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Optical Signal Processing

Book Description

An indispensable treatment of optical signal processing--now in a convenient paperback edition

This introduction to optical signal processing offers an unparalleled look at its underlying theory and selected processing applications. Designed as both a senior-level undergraduate or first-year graduate-level textbook and a reference for professionals working in the field, Optical Signal Processing begins with a clear, methodical look at the fundamentals of optical signal processing, forming a firm foundation for a discussion of the field's ever-evolving technological breadth. Beginning with the second half of the book, special emphasis is given to processing wide bandwidth signals in real time by using acousto-optic technology.

Complete with detailed study problems that test the limits of students' knowledge, this comprehensive text forms a complete one-volume account of the theory and applications of optical signal processing. Professional engineers and physicists will find the sheer breadth of up-to-date coverage and detail of Optical Signal Processing provides them with an indispensable treatment of this influential technology.

Table of Contents

  1. Coverpage
  2. Titlepage
  3. Copyright
  4. Dedication
  5. Preface
  6. Contents
  7. Chapter 1. Basic Signal Parameters
    1. 1.1 Introduction
    2. 1.2 Characterization of a General Signal
      1. 1.2.1. By Bandwidth
      2. 1.2.2. By Time
      3. 1.2.3. By Sample Interval
      4. 1.2.4. By Number of Samples
      5. 1.2.5. By Number of Amplitude Levels or Signal Features
      6. 1.2.6. By Degrees of Freedom
    3. 1.3 The Sample Function
    4. 1.4 Examples of Signals
    5. 1.5 Spatial Signals
  8. Chapter 2. Geometrical Optics
    1. 2.1 Introduction
    2. 2.2 Refractive Index and Optical Path
    3. 2.3 Basic Laws of Geometrical Optics
      1. 2.3.1. Law of Reflection
      2. 2.3.2. Law of Refraction
      3. 2.3.3. Fermat’s Principle
      4. 2.3.4. The Critical Angle
    4. 2.4 Refraction by Prisms
      1. 2.4.1. Minimum Deviation Angle
      2. 2.4.2. Dispersion by a Prism
      3. 2.4.3. Beam Magnification by a Prism
      4. 2.4.4. Counter-Rotating Prisms
      5. 2.4.5. The Wobble Plate
    5. 2.5 The Lens Formulas
      1. 2.5.1. The Sign Convention
      2. 2.5.2. Refraction at a Curved Surface
      3. 2.5.3. The Refraction Equation for Combined Surfaces
      4. 2.5.4. The Condenser Lens Configuration
      5. 2.5.5. The Collimating Lens Configuration
      6. 2.5.6. Principal Planes
      7. 2.5.7. Thin-Lens Systems
      8. 2.5.8. Afocal or Telescopic Configurations
    6. 2.6 The General Imaging Condition
      1. 2.6.1. Ray Tracing
      2. 2.6.2. Lateral Magnification
      3. 2.6.3. The Principal Pupil Ray
    7. 2.7 The Optical Invariant
      1. 2.7.1. Magnification Revisited
      2. 2.7.2. Spatial Resolution
      3. 2.7.3. Space Bandwidth Product
      4. 2.7.4. Matching the Information Capacity of System Components
    8. 2.8 Classification of Lenses and Systems
      1. 2.8.1. The Coddington Shape Factor
      2. 2.8.2. The Coddington Position Factor
    9. 2.9 Aberrations
      1. 2.9.1. Spherical Aberration
      2. 2.9.2. Coma
      3. 2.9.3. Astigmatism
      4. 2.9.4. Curvature of Field
      5. 2.9.5. Distortion
      6. 2.9.6. Splitting the Lens
  9. Chapter 3. Physical Optics
    1. 3.1 Introduction
    2. 3.2 The Fresnel Transform
      1. 3.2.1. Convolution and Impulse Response
      2. 3.2.2. Diffraction by Two Sources
      3. 3.2.3. Fresnel Zones, Chirp Functions, and Holography
      4. 3.2.4. The Fresnel Transform of a Slit
    3. 3.3 The Fourier Transform
      1. 3.3.1. The Fourier Transform of a Periodic Function
