Introduction to Statistical Optics

by O’Neill, Edward L.

• ISBN13: 9780486435787
• ISBN10: 0486435784
• Format: Paperback
• Copyright: 2004-01-15
• Publisher: Dover Publications

Summary

". . . develops its theme logically and is remarkable in its economy of presentation without omission of the physical picture of practical implications."-Physics Today"This is an excellent book; well-organized, and well-written."-Journal of the Optical Society of AmericaDesigned for a senior- or graduate-level course, this text offers an authoritative introduction to classical statistical optics. Chapters 1 and 2 present detailed descriptions of the role of Green's function in mathematical physics and the essential differences between spatial and time filters. Chapter 3 contains a brief review of the fundamental relations of paraxial optics, using compact and efficient matrix notation for the translation and refraction operations. Chapters 4, 5, and 6 describe the effects of various aberration terms on image formation from the standpoints of physical and geometrical optics. The final three chapters explore statistical methods, matrix and coherence theory, and the theory of partial polarization.

Author Biography

Edward L. O'Neill: Department of Physics, Worcester Polytechnic Institute

Table of Contents

Chapter 1. GREEN'S FUNCTION AND LINEAR THEORY
1-1 Linear second-order differential operators	1	(2)
1-2 Self-adjoint operators	3	(2)
1-3 Nonself-adjoint operators	5	(1)
1-4 The inhomogeneous equation	5	(1)
1-5 Determination of the Green's function	6	(4)
1-6 The principle of linear superposition in optical image formation	10	(3)
Chapter 2. SPATIAL VERSUS TIME FILTERS
2-1 Time filters	13	(2)
2-2 Classification of input signals	15	(2)
2-3 Random signals	17	(3)
2-4 Optical spatial filters	20	(2)
2-5 The optical contrast transfer function	22	(3)
2-6 An idealized illustration	25	(2)
2-7 Image motion	27	(3)
Chapter 3. INTRODUCTION TO GEOMETRICAL OPTICS
3-1 Fermat's principle and Snell's law of refraction	30	(2)
3-2 Sign convention	32	(1)
3-3 Refraction matrix	32	(2)
3-4 Translation matrix	34	(2)
3-5 Paraxial approximation	36	(1)
3-6 Image formation	37	(1)
3-7 The cardinal points	38	(2)
3-8 Illustrations	40	(6)
Chapter 4. THE GEOMETRICAL THEORY OF ABERRATIONS
4-1 Wave aberration function	46	(1)
4-2 Geometrical versus physical optics	47	(2)
4-3 Equations for the ray intercepts	49	(9)
4-4 Optimum balancing of third- and fifth-order spherical aberrations	58	(4)
4-5 The Marechal method of aberration balancing	62	(4)
4-6 An illustration, a single reflecting surface	66	(2)
4-7 Zernike polynomials	68	(2)
Chapter 5. DIFFRACTION THEORY OF IMAGE FORMATION
5-1 General considerations	70	(2)
5-2 Basic diffraction problem	72	(3)
5-3 Equations governing image formation	75	(4)
5-4 Diffraction by a slit	79	(1)
5-5 The Michelson stellar interferometer	80	(3)
5-6 Diffraction by a circular aperture	83	(3)
Chapter 6. ANALYSIS AND SYNTHESIS
6-1 General considerations	86	(1)
6-2 Small aberrations	87	(2)
6-3 Amplitude and phase variations in one dimension	89	(6)
6-4 Amplitude and phase variations in two dimensions	95	(4)
6-5 Random phase errors	99	(2)
6-6 The synthesis problem, coherent illumination	101	(4)
Chapter 7. STATISTICAL METHODS
7-1 Random scenes	105	(4)
7-2 Further statistical considerations; graininess and granularity	109	(4)
7-3 Checkerboard model	113	(2)
7-4 Overlapping circular grain model	115	(7)
Chapter 8. MATRIX AND COHERENCE THEORY
8-1 Introduction: Wolf's mutual coherence function	122	(2)
8-2 Image formation	124	(3)
8-3 Matrix theory	127	(6)
Chapter 9. THE THEORY OF PARTIAL POLARIZATION
9-1 Introduction	133	(2)
9-2 Jones method	135	(2)
9-3 The coherency matrix formalism	137	(5)
9-4 The Stokes parameters and the Mueller method	142	(4)
9-5 Selected topics	146	(11)
Appendix A. FOURIER-BESSEL SERIES AND INTEGRALS
A-1 Fourier series	157	(2)
A-2 Fourier integral	159	(1)
A-3 Fourier theory in two dimensions	160	(1)
A-4 The convolution theorem	161	(2)
A-5 The sampling theorem	163	(3)
Appendix B. PROBABILITY AND ENTROPY THEORY
B-1 The binomial, Poisson, and normal distributions	166	(1)
B-2 The concept of entropy	167	(5)
B-3 The illumination matrix in the coherent limit	172	(5)
INDEX	177