| | Contents | |
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| | Preface | XI |
| 1 | Introduction | 1 |
| 1.1 | Scope of the Book | 1 |
| 1.2 | Historical Developments | 3 |
| 1.3 | Holographic Interferometry as a Measurement Tool | 6 |
| 2 | Optical Foundations of Holography | 9 |
| 2.1 | Light Waves | 9 |
| 2.1.1 | Solutions of the Wave Equation | 9 |
| 2.1.2 | Intensity | 12 |
| 2.2 | Interference of Light | 13 |
| 2.2.1 | Interference of Two Waves with Equal Frequency | 13 |
| 2.2.2 | Interference of Two Waves with Different Frequencies | 14 |
| 2.2.3 | Interference of Two Waves with Different Amplitudes | 15 |
| 2.3 | Coherence | 16 |
| 2.3.1 | Temporal Coherence | 17 |
| 2.3.2 | Spatial Coherence | 19 |
| 2.4 | Scalar Diffraction Theory | 21 |
| 2.4.1 | Fresnel-Kirchhoff Diffraction Formula | 21 |
| 2.4.2 | Fresnel Approximation | 23 |
| 2.4.3 | Fraunhofer Approximation | 25 |
| 2.4.4 | Thin Lens | 26 |
| 2.4.5 | Propagation of Light Waves as a Linear System | 29 |
| 2.5 | Speckles | 30 |
| 2.5.1 | Statistics of Speckle Intensity and Phase | 30 |
| 2.5.2 | Speckle Size | 34 |
| 2.6 | Holographic Recording and Optical Reconstruction | 36 |
| 2.6.1 | Hologram Recording | 36 |
| 2.6.2 | Optical Reconstruction of a Wave Field | 40 |
| 2.6.3 | Holographic Imaging Equations | 44 |
| 2.6.4 | Types of Holograms | 47 |
| 2.7 | Elements of the Holographic Setup | 53 |
| 2.7.1 | Laser | 53 |
| 2.7.2 | Recording Media | 58 |
| 2.7.3 | Optical Components | 61 |
| 2.7.4 | Beam Modulating Components | 62 |
| 2.8 | CCD-and CMOS-Arrays | 65 |
| 2.8.1 | CCD Concept | 66 |
| 2.8.2 | CCD Array Performance Parameters | 70 |
| 2.8.3 | CMOS Image Sensors | 73 |
| 2.8.4 | Spatial Sampling with CCD-Arrays | 74 |
| 2.8.5 | Color Still Cameras | 76 |
| 3 | Digital Recording and Numerical Reconstruction of Wave Fields | 81 |
| 3.1 | Digital Recording of Holograms | 81 |
| 3.1.1 | CCD Recording and Sampling | 81 |
| 3.1.2 | Reduction of the Imaging Angle | 84 |
| 3.1.3 | Reference Waves | 89 |
| 3.2 | Numerical Reconstruction by the Fresnel Transform | 93 |
| 3.2.1 | Wave Field Reconstruction by the Finite Discrete Fresnel Transform | 93 |
| 3.2.2 | Real and Virtual Image | 97 |
| 3.2.3 | Digital Fourier Transform Holography | 100 |
| 3.2.4 | The D.C.-Term of the Fresnel Transform | 102 |
| 3.2.5 | Suppression of the D.C.-Term | 105 |
| 3.2.6 | Suppression of the Twin Image | 107 |
| 3.2.7 | Variation of the Reference Wave | 108 |
| 3.2.8 | Anamorphic Correction | 114 |
| 3.3 | Numerical Reconstruction by the Convolution Approach | 115 |
| 3.3.1 | The Diffraction Integral as a Convolution | 115 |
| 3.3.2 | Size of the Image Field | 117 |
| 3.3.3 | Shifting of the Image Field | 118 |
| 3.3.4 | Scaling of the Image Field | 120 |
| 3.4 | Further Numerical Reconstruction Methods | 124 |
| 3.4.1 | Phase-Shifting Digital Holography | 124 |
| 3.4.2 | Local Amplitude and Phase Retrieval | 129 |
| 3.4.3 | Wavelet Approach to Numerical Reconstruction | 132 |
| 3.4.4 | Comparison of Reconstruction Methods | 134 |
| 3.4.5 | Hologram Recording Using Consumer Cameras | 139 |
| 3.5 | Wave-Optics Analysis of Digital Holography | 140 |