      2. 3.3.2. The Fourier Transform for Nonperiodic Signals
      3. 3.3.3. The Fourier Transform in Optics
    4. 3.4 Examples of Fourier Transforms
      1. 3.4.1. Fourier Transforms of Aperture Functions
      2. 3.4.2. A Partitioned Aperture Function
      3. 3.4.3. A Periodic Signal
    5. 3.5 The Inverse Fourier Transform
      1. 3.5.1. Bandlimited Signals
      2. 3.5.2. Rayleigh-Resolution Criterion
      3. 3.5.3. Abbe’s Resolution Criterion
      4. 3.5.4. The Sample Function, Sampling Theorem, and Decomposition
    6. 3.6 Extended Fourier-Transform Analysis
      1. 3.6.1. The Basic Elements of an Optical System
      2. 3.6.2. Operational Notation
      3. 3.6.3. A Basic Optical System
      4. 3.6.4. Cascaded Optical Systems
      5. 3.6.5. The Scale of the Fourier Transform
    7. 3.7 Maximum Information Capacity and Optimum Packing Density
      1. 3.7.1. Maximum Information Capacity
      2. 3.7.2. Optimum Packing Density
      3. 3.7.3. Convergent Illumination
      4. 3.7.4. The Chirp-Z Transform
    8. 3.8 System Coherence
      1. 3.8.1. Spatial Coherence
      2. 3.8.2. Temporal Coherence
      3. 3.8.3. Spatial and Temporal Coherence
  10. Chapter 4. Spectrum Analysis
    1. 4.1 Introduction
    2. 4.2 Light Sources
    3. 4.3 Spatial Light Modulators
      1. 4.3.1. Light Valve Spatial Light Modulators
      2. 4.3.2. Optically Addressed Electro-Optic Spatial Light Modulators
      3. 4.3.3. Liquid-Crystal Spatial Light Modulators
      4. 4.3.4. Magneto-Optic Spatial Light Modulators
    4. 4.4 The Detection Process in the Fourier Domain
      1. 4.4.1. A Special Photodetector Array
      2. 4.4.2. Spectral Responsivity and Typical Power Levels
      3. 4.4.3. The Number of Photodetector Elements
      4. 4.4.4. Array Geometry
      5. 4.4.5. Readout Rate
      6. 4.4.6. Blooming and Electrical Crosstalk
      7. 4.4.7. Linearity and Uniformity of Response
    5. 4.5 System Performance Parameters
      1. 4.5.1. Total Spatial Frequency Bandwidth
      2. 4.5.2. Sidelobe Control and Crosstalk
      3. 4.5.3. Frequency Resolution/Photodetector Spacing
      4. 4.5.4. Array Spacing and Number of Photodetector Elements
    6. 4.6 Dynamic Range
      1. 4.6.1. Intermodulation Products
      2. 4.6.2. Signal-to-Noise Ratio and the Minimum Signal Level
      3. 4.6.3. Integration Time/Bandwidth
      4. 4.6.4. Example
      5. 4.6.5. Quantum Noise Limit
    7. 4.7 Raster-Format Spectrum Analyzer
      1. 4.7.1. The Recording Format
      2. 4.7.2. The Two-Dimensional Spectrum Analyzer
      3. 4.7.3. Illustration of Raster-Format Spectra
    8. 4.8 Summary of the Main Design Concepts
  11. Chapter 5. Spatial Filtering
    1. 5.1 Introduction
    2. 5.2 Some Fundamentals of Signal Processing
      1. 5.2.1. Linear, Space-Invariant Systems
      2. 5.2.2. Parseval’s Theorem
      3. 5.2.3. Correlation
      4. 5.2.4. Input/Output Spectral Densities
      5. 5.2.5. Matched Filtering
      6. 5.2.6. Inverse Filtering
    3. 5.3 Spatial Filters
    4. 5.4 Binary Spatial Filters
      1. 5.4.1. Binary Filters for Signal Detection or Excision
      2. 5.4.2. Other Applications of Binary Filters
    5. 5.5 Magnitude Spatial Filters
    6. 5.6 Phase Spatial Filters
    7. 5.7 Real-Valued Spatial Filters
    8. 5.8 Experimental Examples
    9. 5.9 The Spatial Carrier Frequency Filter
    10. 5.10 Interferometric Methods for Constructing Filters
      1. 5.10.1. Limitations of the Mach-Zehnder Interferometer
      2. 5.10.2. The Rayleigh Interferometer
      3. 5.10.3. The Minimum-Aperture Interferometer
    11. 5.11 Information Processing
    12. 5.12 Arbitrary Reference Function
    13. 5.13 Bandwidth Considerations
    14. 5.14 Multiplexed Filters
    15. 5.15 Computer Generated Filters
    16. 5.16 Reference Function Optical Processors
  12. Chapter 6. Spatial Filtering Systems
