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

References

Chapter 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

References

Chapter 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

References

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

References

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

References

Index