Introduction to Spectropolarimetry

Spectropolarimetry embraces the most complete and detailed measurement and analysis of light, as well as its interaction with matter. This book provides an introductory overview of the subject because it is playing an increasingly important role in modern solar observations. Chapters include a comprehensive description of the polarization state of polychromatic light and its measurement; an overview of astronomical polarimetry; and the formation of spectral lines in the presence of a magnetic field. The text is a valuable reference for graduates and researchers in astrophysics, solar physics and optics.

Preface

xi

Acknowledgements

xv

Historical introduction

1

(8)

Early discoveries in polarization

2

(2)

A mathematical formulation of polarization

4

(1)

Discovery of the Zeeman effect

5

(1)

Radiative transfer for polarized light

6

(3)

A review of some basic concepts

9

(10)

Light as an electromagnetic wave

10

(2)

The monochromatic, time-harmonic plane wave

12

(1)

The polarization tensor

13

(3)

The Stokes parameters of a monochromatic, time-harmonic plane wave

16

(3)

The polarization properties of quasi-monochromatic light

19

(17)

Polychromatic light as a statistical superposition of monochromatic light

19

(2)

The quasi-monochromatic plane wave

21

(1)

The polarization tensor and the Stokes parameters of a quasi-monochromatic plane wave

22

(2)

Degree of polarization and the Poincare sphere

24

(5)

Measuring the polarization state of quasi-monochromatic light

29

(4)

A further perspective on polarization properties

33

(3)

Linear optical systems acting on polarized light

36

(28)

Propagation of light through anisotropic media

36

(6)

Measurable effects of anisotropy

40

(2)

The extraordinary index of refraction and the energy propagation direction

42

(2)

Some notational conventions

44

(1)

Transforming the polarization state of light

45

(1)

The Mueller matrix and some of its properties

45

(4)

Block components of (solar) polarimeters

49

(6)

Rotation of the reference frame

49

(1)

The linear analyzer--polarizer

50

(3)

The partial linear polarizer

53

(1)

The linear retarder

53

(1)

The Mueller matrix of an optical train

54

(1)

Spatial and temporal modulation

55

(9)

Spatial modulation

56

(5)

Temporal modulation

61

(3)

Solar polarimetry

64

(23)

Environmental polarization

65

(9)

Seeing-induced polarization

66

(4)

Instrumental polarization

70

(4)

The polarization analysis system

74

(5)

The optimum modulation matrix

76

(2)

The optimum demodulation matrix

78

(1)

Some solar Stokes polarimeters

79

(4)

Zimpol

79

(2)

ASP

81

(1)

TIP and LPSP

82

(1)

A practical discussion of polarimetric efficiencies

83

(4)

Absorption and dispersion

87

(15)

Light propagation through low-density, weakly conducting media

88

(3)

Absorption and dispersion profiles

91

(4)

A correction from quantum mechanics

95

(2)

Accounting for thermal motions in the medium

97

(3)

Spectral line absorption in moving media

100

(2)

The radiative transfer equation

102

(19)

A little geometry

103

(2)

Variations of the coherency matrix along the ray path

105

(1)

Variation of the Stokes parameters along the ray path

106

(3)

Some properties of the propagation matrix

109

(3)

Emission processes

112

(3)

The RTE for spectral line formation

115

(1)

Radiative transfer through isotropic media

116

(1)

Propagation along the optical axis and in a perpendicular direction

117

(4)

The RTE in the presence of a magnetic field

121

(28)

The Lorentz model of the electron

121

(6)

Symmetry properties of the propagation matrix elements

126

(1)

LS coupling

127

(2)

The Zeeman effect

129

(8)

Allowed atomic transitions

131

(1)

The Zeeman pattern

132

(4)

Relative intensities of the Zeeman components

136

(1)

The elements of the propagation matrix

137

(9)

The effective Zeeman triplet

139

(7)

The RTE in the presence of a magnetic field

146

(3)

Solving the radiative transfer equation

149

(16)

The model atmosphere

149

(1)

The formal solution

150

(4)

Symmetry properties of the solution

150

(2)

The evolution operator

152

(1)

Solving the inhomogeneous equation

152

(1)

The action of macroturbulence on the Stokes profiles

153

(1)

Actual (numerical) solutions of the RTE

154

(4)

Simple solutions of the RTE

158

(4)

The Milne--Eddington atmosphere

159

(1)

Longitudinal magnetic field

160

(2)

Simple diagnostics

162

(3)

Stokes spectrum diagnostics

165

(34)

Probing the medium by scanning spectral lines

166

(7)

The isotropic case

166

(4)

The anisotropic case

170

(3)

Height of formation of spectral lines and the fundamental ill-definition of the CFs

173

(2)

Alternative CF definitions

175

(1)

The sensitivities of Stokes profiles

175

(14)

Linearization of the RTE and response functions

176

(9)

Properties of response functions

185

(4)

A theoretical description of measurement

189

(10)

Generalized response functions

191

(1)

An example

192

(2)

Understanding measurements theoretically

194

(5)

Inversion of the RTE

199

(21)

The χ2 merit function

201

(3)

Derivatives of the χ2 merit function

202

(2)

The Marquardt method

204

(5)

Error calculation

206

(2)

Problems in practice

208

(1)

Parameters at the nodes and equivalent response functions

209

(3)

Less significant parameters and singular value decomposition

212

(4)

Modified singular value decomposition

214

(2)

An example

216

(2)

Current and future inversion techniques

218

(2)

Index

220

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Introduction to Spectropolarimetry

Summary

Table of Contents

Supplemental Materials