Introduction to Matrix Methods in Optics

This book was designed to encourage the adoption of simple matrix methods in teaching optics at the undergraduate and technical college level. Although these methods have been somewhat neglected in the past, the authors point to the economy and elegance with which, for a linear system, a wealth of input-output relations can be expressed by a single matrix. Moreover, the field of optics has been enormously enriched by contributions from other disciplines, such as microwave physics and electrical engineering, which employ matrix methods.
Because it is an introductory text, this work requires little prior knowledge and is confined to just two topics: paraxial imaging and polarization. For those with no previous acquaintance with matrix algebra, Chapter One introduces basic ideas of rectangular matrix arrays and gives the rules for adding them and for forming matrix products. Subsequent chapters deal with paraxial imaging properties of a centered optical system, optical resonators and laser beam propagation, matrices in polarization optics, and propagation of light through crystals.
Six helpful appendixes deal with such topics as aperture properties of centered lens systems, matrix representation of centering and squaring errors, and derivation of Mueller and Jones matrices. A bibliography completes this accessible guide to methods that will be of great assistance to students and workers not only in optics, but in such areas as laser engineering, optoelectronics, mechanical engineering, and more. 1975 edition.

"1000370225"
Introduction to Matrix Methods in Optics

This book was designed to encourage the adoption of simple matrix methods in teaching optics at the undergraduate and technical college level. Although these methods have been somewhat neglected in the past, the authors point to the economy and elegance with which, for a linear system, a wealth of input-output relations can be expressed by a single matrix. Moreover, the field of optics has been enormously enriched by contributions from other disciplines, such as microwave physics and electrical engineering, which employ matrix methods.
Because it is an introductory text, this work requires little prior knowledge and is confined to just two topics: paraxial imaging and polarization. For those with no previous acquaintance with matrix algebra, Chapter One introduces basic ideas of rectangular matrix arrays and gives the rules for adding them and for forming matrix products. Subsequent chapters deal with paraxial imaging properties of a centered optical system, optical resonators and laser beam propagation, matrices in polarization optics, and propagation of light through crystals.
Six helpful appendixes deal with such topics as aperture properties of centered lens systems, matrix representation of centering and squaring errors, and derivation of Mueller and Jones matrices. A bibliography completes this accessible guide to methods that will be of great assistance to students and workers not only in optics, but in such areas as laser engineering, optoelectronics, mechanical engineering, and more. 1975 edition.

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Introduction to Matrix Methods in Optics

Introduction to Matrix Methods in Optics

Introduction to Matrix Methods in Optics

Introduction to Matrix Methods in Optics

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Overview


This book was designed to encourage the adoption of simple matrix methods in teaching optics at the undergraduate and technical college level. Although these methods have been somewhat neglected in the past, the authors point to the economy and elegance with which, for a linear system, a wealth of input-output relations can be expressed by a single matrix. Moreover, the field of optics has been enormously enriched by contributions from other disciplines, such as microwave physics and electrical engineering, which employ matrix methods.
Because it is an introductory text, this work requires little prior knowledge and is confined to just two topics: paraxial imaging and polarization. For those with no previous acquaintance with matrix algebra, Chapter One introduces basic ideas of rectangular matrix arrays and gives the rules for adding them and for forming matrix products. Subsequent chapters deal with paraxial imaging properties of a centered optical system, optical resonators and laser beam propagation, matrices in polarization optics, and propagation of light through crystals.
Six helpful appendixes deal with such topics as aperture properties of centered lens systems, matrix representation of centering and squaring errors, and derivation of Mueller and Jones matrices. A bibliography completes this accessible guide to methods that will be of great assistance to students and workers not only in optics, but in such areas as laser engineering, optoelectronics, mechanical engineering, and more. 1975 edition.


Product Details

ISBN-13: 9780486680446
Publisher: Dover Publications
Publication date: 02/15/2012
Series: Dover Books on Physics Series
Edition description: Reprint
Pages: 384
Product dimensions: 5.50(w) x 8.50(h) x 0.80(d)

Table of Contents

PREFACE
CHAPTER I Introduction to matrix calculations
I.1 Introductory discussion
I.2 Matrix multiplication
I.3 Null matrices
I.4 Unit matrices
I.5 Diagonal matrices
I.6 Multiple products
I.7 Matrix addition and subtraction
I.8 Transpose matrices
I.9 Determinants
I.10 Division of matrices and matrix inversion
I.11 Matrix diagonlaization
I.12 Eigenvalues and eignevectors of a 2 × 2 unimodular matrix
CHAPTER II Matrix methods in paraxial optics
II.1 Introductory discussion
II.2 Ray-transfer matrices
II.3 The translation matrix T
II.4 The refraction matrix R
II.5 The ray-transfer matrix for a system
II.6 Derivation of properties of a system from its matrix
II.7 Illustrative problems
II.8 Experimental determination of the matrix elements of an optical system
II.9 Locating the cardinal points of a system
II.10 Further problems
II.11 Extension of ray-transfer method to reflecting systems
CHAPTER III Optical resonators and laser beam propagation
III.1 Review of results obtained for paraxial imaging systems
III.2 Description of wave propagation in terms of geometrical optics
III.3 "Resolving power, étendue and the space-bandwidth product"
III.4 Marix representation of an optical resonator
III.5 The distinction between stable and unstable resonators
III.6 Propagation of a Gaussian beam and its complex cruvature parameter
III.7 Predicting the output of a laser oscillator
III.8 Application of the ABCD rule to mode-matching problems
III.9 Ray-transfer matrices for distributed lens-like media
III.10 Illustrative problems
CHAPTER IV Matrices in polarization optics
IV.1 Polarized light - its production and analysis
IV.2 The Stokes parameters for specifying polarization
IV.3 Use of the Mueller calulus for transforming a Stokes column
IV.4 Experimental determination of the elements of a Mueller matrix or a Stokes column
IV.5 Use of the Jones calculus for transforming a Maxwell column
IV.6 Experimental determination of the elements of a Jones matrix or a Maxwell column
IV.7 Illustrative problems soled by Mueller calculus and by Jones calculus
CHAPTER V Propagation of light through crystals
V.1 Introductory discussion
V.2 Expression of vector operations in matrx form
V.3 Dielectric properties of an anisotropic medium
V.4 Propagation of plane waves in a uniaxial crystal
V.5 Huygens wavelets in a uniaxial crystal
APPENDIXES
A Aperature properties of centred lens systems
B Matrix representation of centring and squaring errors
C Statistical derivation of the Stokes parameters
D Derivation of Mueller matrices
E Derivation of Jones matrices
F Connection between Jones and Mueller calculi
BIBLIOGRAPHY AND CONCLUSION
INDEX
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