 | Kim M.K. Digital holographic microscopy: principles, techniques, and applications. - New York; London: Springer, 2011. - xvi, 237 p.: ill. - (Springer series in optical sciences; 162). - Incl. bibl. ref. - Ind.: p.231-237. - ISBN 978-1-4419-7792-2
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1 Introduction ................................................. 1
1.1 Conventional (Analog) Holography ........................ 1
1.2 Digital Holography ...................................... 5
References
2 Diffraction and Fourier Optics .............................. 11
2.1 Fourier Transform and Mathematical Background .......... 11
2.1.1 One-Dimensional Definition ...................... 11
2.1.2 Two-Dimensional Definition ...................... 12
2.1.3 Cartesian Geometry .............................. 14
2.1.4 Cylindrical Geometry ............................ 15
2.1.5 Basic Properties of Fourier Transforms .......... 15
2.1.6 Convolution and Correlation ..................... 16
2.1.7 Some Useful Formulas ............................ 18
2.2 Scalar Diffraction Theory .............................. 19
2.3 Diffraction from a 2D Aperture ......................... 20
2.3.1 Paraxial (Fresnel) Approximation ................ 21
2.3.2 Fraunhofer Diffraction .......................... 22
2.4 Propagation of Angular Spectrum ........................ 22
2.5 Propagation Through a Lens ............................. 27
2.5.1 Fourier Transform by a Lens ..................... 27
2.5.2 Imaging by a Lens ............................... 27
2.5.3 Lens of Finite Aperture ......................... 28
References .................................................. 28
3 Principles of Holography .................................... 29
3.1 Introduction ........................................... 29
3.2 Basic Concept .......................................... 29
3.2.1 Holographic Terms ............................... 31
3.3 Holography of Plane Waves .............................. 32
3.4 Holography of Point Sources ............................ 34
3.4.1 Magnifications .................................. 36
3.4.2 Collimated References ........................... 36
3.5 Holographic Processes ................................. 37
3.5.1 Amplitude and Phase Holograms ................... 37
3.5.2 Transmission and Reflection Holograms ........... 38
3.5.3 Thin and Thick Holograms ........................ 38
3.5.4 Hologram Materials .............................. 39
3.5.5 Phase Conjugation by Photorefractive Crystals ... 40
3.5.6 Four-Wave Mixing ................................ 40
3.5.7 Spectral Hole Burning ........................... 40
3.5.8 Stimulated Photon Echo .......................... 41
References .................................................. 42
4 Basic Methods of Numerical Diffraction ...................... 43
4.1 Discrete Fourier Transform ............................. 43
4.1.1 Programming Implementation of Fourier
Transform ....................................... 46
4.2 Fresnel Transform Method ............................... 47
4.3 Huygens Convolution Method ............................. 49
4.4 Angular Spectrum Method ................................ 50
4.5 Comparison of Methods .................................. 51
References .................................................. 53
5 Digital Holography Configurations ........................... 55
5.1 General Behavior of Digital Holographic Images ......... 55
5.2 Digital Gabor Holography ............................... 60
5.3 Digital In-line Holography ............................. 61
5.4 Digital Image Plane Holography ......................... 63
5.5 Digital Fourier Holography ............................. 64
5.6 Digital Fresnel Holography ............................. 66
References .................................................. 68
6 Theoretical Studies of Digital Holography ................... 71
6.1 Digital Sampling of Hologram ........................... 71
6.2 Wigner Distribution Function ........................... 74
6.2.1 Basic Properties of WDF ......................... 74
6.2.2 Fourier Transform by a Lens ..................... 75
6.2.3 Fourier Holography .............................. 76
6.2.4 Fresnel Holography .............................. 77
6.2.5 Space-Bandwidth Product ......................... 77
6.3 Fractional-Order Fourier Transform ..................... 78
6.4 Wavelets ............................................... 80
References .................................................. 82
7 Suppression of DC and Twin-Image Terms ...................... 85
7.1 Suppression of DC Terms ................................ 85
7.2 Phase-Shifting Methods ................................. 88
7.3 Speckle Methods ........................................ 90
7.4 Filtering of Angular Spectrum .......................... 91
References .................................................. 93
8 Phase-Shifting Digital Holography ........................... 95
8.1 Basic Principles of PSDH ............................... 95
8.2 Reduced Number of Steps ................................ 97
8.2.1 Three-Step Method ............................... 97
8.2.2 Two-Step Methods ................................ 98
8.3 Unknown Phase Steps .................................... 99
8.4 Techniques of PSDH .................................... 101
8.4.1 Phase-Shifting Methods ......................... 101
8.4.2 Heterodyne Digital Holography .................. 101
8.4.3 Asynchronous Digital Holography ................ 103
8.4.4 Parallel Phase-Shifting ........................ 103
8.4.5 Fractional Talbot Effect ....................... 103
8.4.6 Spatial Phase-Shifting ......................... 104
8.5 Errors and Noise in PSDH .............................. 105
References ................................................. 105
9 Numerical Techniques of Digital Holography ................. 109
9.1 Numerical Focusing .................................... 109
9.1.1 Extended Focus ................................. 111
9.2 Pixel Resolution Control .............................. 112
9.2.1 Zero-Padding Method ............................ 112
9.2.2 Two-Step Propagation Method .................... 113
