Holography and Coherent Optics

1 Introduction.- § 1.1 Principle of Holography. Interference of Light.- § 1.2 Three-Dimensional Nature of an Image. Parallax.- § 1.3 Plane Hologram.- § 1.4 Diffraction of Light in a Plane Hologram.- § 1.5 Coherence of Light.- § 1.6 Light Sources for Holography.- § 1.7 History of Holography.- 2 Optical Signal and Its Transformations.- § 2.1 Complex Signal in Optics.- § 2.2 Fourier Transformation.- § 2.3 Properties of Fourier Transformation.- § 2.4 Typical Fourier Transformations and Standard Notation for Commonly Occurring Functions.- § 2.5 Optical Systems Performing Fourier Transformation.- § 2.6 Convolution and Its Properties.- § 2.7 Correlation and Its Properties.- § 2.8 Convolution and Correlation in a Plane.- § 2.9 Optical System for Convolution and Cross-Correlation Operations.- § 2.10 Scalar Products of Functions.- § 2.11 Generalized Functions or Distributions.- § 2.12 Examples of Generalized Functions.- § 2.13 Fourier Transformation of Generalized Functions.- § 2.14 Convolution of Generalized Functions.- § 2.15 Fourier Transformation and Convolution of Functions in Multidimensional Spaces.- § 2.16 Delta Functions in a Plane.- § 2.17 Fourier Transformation of Radial Functions Defined in a Plane.- § 2.18 Hankel Transformation.- § 2.19 Truncated Fourier Transformation.- § 2.20 Hilbert Transformation.- § 2.21 Linear Filter.- § 2.22 Linear Two-Dimensional Filter.- § 2.23 Dispersion Relationships and Causality Principle.- § 2.24 Relationship Between Fourier, Hilbert, and Hankel Transformations.- § 2.25 Modulation of a Signal.- § 2.26 Fresnel Transformation.- § 2.27 Relationship Between Fresnel and Fourier Transformations.- § 2.28 Fresnel Sandwich.- § 2.29 Bickel-Bowman System.- § 2.30 Auxiliary Parameter in Fresnel Transformation.- § 2.31 Dirac and Sampling Transformations.- § 2.32 Comparison of Integral Transformations Used in Optics.- 3 Random Signal.- § 3.1 Random Function and Random Signal.- § 3.2 Stationary Random Signal.- § 3.3 Correlation Functions.- § 3.4 Fourier Transformation of Cross-Correlation Functions.- § 3.5 Average Power.- § 3.6 Energy Spectrum and Its Physical Meaning.- § 3.7 Random Noise and Interference.- § 3.8 Correlative Methods for Suppression of Noise and Interference.- § 3.9 Detection of a Signal of Known Waveform.- § 3.10 Indeterminacy Function.- § 3.11 Reconstruction of a Function From Its Autocorrelation.- 4 Coherence of Light.- § 4.1 Mutual Coherence Function.- § 4.2 Properties of an Analytic Signal and of Mutual Coherence Function.- § 4.3 Emission of Light by Atoms.- § 4.4 Temporal and Spatial Coherence.- § 4.5 Temporal Coherence.- § 4.6 Interference of Waves of Different Frequencies.- § 4.7 Generalization of Mutual Coherence Function to Interference of Light of Different Frequencies.- § 4.8 Transverse and Longitudinal Spatial Coherence.- § 4.9 Incoherent Extended Source Generating Spatially Coherent Light.- § 4.10 Relationship Between Coherence and Diffraction of Light.- § 4.11 Coherence Determination and Measurement Methods.- § 4.12 Relationship Between Coherence and Emission Spectrum.- § 4.13 Wave Equation of Mutual Coherence Function.- § 4.14 Integral Representation of Mutual Coherence Function.- § 4.15 Measurement of Coherence of a Laser Beam.- § 4.16 Coherence and Diffusing Screens.- 5 Information Structure of Optical Signals.- § 5.1 Introduction.- § 5.2 Indeterminacy Principle.- § 5.3 Classical Representation of a Signal in Information Theory.- § 5.4 Elementary Signal.- § 5.5 Determinate Function With a Bounded Spectrum.- § 5.6 Properties of Sampling Function.- § 5.7 Determinate Function of Finite Duration.