    1. 6.1 Introduction
    2. 6.2 Optical Signal Processor and Filter Generator
      1. 6.2.1. The Light Source
      2. 6.2.2. The Spatial Light Modulator
      3. 6.2.3. The Fourier Transform Lens
      4. 6.2.4. The Filter Plane
      5. 6.2.5. The Imaging Lens
    3. 6.3 The Readout Module
      1. 6.3.1. The Thresholding Operation
      2. 6.3.2. The Importance of Nonoverlapping Signals
      3. 6.3.3. On-Chip Processing
      4. 6.3.4. Constant False-Alarm Rate
    4. 6.4 The Reference-to-Signal-Beam Ratio
    5. 6.5 Orientation and Scale-Searching Operations
      1. 6.5.1. The Orientation Search
      2. 6.5.2. The Scale Search
    6. 6.6 Methods for Handling Nonuniform Noise Spectral Densities
      1. 6.6.1. Dual Frequency-Plane Processing
      2. 6.6.2. Transposed Processing for Adaptive Filtering
    7. 6.7 Other Applications for Optical Spatial Filtering
      1. 6.7.1. Target Recognition
      2. 6.7.2. Motion Analysis
      3. 6.7.3. Frame Alignment and Stereo Compilation
    8. 6.8 The Effects of Small Displacements of Spatial Filters
      1. 6.8.1. Lateral Displacement
      2. 6.8.2. Longitudinal Displacements
      3. 6.8.3. Random Motion of the Filter
  13. Chapter 7. Acousto-Optic Devices
    1. 7.1 Introduction
    2. 7.2 Acousto-Optic Cell Spatial Light Modulators
      1. 7.2.1. Raman-Nath Mode
      2. 7.2.2. The Bragg Mode
      3. 7.2.3. Diffraction Angles, Spatial Frequencies, and Temporal Frequencies
      4. 7.2.4. The Time Bandwidth Product
    3. 7.3 Dynamic Transfer Relationships
      1. 7.3.1. Diffraction Efficiency
      2. 7.3.2. Input/Output Relationships
    4. 7.4 Time Delays and Notation
    5. 7.5 Phase-Modulation Notation
    6. 7.6 Sign Notation
    7. 7.7 Conjugate Relationships
    8. 7.8 Visualization of the Acousto-Optic Interaction
    9. 7.9 Applications of Acousto-Optic Devices
      1. 7.9.1. Acousto-Optic Modulation
      2. 7.9.2. Acousto-Optic Beam Deflectors
  14. Chapter 8. Acousto-Optic Power Spectrum Analyzers
    1. 8.1 Introduction
    2. 8.2 A Basic Spectrum Analyzer
      1. 8.2.1. The Illumination Subsystem
      2. 8.2.2. A Raman-Nath-Mode Spectrum Analyzer
      3. 8.2.3. A Bragg-Mode Spectrum Analyzer
      4. 8.2.4. The Generalization to Arbitrary Signals
    3. 8.3 Aperture Weighting for Sidelobe Control
    4. 8.4 Resolution
    5. 8.5 Dynamic Range and Signal-to-Noise Ratio
    6. 8.6 Spur-Free Dynamic Range
      1. 8.6.1. Intermodulation Products Due to Acousto-Optic Cells
      2. 8.6.2. Signal Compression
      3. 8.6.3. Scattered Light
    7. 8.7 Photodetector Geometric Considerations
    8. 8.8 Example
    9. 8.9 The Signal-to-Noise Ratio
    10. 8.10 Radiometers
    11. 8.11 Summary of the Main Design Concepts
  15. Chapter 9. Heterodyne Systems
    1. 9.1 Introduction
    2. 9.2 The Interference Between Two Waves
      1. 9.2.1. Spatial Interference
      2. 9.2.2. Temporal and Spatial Interference
    3. 9.3 Overlapping Waves and Photodetector Size
      1. 9.3.1. Optimum Photodetector Size for Plane-Wave Interference
      2. 9.3.2. Optimum Photodetector Size for a Two-Dimensional Chirp
      3. 9.3.3. Optimum Photodetector Size for a One-Dimensional Chirp
      4. 9.3.4. Optimum Photodetector Size for a General Signal
    4. 9.4 The Optical Radio
      1. 9.4.1. Direct Detection
      2. 9.4.2. Heterodyne Detection
    5. 9.5 A Generalized Heterodyne System
  16. Chapter 10. Heterodyne Spectrum Analysis
    1. 10.1 Introduction
    2. 10.2 Basic Theory
    3. 10.3 Spatial and Temporal Frequencies: The Mixed Transform
      1. 10.3.1. The cw Signal
      2. 10.3.2. A Short Pulse
      3. 10.3.3. The Evolving Pulse
    4. 10.4 The Distributed Local Oscillator
      1. 10.4.1. The Ideal Reference Signal
      2. 10.4.2. The Mixed Transform of the Reference Signal
