Application of Optical Fourier Transforms

Application of Optical Fourier Transforms

1st Edition - May 28, 1982

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  • Editor: Henry Stark
  • eBook ISBN: 9780323145930

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Applications of Optical Fourier Transforms is a 12-chapter text that discusses the significant achievements in Fourier optics. The opening chapters discuss the Fourier transform property of a lens, the theory and applications of complex spatial filters, and their application to signal detection, character recognition, water pollution monitoring, and other pattern recognition problems. These topics are followed by a computation of the statistical characteristics of the Fourier irradiance patterns and the hybrid systems that combine the best of optics, analog electronics, and digital computers to solve problems. The subsequent chapters examine the pulse-Doppler and chirp signals, the significance of signal-to-noise power spectrum in the information content measurement of photographic film and in image quality determinations. This text also considers the application of nonlinear systems and their components to Fourier optics. The discussions then shift to the application of Fourier methods to the study of spatial information transmission through the human visual system, as well as the application of coherent techniques to vision research. The concluding chapters deal with the well-known pattern recognition problems related to the digital signal processing community. These chapters also look into a general theoretical model of light field propagation from input to output. This book will be of value to optical scientists and vision researchers.

Table of Contents

  • List of Contributors



    Chapter 1 Theory and Measurement of the Optical Fourier Transform

    1.1 Plane Waves

    1.2 The Diffraction Integral

    1.3 Fourier Transform Property of a Lens

    1.4 The Sample Spectrum

    1.5 Stability and Fidelity

    1.6 Optimum Smoothing of the Spectrum with a Finite-Size Lag Window

    1.7 Smoothing with a Finite-Bandwidth Frequency Window

    1.8 An Optimum Finite-Bandwidth Frequency Window

    1.9 Estimating the Spectrum at Low Spatial Frequencies and at the Origin

    1.10 Extrapolating the Fourier Spectrum of Spatially Bounded Objects

    1.11 Conclusion


    Chapter 2 Pattern Recognition via Complex Spatial Filtering


    2.1 Historical Overview

    2.2 Complex Spatial Filtering

    2.3 Pattern Recognition via Matched Filtering

    2.4 Applications of Spatial Filtering

    2.5 Conclusion


    Chapter 3 Particle Identification and Counting by Fourier-Optical Pattern Recognition


    3.1 The Fourier-Optical Approach

    3.2 The Fourier Spectrum of Randomly Assorted Scatterers

    3.3 Statistical Characteristics of Irradiance Patterns

    3.4 Data Inversion: General Considerations

    3.5 Applicability of the Model; Stability of Estimates

    3.6 Implementing the Inversion: Hybrid Methods

    3.7 Implementing the Inversion Optically

    3.8 Experimental Investigations and Results

    3.9 Summary and Conclusions


    Chapter 4 Signal Processing Using Hybrid Systems


    4.1 A Generalized Hybrid System and Its Design Considerations

    4.2 Hybrid Systems Based on Optical Power Spectrum Measurements

    4.3 Hybrid Systems Based on Spatial Filtering

    4.4 Hybrid Systems Using Incoherent Light

    4.5 Summary



    Chapter 5 Fourier Optics and Radar Signal Processing

    5.1 Introduction

    5.2 Radar Signal Processing

    5.3 Optical Processors for Radar Signals


    Chapter 6 Application of Optical Power Spectra to Photographic Image Measurement

    6.1 Introduction

    6.2 Power Spectral Measurements

    6.3 Experimental Configuration

    6.4 Generation of the SNPS

    6.5 Effect of Film Tube and Sampling Area

    6.6 Description of Granularity

    6.7 Conclusion


    Chapter 7 Fourier Optics and SAW Devices

    7.1 Introduction

    7.2 Surface Acousto-Optic Interaction

    7.3 Applications

    7.4 Conclusion


    Chapter 8 Space-Variant Optical Systems and Processing

    8.1 Introduction

    8.2 Representation and Analysis of Space-Variant Linear Systems

    8.3 Examples of Space Variance

    8.4 Systems for Space-Variant Processing of 1-D Signals

    8.5 Systems for Space-Variant Processing of 2-D Signals

    8.6 Concluding Remarks


    Chapter 9 Fourier Optics in Nonlinear Signal Processing

    9.1 Introduction

    9.2 Characteristics of Nonlinear Systems

    9.3 Applications of Nonlinearities

    9.4 Point Nonlinear Systems

    9.5 Composite Nonlinear Systems

    9.6 Summary


    Chapter 10 Optical Information Processing and the Human Visual System

    10.1 Spatial Information Processing in the Visual System

    10.2 Measurement of the Contrast Sensitivity Function of the Visual Pathway by Generation of Sinusoidal Patterns on the Retina

    10.3 Measurement of the Optics of the Eye by Generation of a Speckle Pattern on the Retina

    10.4 Applications of Two-Dimensional Spatial Transformations in Vision Research

    10.5 Image Science and Vision

    10.6 Summary


    Chapter 11 Statistical Pattern Recognition Using Optical Fourier Transform Features

    11.1 Introduction

    11.2 An Optical-Digital Computer for Texture Analysis

    11.3 Feature Extraction and Classification

    11.4 Pattern Recognition of Coal Workers' Pneumoconiosis

    11.5 A Four-Class Texture Problem: The ODC Versus the All-Digital Approach

    11.6 Summary


    Chapter 12 Incoherent Optical Processing

    12.1 Introduction

    12.2 General Theoretical Analysis

    12.3 Spatially Incoherent Processing

    12.4 Applications of Spatially Incoherent Processing

    12.5 Temporally Incoherent Processing

    12.6 Applications of Temporally Incoherent Processing

    12.7 Conclusion



Product details

  • No. of pages: 564
  • Language: English
  • Copyright: © Academic Press 1982
  • Published: May 28, 1982
  • Imprint: Academic Press
  • eBook ISBN: 9780323145930

About the Editor

Henry Stark

Affiliations and Expertise

Illinois Institute of Technology

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