9.3 Optical Phase Unwrapping .............................. 114
9.4 Diffraction Between Tilted Planes ..................... 119
9.5 Aberration Compensation ............................... 122
References ................................................. 123
10 Special Techniques of Digital Holography ................... 129
10.1 Synthetic Aperture Methods ............................ 129
10.2 Multiplane Phase Retrieval ............................ 131
10.2.1 Noniterative Methods ........................... 131
10.2.2 Iterative Methods .............................. 134
10.2.3 Other Methods of Phase Retrieval ............... 135
10.3 Dynamic Systems ....................................... 135
10.4 Noise Reduction ....................................... 137
10.5 Nonlinear Optics ...................................... 137
10.5.1 Imaging of NLO Materials ....................... 137
10.5.2 Digital Holography by NLO Light ................ 138
10.6 Optical Parameters of Digital Holography .............. 139
10.6.1 Color Digital Holography ....................... 139
10.6.2 Polarization Digital Holography ................ 141
10.6.3 Other Wavelengths and Particles ................ 141
References ................................................. 142
11 Digital Holographie Microscopy ............................. 149
11.1 Optical Microscope Basics ............................. 149
11.1.1 Optical Configuration .......................... 149
11.1.2 Magnification .................................. 151
11.1.3 Resolution ..................................... 151
11.1.4 Objective Lenses ............................... 152
11.1.5 Eye ............................................ 152
11.1.6 Camera ......................................... 153
11.2 Optical Microscopy Techniques ......................... 153
11.2.1 Bright Field Microscopy ........................ 153
11.2.2 Dark-Field Microscopy .......................... 154
11.2.3 Zernike Phase-Contrast Microscopy .............. 154
11.2.4 Differential Interference Contrast ............. 155
11.2.5 Interference Microscopy ........................ 156
11.2.6 Polarization Microscopy ........................ 157
11.2.7 Fluorescence Microscopy ........................ 157
11.2.8 Confocal Laser Scanning Microscopy ............. 158
11.2.9 Multiphoton Excitation and Nonlinear Optical
Microscopy ..................................... 159
11.3 Digital Holographic Microscopy ........................ 159
11.3.1 Light Source ................................... 160
11.3.2 Interferometers ................................ 160
11.3.3 Camera ......................................... 163
11.3.4 Computer ....................................... 163
11.3.5 Examples ....................................... 165
11.3.6 Comparisons of Analog and Digital Holographic
Microscopy ..................................... 166
11.4 Quantitative Phase Microscopy by DHM .................. 168
11.5 Cell Microscopy and Other Applications ................ 169
11.6 Special Techniques of DHM ............................. 174
11.6.1 Total Internal Reflection Digital Holographic
Microscopy ..................................... 174
11.6.2 Multimode Microscopy from a Single Hologram .... 177
11.6.3 Dark-Field DHM ................................. 179
11.6.4 DH Interferometer with a Beam-Splitter Cube .... 179
11.6.5 Lens-Free On-Chip Holographic Microscopy ....... 180
11.7 Other Methods of Quantitative Phase Microscopy ........ 181
11.7.1 Fourier Phase Microscopy ....................... 181
11.7.2 Hilbert Phase Microscopy ....................... 181
11.7.3 Diffraction Phase Microscopy ................... 182
11.7.4 Quantitative DIC ............................... 183
11.7.5 Spiral Phase-Contrast Microscopy ............... 184
11.7.6 Low-Coherence Interference Microscopy .......... 185
References ................................................. 187
12 Low-Coherence and Tomographic Techniques ................... 191
12.1 Techniques of Low-Coherence Digital Holographic
Microscopy ............................................ 191
12.1.1 Low-Coherence Sources .......................... 192
12.1.2 Rotating Ground Glass .......................... 193
12.1.3 Fresnel Incoherent Correlation Holography ...... 195
12.1.4 Achromatic Fringe System ....................... 197
12.1.5 Triangular Interferometer ...................... 198
12.1.6 Conoscopic Holography .......................... 199
12.2 Optical Scanning Holography ........................... 200
12.2.1 Basic Principles of OSH ........................ 200
12.2.2 Imaging Characteristics of OSH ................. 201
12.2.3 Related Techniques and Applications ............ 203
12.3 Optical Coherence Tomography .......................... 204
12.3.1 Time-Domain OCT ................................ 204
12.3.2 Fourier-Domain OCT ............................. 205
12.3.3 Doppler OCT .................................... 206
12.3.4 Optical Coherence Microscopy ................... 206
12.3.5 Phase-Sensitive OCT ............................ 208
12.3.6 Differential Phase-Contrast OCT ................ 208
12.3.7 Phase-Dispersion Microscopy .................... 208
12.3.8 Phase-Referenced Interferometry ................ 209
12.4 Full-Field Optical Coherence Tomography ............... 209
12.4.1 Principles of FFOCT ............................ 209
12.4.2 Techniques and Applications of FFOCT ........... 212
12.4.3 Light-in-Flight Digital Holography ............. 215
12.5 Digital Interference Holography ....................... 215
12.5.1 Principles of DIH .............................. 215
12.5.2 Related Techniques and Applications of DIH ..... 220
12.6 Tomography ............................................ 221
12.6.1 Optical Projection Tomography .................. 221
12.6.2 Optical Diffraction Tomography ................. 222
12.6.3 Holographic Optical Coherence Imaging .......... 223
12.6.4 Turbid Imaging ................................. 223
References ................................................. 225
Index ......................................................... 231
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