ................... 163
4.4.3.2 Applications of the Morlet Transform
Analysis in TSPI and Other Related
Techniques ............................ 166
4.4.3.3 The Chirped Wavelet Transform ......... 168
4.4.3.4 Other Wavelet Transforms .............. 171
4.4.4 The Quadratic Time-Frequency Distribution ...... 172
4.4.5 The Empirical Mode Decomposition and the
Hilbert Transform .............................. 176
4.4.5.1 The Empirical Mode Decomposition
Method ................................ 178
4.4.5.2 The Hilbert Transform ................. 179
4.4.6 The Generalized S-Transform .................... 182
4.4.7 Two- and Three-Dimensional Approaches .......... 188
4.4.7.1 The Windowed Fourier Transform
Method ................................ 189
4.4.7.2 Wavelet Transform Methods ............. 190
4.5 Concluding Remarks .................................... 199
References ................................................. 200
5 Optical Vortex Metrology ................................... 207
Wei Wang, Steen C. Hanson, and Mitsuo Takeda
5.1 Introduction .......................................... 207
5.2 Speckle and Optical Vortices .......................... 207
5.3 Core Structure of Optical Vortices .................... 209
5.4 Principle of Optical Vortex Metrology ................. 211
5.4.1 Complex Signal Representation of a Speckle-
Like Pattern ................................... 211
5.4.2 Principle of Optical Vortex Metrology .......... 213
5.5 Some Applications ..................................... 214
5.5.1 Nanometric Displacement Measurement ............ 214
5.5.2 Linear and Angular Encoder ..................... 217
5.5.3 Fluid Mechanical Analysis ...................... 224
5.5.4 Biological Kinematic Analysis .................. 230
5.6 Conclusion ............................................ 235
References ................................................. 236
6 Speckle Coding for Optical and Digital Data Security
Applications ............................................... 239
Arvind Kumar, Madan Singh, and Kehar Singh
6.1 Introduction .......................................... 239
6.2 Double Random Fourier Plane Encoding .................. 242
6.2.1 Influence of Coded Image Perturbations, Noise
Robustness, and SNR ............................ 245
6.3 Variants of the DRPE and Various Other Encryption
Techniques ............................................ 245
6.3.1 Fresnel and Fractional Fourier Transform
Domain Encoding ................................ 245
6.3.2 Color Image Encoding and Digital Simulation/
Virtual Optics-Based Techniques ................ 246
6.3.3 Phase Retrieval- and Polarization-Based
Techniques ..................................... 246
6.3.4 Interference and Joint Transform Correlator
Architecture-Based Techniques .................. 246
6.3.5 Fully Phase Encryption Techniques and
Encrypted Holographic Memory ................... 246
6.4 Attacks against Random Encoding ....................... 247
6.5 Speckle Coding for Optical and Digital Data
Security .............................................. 247
6.6 Encryption Using a Sandwich Phase Mask Made of
Normal Speckle Patterns ............................... 248
6.6.1 Theoretical Analysis ........................... 248
6.6.2 Description of the Experimental Work ........... 250
6.6.2.1 Preparation of Speckle Phase Masks .... 250
6.6.2.2 Making a Sandwich Phase Mask .......... 251
6.6.2.3 Technique for Easy Alignment of
the Constituent Speckle Phase Masks ... 251
6.6.2.4 Experimental Results .................. 252
6.6.2.5 Computer Simulation ................... 253
6.7 Optical Encryption Using a Sandwich Phase Mask Made
of Elongated Speckle Patterns ......................... 256
6.7.1 Preparation of the Elongated Speckle Phase
Mask ........................................... 256
6.7.2 Description of the Method ...................... 256
6.7.3 Computer Simulation Results .................... 257
6.8 Speckles for Multiplexing in Encryption and
Decryption ............................................ 262
6.9 Multiplexing in Encryption Using Apertures in the FT
Plane ................................................. 264
6.9.1 Methodology .................................... 264
6.9.2 Computer Simulation ............................ 266
6.9.3 Effect of Aperture Size on the Encryption and
Decryption ..................................... 267
6.9.4 Effect of Increasing the Number and Size of
the Apertures .................................. 267
6.9.5 Multiplexing in Encryption Using Circular
Apertures ...................................... 271
6.9.6 Multiplexing in Encryption Using Square
Apertures ...................................... 271
6.10 Multiplexing by In-Plane Rotation of Sandwich Phase
Diffuser and Aperture Systems ......................... 272
6.10.1 Methodology .................................... 273
6.10.2 Effect on Decrypted Images of Rotation of One
of the Constituent Phase Diffusers ............. 274
6.10.3 Multiplexing in Encryption Using the Rotation
of the RPM Rsm ................................. 277
6.10.4 Multiplexing by Using Set of Apertures and
Angular Rotation of Rsm ........................ 278
6.11 Speckles in Digital Fresnel Field Encryption .......... 282
6.11.1 Digital Recording and Numerical
Reconstruction of an Off-Axis Fresnel
Hologram ....................................... 282
6.11.2 Digital Fresnel Field Encryption ............... 283
6.11.2.1 Digital Encryption of Fresnel Field
Using Single Random Phase Encoding .... 284
6.11.2.2 Direct Decryption of 3D Object
Information from Encrypted Fresnel
Field ................................. 284
6.11.3 Experiment ..................................... 286
6.11.4 Results and Discussion ......................... 288
6.11.4.1 Discussion of Encryption and
Decryption by the Proposed Method ..... 288
6.11.4.2 Some General Remarks on Digital
Encryption of Holographic
Information ........................... 290
6.12 Conclusions ........................................... 291
References ................................................. 292
Index ...................................................... 301
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