| 3.5.1 | Frequency Analysis of Digital Holography with Reconstruction by Fresnel Transform | 141 |
| 3.5.2 | Frequency Analysis of Digital Holography with Reconstruction by Convolution | 148 |
| 3.5.3 | The Transfer Function as a Filter | 151 |
| 3.6 | Non-Interferometric Applications of Digital Holography | 159 |
| 3.6.1 | Particle Analysis by Digital Holography | 160 |
| 3.6.2 | Microscopy by Digital Holography | 169 |
| 3.6.3 | Data Encryption with Digital Holography | 180 |
| 4 | Holographic Interferometry | 185 |
| 4.1 | Generation of Holographic Interference Patterns | 186 |
| 4.1.1 | Recording and Reconstruction of a Double Exposure Holographic Interferogram | 186 |
| 4.1.2 | Recording and Reconstruction of a Real-Time Holographic Inter ferogram | 188 |
| 4.1.3 | Time Average Holography | 190 |
| 4.1.4 | Interference Phase Variation Due to Deformation | 191 |
| 4.1.5 | Interference Phase Variation Due to Refractive Index Variation | 194 |
| 4.1.6 | Computer Simulation of Holographic Interference Patterns | 196 |
| 4.2 | Variations of the Sensitivity Vectors | 198 |
| 4.2.1 | Optimization of the Holographic Arrangement | 198 |
| 4.2.2 | Two Reference Beam Holographic Interferometry | 201 |
| 4.3 | Fringe Localization | 203 |
| 4.3.1 | Fringe Formation with Diffusely Scattering Surfaces | 203 |
| 4.3.2 | Fringe Localization with Collimated Illumination | 206 |
| 4.3.3 | Fringe Localization with Spherical Wave Illumination | 211 |
| 4.3.4 | Fringe Localization with Phase Objects | 211 |
| 4.3.5 | Observer Projection Theorem | 214 |
| 4.4 | Holographic Interferometric Measurements | 215 |
| 4.4.1 | Qualitative Evaluation of Holographic Interferograms | 215 |
| 4.4.2 | Holographically Measurable Physical Quantities | 216 |
| 4.4.3 | Loading of the Objects | 218 |
| 5 | Quantitative Determination of the Interference Phase | 221 |
| 5.1 | Role of Interference Phase | 221 |
| 5.1.1 | Sign Ambiguity | 222 |
| 5.1.2 | Absolute Phase Problem | 224 |
| 5.2 | Disturbances of Holographic Interferograms | 225 |
| 5.2.1 | Varying Background Illumination | 226 |
| 5.2.2 | Electronic Noise | 226 |
| 5.2.3 | Speckle Decorrelation | 227 |
| 5.2.4 | Digitization and Quantization | 227 |
| 5.2.5 | Environmental Distortions | 228 |
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| 5.3 | Fringe Skeletonizing | 229 |
| 5.3.1 | Pattern Preprocessing. | 229 |
| 5.3.2 | Fringe Skeletonizing by Segmentation | 231 |
| 5.3.3 | Skeletonizing by Fringe Tracking | 233 |
| 5.3.4 | Other Fringe Skeletonizing Methods | 233 |
| 5.3.5 | Fringe Numbering and Integration | 234 |
| 5.4 | Temporal Heterodyning | 235 |
| 5.4.1 | Principle of Temporal Heterodyning | 235 |
| 5.4.2 | Technical Realization of Temporal Heterodyning | 237 |
| 5.4.3 | Errors of Temporal Heterodyning | 238 |
| 5.4.4 | Experimental Application of Temporal Heterodyning | 240 |
| 5.5 | Phase Sampling Evaluation | 242 |
| 5.5.1 | Phase Shifting and Phase Stepping | 243 |
| 5.5.2 | Solution of the Phase Sampling Equations with Known Phase Shifts | 245 |
| 5.5.3 | Solution of the Phase Sampling Equations with Unknown Phase Shifts | 248 |
