Introduction to Matrix Methods in Optics

Clear, accessible guide requires little prior knowledge and considers just two topics: paraxial imaging and polarization. Lucid discussions of paraxial imaging properties of a centered optical system, optical resonators and laser beam propagation, matrices in polarization optics and propagation of light through crystals, much more. 60 illustrations. Appendixes. Bibliography.

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