Owing to the advance in faster electronics and digital processing power, the past decade has seen an impressive re-emergence of digital holography. Digital holography is a topic of growing interest and it finds applications in three dimensional imaging, three-dimensional displays and systems, as well as biomedical imaging and metrology. While research in digital holography continues to be vibrant and digital holography is maturing, we find that there is a lack of textbooks in the area. The present book tries to serve this need:to promote and teach the foundations of digital holography. In addition to presenting traditional digital holography and applications in Chapters 1-4, we also discuss modern applications and techniques in digital holography such as phase-shifting holography, low-coherence holography, diffraction tomographic holography, optical scanning holography, sectioning in holography, digital holographic microscopy as well as computer-generated holography in Chapters 5-7. This book is geared towards undergraduate seniors or first-year graduate-level students in engineering and physics. The material covered is suitable for a one-semester course in Fourier optics and digital holography. The book is also useful for scientists and engineers, and for those who simply want to learn about optical image processing and digital holography.
We believe in the inclusion of MATLAB®in the textbook because digital holography relies heavily on digital computations to process holographic data. MATLAB®will help the reader grasp and visualize some of the important concepts in digital holography. The use of MATLAB®not only helps to illustrate the theoretical results, but also makes us aware of computational issues such as aliasing, zero padding, sampling, etc. that we face in implementing them. Nevertheless, this text is not about teaching MATLAB®, and some familiarity with MATLAB®is required to understand the codes.
The MATLAB®codes included in this book are all available to download from the publisher at www. cambridge. org/digitalholography.
Ting-Chung Poon would like to thank his wife, Eliza, and his children, Christina and Justine, for their love. This year is particularly special to him as Christina gave birth to a precious little one-Gussie. Jung-Ping Liu would like to thank his wife, Hui-Chu, and his parents for their understanding and encouragement.

Preface page ix

1 Wave optics 1

1.1 Maxwell’s equations and the wave equation 1

1.2 Plane waves and spherical waves 3

1.3 Scalar diffraction theory 5

      1.3.1 Fresnel diffraction 9

      1.3.2 Fraunhofer diffraction 10

      1.4 Ideal thin lens as an optical Fourier transformer 14

      1.5 Optical image processing 15

      Problems 24

      References 26

2 Fundamentals of holography 27

2.1 Photography and holography 27

2.2 Hologram as a collection of Fresnel zone plates 28

2.3 Three-dimensional holographic imaging 33

      2.3.1 Holographic magnifications 38

      2.3.2 Translational distortion 39

      2.3.3 Chromatic aberration 40

2.4 Temporal and spatial coherence 42

      2.4 1 Temporal coherence 43

      2.4.2 Coherence time and coherence length 45

      2.4.3 Some general temporal coherence considerations 46

      2.4.4 Fourier transform spectroscopy 48

      2.4.5 Spatial coherence 51

      2.4.6 Some general spatial coherence considerations 53

      Problems 56

      References 58

3 Types of holograms 59

3.1 Gabor hologram and on-axis (in-line) holography 59

3.2 Off-axis holography 61

3.3 Image hologram 64

3.4 Fresnel and Fourier holograms 68

      3.4.1 Fresnel hologram and Fourier hologram 68

      3.4.2 Lensless Fourier hologram 70

3.5 Rainbow hologram 73

Problems 78

References 78

4 Conventional digital holography 79

4.1 Sampled signal and discrete Fourier transform 79

4.2 Recording and limitations of the image sensor 89

      4.2.1 Imager size 91

      4.2.2 Pixel pitch 91

      4.2.3 Modulation transfer function 92

4.3 Digital calculations of scalar diffraction 95

      4.3.1 Angular spectrum method (ASM) 95

      4.3.2 Validity of the angular spectrum method 97

      4.3.3 Fresnel diffraction method (FDM) 99

      4.3.4 Validation of the Fresnel diffraction method 101

      4.3.5 Backward propagation 103

4.4 Optical recording of digital holograms 105

      4.4 1 Recording geometry 105

      4.4 2 Removal of the twin image and the zeroth-order light 108

4.5 Simulations of holographic recording and reconstruction 111

Problems 116

References 117

5 Digital holography: special techniques 118

5.1 Phase-shifting digital holography 118

      5.1.1 Four-step phase-shifting holography 119

      5.1.2 Three-step phase-shifting holography 120

      5.1.3 Two-step phase-shifting holography 120

      5.1.4 Phase step and phase error 122

      5.1.5 Parallel phase-shifting holography 124

5.2 Low-coherence digital holography 126

5.3 Diffraction tomographic holography 133

5.4 Optical scanning holography 137

      5.4.1 Fundamental principles 138

      5.4.2 Hologram construction and reconstruction 142

      5.4.3 Intuition on optical scanning holography 144

Problems 147

References 148

6 Applications in digital holography 151

6.1 Holographic microscopy 151

      6.1.1 Microscope-based digital holographic microscopy 151

      6.1.2 Fourier-based digital holographic microscopy 154

      6.1.3 Spherical-reference-based digital holographic

      microscopy 156

6.2 Sectioning in holography 158

6.3 Phase extraction 164

6.4 Optical contouring and deformation measurement 168

      6.4.1 Two-wavelength contouring 169

      6.4.2 Two-illumination contouring 172

      6.4.3 Deformation measurement 175

Problems 175

References 175

7 Computer-generated holography 179

7.1 The detour-phase hologram 179

7.2 The kinoform hologram 185

7.3 Iterative Fourier transform algorithm 187

7.4 Modern approach for fast calculations and holographic

information processing 189

      7.4.1 Modern approach for fast calculations 189

      7.4.2 Holographic information processing 196

7.5 Three-dimensional holographic display using spatial light

modulators 199

      7.5.1 Resolution 199

      7.5.2 Digital mask programmable hologram 201

      7.5.3 Real-time display 205

      7.5.4 Lack of SLMs capable of displaying a complex function 206

Problems 210

References 211

Index 214

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