- § 5.8 One-Dimensional Functions With Finite Spectra.- § 5.9 Two-Dimensional Functions With Finite Spectra.- § 5.10 Sampling Theorem in Optics.- § 5.11 Illumination Matrix.- § 5.12 Intensity Matrix.- § 5.13 Image and Detector Matrices.- § 5.14 Temporal Sampling Points.- 6 Holography.- § 6.1 Introduction.- § 6.2 Basic Holographic System.- § 6.3 Development of Photographic Emulsions.- § 6.4 Relationship Between an Object and a Light Wave Reaching Entrance Pupil.- § 6.5 Holograms of Very Simple Objects.- § 6.6 Holographic Microscope.- § 6.7 Relation Between an Object and a Light Wave Reaching Entrance Pupil for Arbitrary Illumination.- § 6.8 Theory of Most General Holographic System.- § 6.9 Alternative Representations of Spherical Fresnel Transform and Its Fourier Transform.- § 6.10 Rigorous Classification of Holograms.- § 6.11 Most Typical Systems for Obtaining Different Types of Hologram.- § 6.12 Absorption and Relief-Phase Holograms.- § 6.13 Amplitude Synthesis of Images.- § 6.14 Correlative Compensation of Extended Reference Source Effects.- § 6.15 Theory of Correlative Compensation of Extended Source Effects.- § 6.16 Holograms of Phase Objects.- § 6.17 Information Capacity of a Photographic Emulsion and Its Use in Holography.- § 6.18 Some Features of Amplitude Synthesis of Images by Holography.- § 6.19 Synthesized Holograms.- § 6.20 Coherence in Holography.- § 6.21 Intensity Holograms Obtained Under Incoherent Illumination Conditions.- § 6.22 Holograms Formed with a Fresnel Zone Plate.- § 6.23 Achromatic Holography.- § 6.24 Volume Holograms.- § 6.25 Vector Field Holograms of Two Polarization States.- § 6.26 Ghost Images.- § 6.27 Polychromatic Images.- § 6.28 Aberrations in Holography.- § 6.29 Generalized Hologram and Principle of a Reference Object.- § 6.30 Stroboscopic Holograms.- 7 Optical Information Processing Methods.- § 7.1 Increasing Importance of Optics in Computing Technology.- § 7.2 Fourier Transformation in a Coherent Optical System.- § 7.3 Linear Optical Filter.- § 7.4 Principle of Spatial Filtering of Images.- § 7.5 Optical Correlator.- § 7.6 Convolution and Correlation in Coherent Optical Systems.- § 7.7 Image Recognition.- § 7.8 Binary Matched Filter.- § 7.9 Main Components of a Coherent Optical System.- § 7.10 Generalized Fresnel Function.- § 7.11 Optical Stage.- § 7.12 Imaging Condition.- § 7.13 Condition for Obtaining a Fourier Transform.- § 7.14 Change of Scale in a Fourier Transform.- § 7.15 Multistage Optical Systems.- § 7.16 Multichannel Systems.- § 7.17 Spatial Invariance of Linear Optical Filter.- § 7.18 Suppression of Noise by Spatial Differentiation of Optical Signals.- § 7.19 Permissible Displacements of a Filter.- § 7.20 Some Optical Systems Used in Preparation of Matched Filters.- § 7.21 File of Matched Filters.- § 7.22 Capacity of Matched-Filter File.- § 7.23 Incoherent Optical Information Processing Systems.- § 7.24 Two-Dimensional Translator.- § 7.25 Temporal Holographic Filter.- § 7.26 Correlative Comparison of Two Signals.- § 7.27 Redistribution of Information Degrees of Freedom.- § 7.28 Operation of a Coherent Side-Looking Radar Station.- § 7.29 Theory of Coherent Side-Looking Radar.- § 7.30 Analysis of Data in a Coherent Radar Frame.- § 7.31 A Posteriori Image Processing Apodization.- § 7.32 Removal of Spherical Aberration of Lenses.- Optical Computing, by George W. Stroke.- Retrieval of Good Images from Accidentally Blurred Photographs, by George W. Stroke, Maurice Halioua, Venugopal Srinivasan, and Morimasa Shinoda.- Image Improvement and Three-Dimensional Reconstruction Using Holographic Image Processing by George W. Stroke, Maurice Halioua, Friedrich Thon, and Dieter H. Willasch.