Transfer Of Polarized Light In Planetary Atmospheres

by Mee, C. V. M. van der; Van Der Mee, Cornelis; Domke, Helmut

• ISBN13: 9781402028557
• ISBN10: 1402028555
• Format: Hardcover
• Copyright: 2005-06-30
• Publisher: Kluwer Academic Pub

Summary

The principal elements of the theory of polarized light transfer in planetary atmospheres are expounded in a systematic but concise way. Basic concepts and practical methods are emphasized, both for single and multiple scattering of electromagnetic radiation by molecules and particles in the atmospheres of planets in the Solar System, including the Earth, and beyond. A large part of the book is also useful for studies of light scattering by particles in comets, the interplanetary and interstellar medium, circumstellar disks, reflection nebulae, water bodies like oceans and suspensions of particles in a gas or liquid in the laboratory. Throughout the book symmetry principles, such as the reciprocity principle and the mirror symmetry principle, are employed. In this way the theory is made more transparent and easier to understand than in most papers on the subject. In addition, significant computational reductions, resulting from symmetry principles, are presented. Hundreds of references to relevant literature are given at the end of the book. Appendices contain supplementary information such as a general exposition on properties of matrices transforming Stokes parameters of light beams. Each chapter concludes with a number of problems with answers or hints for solution. The readers should have some basic knowledge of physics and mathematics. The book is suitable as a textbook for advanced undergraduates and graduate students. It will also be of interest to science professionals in one of the many disciplines in which electromagnetic scattering plays an important role, like astrophysics, atmospheric optics, remote sensing, marine optics, biophysics and biomedicine.

Table of Contents

Preface	ix
Acknowledgments	xiii
Description of Polarized Light	1	(22)
Intensity and Flux	1	(1)
Polarization Parameters	2	(21)
Trigonometric Wave Functions	3	(4)
General Properties of Stokes Parameters for Quasi-monochromatic Light	7	(6)
Exponential Wave Functions	13	(3)
CP-representation of Quasi-monochromatic Polarized Light	16	(2)
Alternative Representations of Quasi-monochromatic Polarized Light	18	(5)
Single Scattering	23	(40)
Introduction	23	(1)
Scattering by One Particle	23	(5)
Scattering by a Collection of Particles	28	(1)
Symmetry Relationships for Single Scattering	29	(8)
Reciprocity	29	(6)
Mirror Symmetry	35	(2)
Special Scattering Directions and Extinction	37	(3)
Some Special Cases of Single Scattering	40	(8)
Particles Small Compared to the Wavelength	40	(4)
Spheres	44	(3)
Miscellaneous Types of Particles	47	(1)
The Scattering Matrix	48	(4)
Expansion of Elements of the Scattering Matrix in Generalized Spherical Functions	52	(4)
Introduction	52	(1)
Expansions for the Elements of F(Θ): Results	53	(3)
Expansion Coefficients for Rayleigh Scattering	56	(1)
Some Properties of the Expansion Coefficients	56	(7)
Plane-parallel Media	63	(34)
Geometrical and Optical Characteristics	63	(3)
The Phase Matrix	66	(6)
Properties of the Elements of the Phase Matrix	72	(9)
Symmetry Relations	72	(7)
Interrelations	79	(1)
Relations for Special Directions	80	(1)
The Azimuth Dependence	81	(16)
Derivation of the Components	81	(5)
Algebraic Properties of the Components	86	(2)
Separation of Variables in the Components	88	(5)
An Example: Rayleigh Scattering	93	(4)
Orders of Scattering and Multiple-Scattering Matrices	97	(38)
Basic Equations	97	(3)
Orders of Scattering for Intensity Vectors	100	(6)
Multiple-Scattering Matrices	106	(3)
Orders of Scattering for Multiple-Scattering Matrices	109	(4)
Relationships for Multiple-Scattering Matrices	113	(13)
Symmetry Relations	113	(8)
Interrelations	121	(1)
Perpendicular Directions	121	(5)
Fourier Decompositions	126	(9)
Functions of u, u' and Φ -- Φ	126	(1)
Functions of μ, μ0 and Φ -- Φ0	127	(2)
Symmetry Relations for the Components	129	(6)
The Adding-doubling Method	135	(52)
Introduction	135	(5)
Principle of the Adding-doubling Method	140	(7)
Azimuth Dependence	147	(4)
Supermatrices	151	(4)
Repeated Reflections	155	(4)
Reflecting Ground Surfaces	159	(9)
The Internal Radiation Field	168	(4)
Computational Aspects	172	(9)
Computing Repeated Reflections	172	(1)
Computing the Azimuth Dependence	173	(3)
Criteria for Computing Fourier Terms	176	(2)
Choosing the Initial Layer	178	(1)
Number of Division Points and Renormalization	179	(2)
Very thick atmospheres	181	(6)
A. Mueller Calculus	187	(20)
Pure Mueller Matrices	188	(10)
Relating Jones Matrices and Pure Mueller Matrices	188	(5)
Internal Structure of a Pure Mueller Matrix	193	(4)
Inequalities	197	(1)
Relationships for Sums of Pure Mueller Matrices	198	(2)
Testing Matrices	200	(4)
Discussion	204	(3)
B. Generalized Spherical Functions	207	(10)
Definitions and Basic Properties	207	(4)
Expansion Properties	211	(2)
The Addition Formula	213	(2)
Connections with Angular Momentum, Theory	215	(2)
C. Expanding the Elements of F (Θ)	217	(4)
D. Size Distributions	221	(4)
E. Proofs of Relationships for Multiple-Scattering Matrices	225	(4)
Introduction	225	(1)
Proving Symmetry Relations for the Multiple-Scattering Matrices U, D, U* and D*	225	(3)
Multiple-Scattering Matrices as SPM Matrices	228	(1)
F Supermatrices and Extended Supermatrices	229	(4)
Bibliography	233	(22)
Index	255