Synopses & Reviews
"This book is an introduction to digital optics, presenting the basic concepts necessary to master working in the field on a professional level. It represents an attempt to unify two allied directions which have appeared at the boundary between optics and computer science, digital image processing and digital holography. It reflects the integration of computers into modern optical and imaging systems. The book is aimed at comprehensive exposition of fundamentals of digital optics, or digital processing of optical and similar analog signals such as images, holograms, interferograms, etc. Distinctive features of the exposition are consecutive observance of the correspondence principle between analog signal transformations and their discrete representations, and emphasis on fast computational algorithms and adaptive processing methods. A number of new contributions make the book a unique supplement to the existing literature on digital signal and image processing. Among these are a new approach to characterizing digital filters, a modified discrete representation of Fourier and Fresnel integral transforms, new efficient computational algorithms for signal convolution, spectral analysis, interpolation and generating 2-D random signals, a unified representation of fast orthogonal transform design of local adaptive linear and rank filters for image restoration, enhancement and object location. The book also discusses solutions of a broad circle of practical problems of digital optics including automated diagnosis of interference in optical signals and images, image restoration and enhancement, object location in images, and the digital synthesis of holograms. Please note: In Figures 8.12 on page 230, a) and b) are reversed in the book"
Synopsis
1.1 Digital Optics as a Subject Improvement of the quality of optical devices has always been the central task of experimental optics. In modern terms, improvements in sensitivity and resolution have equated higher quality with greater informational throughput. For most of today's applications, optics and electronics have, in essence, solved the problem of generating high quality pictures with great informational ca- pacity. Effective use of the enormous amount of information contained in the images necessitates processing pictures, holograms, and interferograms. The manner in which information might be extracted from optical entities has be- come a topic of current interest. The informational aspects of optical signals and systems might serve as a basis for attacking this question by making use of information theory and signal communication theory, and by enlisting modern tools and methods for data processing (the most important and powerful of which are those of digi- tal computation). Exploiting modern advances in electronics has allowed new wavelength ranges and new kinds of radiation to be used in optics. Comput- ers have extended our knowledge of the informational essence of radiation. Thus, computerized optical devices enhance not only the optical capabilities of sight, but also its analytical capabilities as well, thus opening qualitatively new horizons to all the areas in which optical devices have found application.
Table of Contents
"Chapter
1: Introduction
1.1 Digital Optics as a Subject
1.2 Contents of this Book
Chapter
2: Elements of Signal Theory
2.1 Mathematics Models of Optical Signals
2.2 integral Representation of Signals
2.3 Signal Transform and Models of optical Signals
Chapter
3: Digital Representation of Optical Signals
3.1 Principals of Signal Discretization and Quantizing
3.2 Discretization by Rastering and Sampling Theorems
3.3 Optimal Element-Wise Quantization
3.4 Application Problems in Rastering and Quantization of Images, Holograms and Interferograms
3.5 Principles of Image Coding Techniques
Chapter
4: Digital Representation of Signal Transforms
4.1 Principles for the Digital Representation of Signal Transformations
4.2 Digital Filters
4.3 Discrete Fourier Transforms
4.4 Discrete Fresnel Transform
4.5 Discrete Hartley Transform
Chapter
5: Efficient Computational Procedures for Digital Filtering
5.1 Methods for Computing Discrete Fourier Transforms Fast Fourier Transform Algorithm
5.2 Using Discrete Fourier Transformations in Computing the Convolution, Interpolation, and Spectral Analysis of the Signals
5.3 Digital Filtering Algorithms in a Space Domain
Chapter
6: Discrete Orthogonal Transforms and Fast Algorithms in a Matrix Representation
6.1 Class of Discrete Transforms and Fast Algorithms
6.2 Elements of Matrix Tools for Derivation of Fast Algorithms
6.3 Algorithms of Fast Fourier Transforms (FFT) in Matrix Representation
6.4 An Overview of Other Orthogonal Transform Fast Algorithm
6.5 Quantized Discrete Fourier Transform and its Fast Algorithm
Chapter
7: Digital Statistical Simulation and Measurements
7.1 Digital Statistical Models of Random Images and Wave Fields
7.2 EWT Models and Generation of Spatially Homogeneous and Inhomogeneous Sequences with a Given Distribution Law
7.3 LF Model and Generation of Spatial Homogeneous and Inhomogeneous Sequences with Gaussian Distribution and a Given Correlation Function
7.4 Examples of More Sophisticated Algorithmic Models: Evolutionary Algorithmic Models and Deterministic Chaos
7.5 Measurement of Statistical Characteristics of Signals
7.6 Measuring the Parameters of Random Interfaces in Images, Holograms, and Interferograms
Chapter
8: Linear and Rank Adaptive Filters for Picture Processing
8.1 Linear and Rank Filters as Structural Units in Picture Processing
8.2 Local Criteria of Processing Quality
8.3 Linear Locally Adaptive Filters
8.
3.1 Optimal Scalar Filters
8.
3.2 Locally Adaptive Linear Filters for Supressing Additive Signal-Independent Noise
8.
3.3 Correction of Linear Distribution
8.
3.4 Linear Filters for Picture Preparation
8.
3.5 Verification and Application Examples of Adaptive Linear Filters
8.4 Rank Algorithms
8.
4.1 Background and Historical Overview
8.
4.2 Rank Algorithms for Picture Smoothing
8.
4.3 Enhancement and Extraction of Details in Pictures
8.
4.4 Localization of Picture Details and their Edges
8.
4.5 Verification and Examples of Applications of Rank Filters
8.5 Implementation of Adaptive Linear and Rank Filters
Chapter
9: Adaptive Linear Filters for Objects Localization in Pictures
9.0 Background
9.1 The Accuracy and Reliability of Two-Dimensional Object Localization on a Plane
9.
1.1 Localization of a Single Object in the Presence of Additive White Gaussian Noise: Optimal Coordinate Estimator and Two Types of Estimation Errors
9.
1.2 Localization of a Single Object in the Presence of Additive Gaussian Noise: Potential Accuracy of Measurement of Coordinates
9.
1.3 Localization of a Single Object in the Presence of Additive Gaussian Noise: Measurement Accuracy for Non-Optimal Estimator. Localization in Non-White Noise
9.
1.4 Optimal Localization in Color (Multicomponent) Pictures
9.
1.5 Localization of a Single Object in the Presence of Additive Gaussian Noise: Reliability of Measurements of Coordinates
9.
1.6 Localization Reliability in the Presence of Additive White Gaussian Noise and Multiple Outside Objects
9.2 Localization of Objects on a Complex Background with Minimum Anomalous Errors
9.
2.1 Formulation of the Problem
9.
2.2 Localization of a Precisely Known Object Based on a Spatially Homogeneous Optimality Criterion
9.
2.3 Localization of Inexactly Known Objects (Spatially homogeneous Criterion)
9.
2.4 Localization in the Case of a Spatially Inhomogeneous Criterion
9.
2.5 Localization on Blurred Pictures
9.
2.6 Detection Characteristics
9.
2.7 Phase-only, Binary Phase-only, Minimum Average Correlation Energy, Entropy Optimized, and Other Filters for Optical Pattern Recognition. Reliable Localization and Picture Contours
9.
2.8 Selection of the Reference Objects from the Standpoint of Localization Reliability
9.
2.9 Detection and Filtration of Pulse Interfaces
Chapter
10: Synthesis of Holograms
10.1 Mathematical Model
10.2 Discrete Representation of Fourier and Fresnel holograms
10.3 Methods and Means for Recording Synthesized holograms
10.4 Reconstruction of Synthesized Holograms
Index"