| 5.5.4 | Application of Phase Shift Evaluation Methods | 251 |
| 5.5.5 | Discussion of Phase Shift Evaluation Methods | 255 |
| 5.6 | Fourier Transform Evaluation | 256 |
| 5.6.1 | Principle of the Fourier Transform Evaluation Method | 256 |
| 5.6.2 | Noise Reduction by Spatial Filtering | 258 |
| 5.6.3 | Spatial Filtering and Sign Ambiguity | 260 |
| 5.6.4 | Fourier Transform Evaluation of Phase Shifted Interferograms | 261 |
| 5.6.5 | Spatial Heterodyning | 263 |
| 5.6.6 | Spatial Synchronous Detection | 265 |
| 5.7 | Dynamic Evaluation | 266 |
| 5.7.1 | Principles of Dynamic Evaluation | 266 |
| 5.7.2 | Dynamic Evaluation by a Scanning Reference Beam | 268 |
| 5.8 | Digital Holographic Interferometry | 269 |
| 5.8.1 | Digital Phase Subtraction | 269 |
| 5.8.2 | Enhancement of Interference Phase Images by Digital Filtering | 273 |
| 5.8.3 | Evaluation of Series of Holograms | 275 |
| 5.8.4 | Compensation of Motion Components | 278 |
| 5.8.5 | Multiplexed Holograms Discriminated in Depth | 280 |
| 5.8.6 | Multiplexed Holograms with Discrimination by Partial Spectra | 282 |
| 5.9 | Interference Phase Demodulation | 287 |
| 5.9.1 | Prerequisites for Interference Phase Demodulation | 287 |
| 5.9.2 | Path-Dependent Interference Phase Demodulation | 288 |
| 5.9.3 | Path-Independent Interference Phase Demodulation | 289 |
| 5.9.4 | Interference Phase Demodulation by Cellular Automata | 292 |
| 5.9.5 | Further Approaches to Interference Phase Demodulation | 294 |
| 6 | Processing of the Interference Phase | 297 |
| 6.1 | Displacement Determination | 297 |
| 6.1.1 | Displacement Determination with Known Reference Displacement | 298 |
| 6.1.2 | Displacement Determination with Unknown Reference Displacement | 299 |
| 6.1.3 | Elimination of Overall Displacement | 301 |
| 6.1.4 | Non-Vibration Isolated Objects | 303 |
| 6.2 | The Sensitivity Matrix | 306 |
| 6.2.1 | Determination of the Sensitivity Vectors | 306 |
| 6.2.2 | Correction of Perspective Distortion | 307 |
| 6.2.3 | Condition of the Sensitivity Matrix | 310 |
| 6.3 | Holographic Strain and Stress Analysis | 311 |
| 6.3.1 | Definition of Elastomechanical Parameters | 311 |
| 6.3.2 | Beams and Plates | 314 |
| 6.3.3 | Numerical Differentiation | 317 |
| 6.3.4 | Fringe Vector Theory | 318 |
| 6.4 | Hybrid Methods | 321 |
| 6.4.1 | Finite Element Methods and Holographic Interferometry | 321 |
| 6.4.2 | Boundary Element Methods and Holographic Interferometry | 322 |
| 6.4.3 | Fracture Mechanics | 322 |
| 6.5 | Vibration Analysis | 323 |
| 6.5.1 | Surface Vibrations | 323 |
| 6.5.2 | Stroboscopic and Real-Time Holographic Interferometry | 325 |
| 6.5.3 | Time Average Holographic Interferometry | 326 |
| 6.5.4 | Temporally Modulated Reference Wave | 327 |
| 6.5.5 | Numerical Analysis of Time Average Holograms | 331 |
| 6.5.6 | Vibration Analysis by Digital Holography | 332 |
| 6.6 | Holographic Contouring | 333 |
| 6.6.1 | Contouring by Wavelength Differences | 333 |
| 6.6.2 | Contouring by Refractive Index Variation | 336 |
| 6.6.3 | Contouring by Varied Illumination Direction | 337 |
