Application of Optical Fourier Transforms

List of Contributors Preface Acknowledgments 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 References Chapter 2 Pattern Recognition via Complex Spatial Filtering Introduction 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 ReferencesChapter 3 Particle Identification and Counting by Fourier-Optical Pattern Recognition Introduction 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 References Chapter 4 Signal Processing Using Hybrid Systems Introduction 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 Appendix References Chapter 5 Fourier Optics and Radar Signal Processing 5.1 Introduction 5.2 Radar Signal Processing 5.3 Optical Processors for Radar Signals References 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 ReferencesChapter 7 Fourier Optics and SAW Devices 7.1 Introduction 7.2 Surface Acousto-Optic Interaction 7.3 Applications 7.4 Conclusion References 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 References 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 References 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 ReferencesChapter 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.