Optical Signal Processing: Fundamentals

ISBN-13: 9783642749643 / Angielski / Miękka / 2011 / 483 str.

Pankaj K. Das

Opis

The subject "optical signal processing" can and should include all aspects of optics and signal processing. However, that is too large a scope for a textbook that, like this one, is intended as an introduc tion to the subject at a level suitable for first year graduate students of electrical engineering, physics, and optical engineering. There fore, the subject matter has been restricted. The book begins with basic background material on optics, signal processing, matrix alge bra, ultrasound and SAWs, and CCDs. One might argue about this choice of topics. For example, there already exist very good books on matrix algebra. However, matrix algebra is so important in sig nal processing, especially in connection with devices such as optical matrix processors, that it was felt that a review was essential. Also, the matrix algebra needed for systolic arrays and parallel computing has made great advances in recent years. My original intention was to write a single-volume textbook cov ering most of the fundamental concepts and applications of optical signal processing. However, it soon became apparent that the large amount of material to be included would make publication in a single volume impracticable. Therefore this volume treats the "fundamen tals" and a second volume will appear dealing with devices and applications. This textbook was stimulated by a set of short courses that I have directed and lectured since 1976, as well as regular courses that I have taught at Rensselaer Polytechnic Institute since 1974."

Spis treści

1. Introduction.- 1.1 Why Optical Signal Processing?.- 1.2 Signal Processing: Tools and Applications.- 1.3 Arrangement of the Book.- 1.3.1 Guide for Selective Use of the Book.- 1.3.2 Note on References.- 2. Optics Fundamentals.- 2.1 Maxwell’s Equations.- 2.2 Boundary Conditions.- 2.3 Snell’s Laws.- 2.4 Total Internal Reflection and Optical Tunneling.- 2.5 Transmission Lines.- 2.6 Reflection and Transmission Coefficients for Electromagnetic Waves.- 2.6.1 Normal Incidence: ?i = 0.- 2.6.2 General Case.- 2.7 Group and Phase Velocity.- 2.7.1 Poynting Vector, Ray Velocity, Phase Velocity, and Group Velocity.- 2.7.2 Goos-Hänchen Effect.- 2.8 Gaussian Beam Propagation.- 2.9 Geometrical Optics.- 2.9.1 Eikonal Equation.- 2.9.2 Matrix Formulation of Geometrical Optics.- 2.9.3 Gaussian Optics Including Lenses.- 2.9.4 Optical Fiber.- 2.10 Gradient Optical Fiber.- 2.11 Integrated Optics and Step-Index Optical Fibers.- 2.11.1 Electromagnetic Waveguide Solutions.- 2.11.2 Parallel Plate Waveguide: TE Solution.- 2.11.3 Integrated Optics Problem.- 2.11.4 Multimode Group Delay in a Dielectric Waveguide.- 2.11.5 Cylindrical Waveguide.- 2.11.6 Stepped-Index Optical Fiber.- 2.12 Propagation in Anisotropic Media.- 2.12.1 Wave Vector Surface, Phase Velocity Surface, and Ray Velocity Surface.- 2.12.2 Double Refraction.- 2.13 Electro-optic Effect.- 2.13.1 General Discussion.- 2.13.2 Kerr Effect.- 2.13.3 Indirect Electro-optic Effect.- 2.14 The Acousto-optic or Elasto-optic Effect.- 2.14.1 Acousto-optic Coefficients.- 2.14.2 Acousto-optic Interaction: Thin Grating.- 2.14.3 Acousto-optic Interaction: Thick Grating.- 2.14.4 Acousto-optic Interaction Including Light Polarization: Isotropic Solids.- 2.14.5 Bragg Acousto-optic Interaction: Light Polarization Included.- 2.14.6 Bragg Diffraction: Anisotropic Case.- 2.15 Magneto-optics.- 2.15.1 Polarization and the Jones Matrix.- 2.15.2 Optical Activity.- 2.15.3 Magneto-optics: The Faraday Effect, the Voigt Effect and the Kerr Effect.- 2.16 Wave Equation with Source and Boundary.- 2.16.1 Diffraction.- 2.16.2 Solution of the Scalar Wave Equation with Source and Boundary.- 2.16.3 Solution of the Vector Wave Equation with Source and Boundary.