| 6.6.4 | Contouring by Light-in-Flight recording | 338 |
| 6.7 | Contour Measurement by Digital Holography | 339 |
| 6.7.1 | Contouring by Digital Holographic Interferometry | 340 |
| 6.7.2 | Contouring by Digital Multi-Wavelength Holography | 343 |
| 6.7.3 | Holographic Contouring by Digital Light-in-Flight Measurement | 345 |
| 6.8 | Comparative Holographic Interferometry | 349 |
| 6.8.1 | Principles of Comparative Holographic Interferometry | 349 |
| 6.8.2 | Digital Comparative Holography | 353 |
| 6.9 | Measurement Range Extension | 356 |
| 6.9.1 | Two-Wavelength Holographic Interferometry | 357 |
| 6.9.2 | Holographic Moiré | 358 |
| 6.9.3 | Holographic Interferometry at Rotating Objects | 360 |
| 6.9.4 | Endoscopic Holographic Interferometry | 364 |
| 6.9.5 | Desensitized Holographic Interferometer | 365 |
| 6.10 | Refractive Index Fields in Transparent Media | 366 |
| 6.10.1 | Refraction of Phase Objects | 366 |
| 6.10.2 | Physical Quantities Affecting the Refractive Index Field | 370 |
| 6.10.3 | Two-Dimensional Refractive Index Fields | 374 |
| 6.10.4 | Holographic Interferometry of Circular Symmetric Refractive Index Fields | 376 |
| 6.10.5 | Multidirectional Recording of Asymmetric Refractive Index Fields | 377 |
| 6.10.6 | Tomographic Reconstruction in the Refractionless Limit | 378 |
| 6.10.7 | Tomographic Reconstruction of Strongly Refracting Fields | 382 |
| 6.10.8 | Analysis of Transparent Media with Digital Holography | 384 |
| 6.10.9 | Resonance Holographic Interferometry | 385 |
| 6.11 | Defect Detection by Holographic Non-Destructive Testing | 387 |
| 6.11.1 | Classification of Defects | 387 |
| 6.11.2 | Data Reduction for Automatic Qualitative Evaluation | 389 |
| 6.11.3 | Neural Network Approach to Qualitative Evaluation | 393 |
| 7 | Speckle Metrology | 399 |
| 7.1 | Speckle Photography | 399 |
| 7.2 | Electronic and Digital Speckle Interferometry | 400 |
| 7.3 | Electro-optic Holography | 404 |
| 7.4 | Speckle Shearography | 405 |
| | Appendix | |
| A | Signal Processing Fundamentals | 409 |
| A.1 | Overview | 409 |
| A.2 | Definition of the Fourier Transform | 410 |
| A.3 | Interpretation of the Fourier Transform | 412 |
| A.4 | Properties of the Fourier Transform | 415 |
| A.5 | Linear Systems | 416 |
| A.6 | Fourier Analysis of Sampled Functions | 420 |
| A.7 | The Sampling Theorem and Data Truncation Effects | 423 |
| A.8 | Interpolation and Resampling | 427 |
| A.9 | Two-Dimensional Image Processing | 429 |
| A.10 | The Fast Fourier Transform | 434 |
| A.11 | Fast Fourier Transform for N 2n | 437 |
| A.12 | Cosine and Hartley Transform | 439 |
| A.13 | The Chirp Function and the Fresnel Transform | 441 |
| B | Computer Aided Tomography | 447 |
| B.1 | Mathematical Preliminaries | 447 |
| B.2 | The Generalized Projection Theorem | 448 |
| B.3 | Reconstruction by Filtered Backprojection | 451 |
| B.4 | Practical Implementation of Filtered Backprojection | 453 |
| B.5 | Algebraic Reconstruction Techniques | 454 |
| C | Bessel Functions | 459 |
| | Bibliography | 463 |
| | Author Index | 513 |
| | Subject Index | 527 |
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