    5. 10.5 Photodetector Geometry and Bandwidth
      1. 10.5.1. The Bandpass Filter Shape
      2. 10.5.2. Crosstalk
      3. 10.5.3. Resolution, Accuracy, and Photodetector Size
    6. 10.6 Temporal Frequencies of the Reference Bias Term
    7. 10.7 Dynamic Range
    8. 10.8 Comparison of the Heterodyne and Power Spectrum Analyzer Performance
      1. 10.8.1. Both Systems Thermal-Noise Limited
      2. 10.8.2. Both Systems Shot-Noise Limited
      3. 10.8.3. Power Spectrum Analyzer Thermal-Noise Limited; Heterodyne Spectrum Analyzer Shot-Noise Limited
      4. 10.8.4. Power Spectrum Analyzer Using a CCD Array
    9. 10.9 Hybrid Heterodyne Spectrum Analyzer
  17. Chapter 11. Decimated Arrays and Cross-Spectrum Analysis
    1. 11.1 Introduction
    2. 11.2 Background for the Heterodyne Spectrum Analyzer
    3. 11.3 Photodetector Geometry and Detection Scheme
    4. 11.4 The Reference and Scanning Functions
    5. 11.5 Signal-to-Noise Ratio and Dynamic Range
    6. 11.6 Improved Reference Waveform
    7. 11.7 The Cross-Spectrum Analyzer
      1. 11.7.1. Cross-Spectrum Analysis with Spatial Heterodyning
      2. 11.7.2. Cross-Spectrum Analysis with Temporal Heterodyning
  18. Chapter 12. The Heterodyne Transform and Signal Excision
    1. 12.1 Introduction
    2. 12.2 The Heterodyne Transform
    3. 12.3 The Temporal Frequency Range of the Baseband Terms
    4. 12.4 Probing Arbitrary Three-Dimensional Fields
    5. 12.5 Signal Excision
    6. 12.6 Arbitrary Filter Function
  19. Chapter 13. Space-Integrating Correlators
    1. 13.1 Introduction
    2. 13.2 Reference-Function Correlators
      1. 13.2.1. Real-Valued Impulse Responses
      2. 13.2.2. Complex-Valued Impulse Responses
      3. 13.2.3. A Wavefront View of Matched Filtering
      4. 13.2.4. The Photodetector Bandwidth
      5. 13.2.5. Correlation in the Presence of Doppler Frequency Shifts
      6. 13.2.6. Programmable Matched Filter
    3. 13.3 Multichannel Operation
    4. 13.4 Heterodyne/Homodyne Detection
    5. 13.5 Homodyne Detection in the Fourier Domain
    6. 13.6 Heterodyne Detection
    7. 13.7 Carrier Frequency Requirements
    8. 13.8 Illumination Requirements
    9. 13.9 Integrate and Dump
    10. 13.10 Some More Configurations
  20. Chapter 14. Time-Integrating Systems
    1. 14.1 Introduction
    2. 14.2 Spectrum Analysis
      1. 14.2.1. Requirements on the Reference Signals
      2. 14.2.2. The Basic Operation of the Spectrum Analyzer
      3. 14.2.3. The Key Features of the Time-Integrating Spectrum Analyzer
    3. 14.3 Time-Integrating Correlation
      1. 14.3.1. Time-Integrating Correlator Due to Montgomery
      2. 14.3.2. Time-Integrating Correlator Due to Sprague and Koliopoulos
    4. 14.4 Electronic Reference Correlator
    5. 14.5 Comparison of Features
    6. 14.6 Integrated Optical Systems
  21. Chapter 15. Two-Dimensional Processing
    1. 15.1 Introduction
    2. 15.2 Triple-Product Processing
    3. 15.3 Crossed Acousto-Optic Cell Geometry
    4. 15.4 The Bispectrum
    5. 15.5 Spectrum Analysis
      1. 15.5.1. Real-Time Raster-Format Spectrum Analysis
      2. 15.5.2. Frequency Resolution
      3. 15.5.3. Experimental Results
    6. 15.6 Ambiguity Function Generation
      1. 15.6.1. Ambiguity Function for a cw Signal
      2. 15.6.2. Ambiguity Function for a Short-Pulse Signal
      3. 15.6.3. Ambiguity Function for an Infinite Time Duration Chirp Signal
    7. 15.7 Wigner-Ville Distributions
    8. 15.8 Range and Doppler Signal Processing
    9. 15.9 Optical Transversal Processor for Notch Filtering
      1. 15.9.1. Sampled Time Analysis
      2. 15.9.2. Continuous-Time Analysis
      3. 15.9.3. A Frequency Plane Implementation
    10. 15.10 Phased Array Processing
  22. Appendix I
  23. Appendix II
  24. References
  25. Bibliography
  26. Index