- 2.17 Fourier Optics.- 2.17.1 Holography.- Problems.- 3. Signal Processing Fundamentals.- 3.1 Analog Signals and Systems.- 3.1.1 Linear Systems.- 3.1.2 Fourier Transforms and Frequency Response.- 3.1.3 Examples.- 3.1.4 Hilbert Transform and Causality.- 3.1.5 Time-Variant Systems.- 3.2 Discrete Systems.- 3.2.1 Examples.- 3.2.2 Sampling Theorem and Aliasing.- 3.2.3 Frequency Response of a Discrete Time Filter.- 3.3 Noise and Stochastic Processes.- 3.3.1 Linear Systems with Stochastic Input.- 3.3.2 Matched Filters.- 3.3.3 Matched Filters from the Point of View of Maximum Output.- 3.3.4 Matched Filtering of Stochastic Signals.- 3.3.5 Noise and Stochastic Processes: Discrete.- 3.3.6 Matrix Methods.- 3.3.7 Matched Filters: Discrete Case.- 3.4 Filters.- 3.5 Adaptive Filters.- 3.5.1 Linear Mean Squares Estimation.- 3.5.2 Least Mean Squares Adaptive Filters.- 3.5.3 Lattice Filters.- 3.6 Power Spectra Estimation.- 3.6.1 MA Model.- 3.6.2 AR Model.- 3.6.3 ARMA Model.- 3.7 Kalman Filtering.- 3.7.1 State-Space Formulation.- 3.7.2 The Kalman Filter.- 3.7.3 Solution of the Ricatti Equation with Constant Coefficients.- 3.7.4 Square Root Filtering.- 3.8 Two-Dimensional Signal Processing.- 3.8.1 Analog Signals and Systems.- 3.8.2 Linear Systems.- 3.8.3 The Fourier Transform and the Spatial Frequency Response.- 3.8.4 Examples of Fourier Transformation, Imaging, etc..- 3.8.5 Space-Variant Systems.- 3.8.6 Discrete Signals and Matrix Representation.- 3.9 Stochastic Processes: Multidimensional.- 3.9.1 Point Source.- 3.9.2 Partially Coherent Source Distribution.- 3.9.3 Coherent Source.- 3.9.4 Effect of a Mask.- 3.9.5 General Case.- 3.9.6 Coherency Matrix.- 3.10 The Ambiguity Function, Wigner Distribution Function and Triple Correlation.- 3.10.1 The Ambiguity Function.- 3.10.2 Wigner Distribution Function.- 3.10.3 Two-Dimensional Ambiguity and Wigner Distribution Functions.- 3.10.4 Triple and Higher-Order Correlations.- Problems.- 4. Introduction to SAW and CCD Technology.- 4.1 History of CCD and SAW Devices.- 4.1.1 Charge Coupled Devices.- 4.1.2 Surface Acoustic Waves.- 4.2 Why SAWs Became Popular and Useful in the 1960s.- 4.2.1 Bulk Ultrasound Devices.- 4.2.2 Advantages of SAWs.- 4.2.3 SAW Devices.- 4.3 Charge Coupled Devices.- 4.4 Magneto-Static Waves.- 4.4.1 MSW Field Equations and Dispersion Relations.- 4.4.2 MSW Devices.- 4.5 ACT Devices.- 4.6 Comparison of Technologies.- 4.6.1 SAW Technology.- 4.6.2 Bulk Ultrasound Devices.- 4.6.3 Charge Coupled Devices.- 4.6.4 Acoustic Charge Transport.- 4.6.5 Acousto-optics.- 4.6.6 Digital Devices: IC/VHSIC.- Appendices.- A. Matrices.- A.1 The Hamilton-Cayley Theorem.- A.2 Some Definitions.- A.3 Matrix Inversion.- A.4 Gaussian Elimination Method.- A.5 Successive Orthogonalization of a Matrix.- A.6 Circulant Matrices and Fourier Matrices.- A.7 Pseudo-Inverse, Singular-Value Decomposition, Overdetermination and Principle of Least Squares: Kalman Filtering.- A.8 Coordinate Transformation.- B. Orthogonal Functions and Polynomials.- B.1 Sturm-Liouville Equation.- B.2 Fourier Series.- B.3 Hypergeometric Series.- B.4 Legendre Polynomials.- B.5 Hermite Polynomials.- B.6 Laguerre Polynomials.- B.7 Generalized Laguerre Polynomials.- B.8 Chebyshev Polynomials.- B.9 Bessel Functions.- C. Principle of Stationary Phase.- D. Vectors.- D.1 Important Results.- D.2 Green’s Theorem: Scalar.- D.3 Green’s Theorem: Vector.- E. Symmetry Properties of Different Coefficients in Crystal Classes.- References.

O autorze

Optical Signal Processing: Fundamentals presents the background material necessary for an understanding of modern optical methods of signal processing. Intended for graduate students in electrical engineering, physics, and optical engineering, this text covers fundamentals of optics; the electro-optic, acousto-optic, and magneto-optic effects; stochastic processes; and filters.