Light Scattering in Inhomogeneous Atmospheres
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portes grátis
Light Scattering in Inhomogeneous Atmospheres
Yanovitskij, E. G.; Ginsheimer, S.; Yanovitskij, O.
Springer-Verlag Berlin and Heidelberg GmbH & Co. KG
11/1996
388
Dura
Inglês
9783540613626
3540613625
15 a 20 dias
705
This monograph gives a systematic presentation of the theory of light scattering in homogeneous, mulitlayered and inhomogeneous atmospheres. Simple asymptotical formulas, numerical algorithms, and example solutions of astrophysical and geophysical problems are given.
1. Basic Concepts, Equations and Problems.- 1.1 Intensity of Radiation.- 1.2 Interaction of Radiation with Matter.- 1.3 Radiative Transfer Equation.- 1.4 Radiative Transfer Equation in a Stratified Medium.- 1.5 The Parallel External Flux Problem.- 1.5.1 Azimuthal Harmonics of the Radiation Intensity.- 1.5.2 Integral Equation for the Source Function.- 1.6 The Milne Problem.- 1.7 The Problem for Two-Sided Infinity.- 1.8 Radiation Flux.- 1.9 Characteristics of Radiation at the Boundaries of an Atmosphere. The Problem of Diffuse Reflection and Diffuse Transmission of Light.- 1.10 The Flux Integral and K Integral.- 1.11 Green Function and Reciprocity Relations.- 1.12 Invariance Principles.- I. Homogeneous Atmosphere.- 2. Radiation Field in an Infinite Atmosphere.- 2.1 Conservatively Scattering Atmosphere.- 2.2 General Case.- 2.3 Characteristic Equation and Method of Its Solution.- 2.4 Normalization Constant M.- 2.5 Radiation Field with Nearly Conservative Scattering.- 3. Semi-Infinite Medium.- 3.1 Invariance Relation for the Parallel External Flux Problem.- 3.2 The Milne Problem.- 3.3 Relationship Between the Milne Problem and the Parallel External Flux Problem.- 3.4 Corollaries.- 3.5 Ambartsumian's Equation for the Reflection Coefficient and a Method for Its Solution.- 3.6 Some Integral Relations Involving Escape Functions.- 3.7 Integrals of the Transfer Equation.- 3.8 Separation of Variables. Angular Relaxation of Photons.- 3.9 Radiation Field in Deep Atmosphere Layers.- 3.10 Doubling Formula. Radiation Field in an Atmospheric Surface Layer.- 3.11 Atmosphere with Nearly Conservative Scattering.- 3.11.1 Initial Relations.- 3.11.2 Radiation Intensity at the Boundary of an Atmosphere.- 3.11.3 Asymptotic Formulas for N and C.- 3.11.4 Radiation Intensity at an Arbitrary Optical Depth.- 3.11.5 Radiation Flux and K Integral.- 3.11.6 Albedo of Atmosphere.- 3.12 Q Form of the Transfer Equation and Solution to the General Problem.- 3.12.1 Function Q( , 0,?) and Its Physical Meaning.- 3.12.2 Q Form of the Transfer Equation.- 3.12.3 Conservative Scattering.- 3.12.4 Q Representation of the Green Function for the Transfer Equation in a Plane Atmosphere.- 3.12.5 Solution to the General Problem.- 4. Atmosphere of Finite Optical Thickness.- 4.1 Invariance Relation.- 4.2 Equation for Radiation Intensity in Medium.- 4.3 Radiation Intensity at Atmosphere Boundaries.- 4.4 Further Consequences of the Basic Invariance Relation.- 4.5 Doubling Method for Calculation of Transmission and Reflection Coefficients.- 4.6 Radiation Field in a Layer.- 4.7 Integrals of the Transfer Equation for a Layer of Finite Thickness.- 4.8 Atmosphere with Large Optical Thickness.- 4.8.1 Reflection and Transmission Coefficients and Other Quantities.- 4.8.2 Conservative Scattering.- 4.8.3 Nearly Conservative Scattering in an Optically Thick Layer.- 4.8.4 Estimation of the Accuracy of Asymptotic Formulas.- 4.9 Illumination of the Boundary and Albedo of Atmospheres of Arbitrary Optical Thickness for Nearly Conservative Scattering.- 4.10 Algorithm for Solving the General Problem.- 4.10.1 Q Form Equation for the Green Function: Conservative Scattering.- 4.10.2 Solution of the General Problem: Conservative Scattering.- 4.10.3 Solution Algorithm for Nonconservative Scattering.- 5. Atmosphere Above a Reflecting Surface.- 5.1 Radiation Field in Atmospheres.- 5.2 Reflection and Transmission Coefficients.- 5.3 The Case of a Lambertian Surface.- 5.4 Albedo of Atmospheres and Illumination of Surfaces.- 5.5 Optically Thick Atmosphere Above a Reflective Surface.- 5.5.1 The Milne Problem with Reflection.- 5.5.2 Radiation Field in Atmospheres.- 5.5.3 Atmosphere with Nearly Conservative Scattering.- Bibliographical Comments and Additions to Part I.- II. Multilayer Atmosphere.- 6. Parallel External Flux Problem and the Milne Problem.- 6.1 Formulation of the Problem.- 6.2 A Two-Layer Atmosphere.- 6.3 Choosing the Direction to Add Layers.- 6.4 Radiation Field in a Multilayer Atmosphere.- 6.5 A Semi-Infinite Multilayer Atmosphere.- 6.6 A Multilayer Atmosphere Above a Reflecting Surface.- 6.7 The Milne Problem.- 6.8 The Milne Intensity at a Large Depth in Layer n.- 6.9 Normalization of the Solution of the Milne Problem.- 6.10 Solution of the General Problem.- 7. Light Scattering in Two Adjacent Half-Spaces.- 7.1 Statement of the Problem and Main Equations.- 7.2 Radiation Intensity at the Boundary.- 7.3 Isotropic Scattering.- 7.4 Radiation Field for Nearly Conservative Scattering.- 7.5 Radiation Field Away from the Boundary.- 8. Atmosphere Consisting of Layers with Large Optical Thickness.- 8.1 Parallel External Flux Problem: General Discussion.- 8.2 Asymptotic Formulas for Intensity at a Boundary and for Transmission and Reflection Coefficients.- 8.3 Radiation Field in a Medium.- 8.4 Conservatively Scattering Atmosphere.- 8.5 The Milne Problem.- 8.6 Normalization of the Milne Problem.- 8.7 A Two-Layer Atmosphere: Basic Formulas.- 8.7.1 A Two-Layer Semi-Infinite Atmosphere.- 8.7.2 Optically Thick Layers.- 8.7.3 Conservative Scattering.- Bibliographical Comments and Additions to Part II.- III. Atmosphere with Continuously Varying Parameters.- 9. Diffuse Reflection and Transmission of Light by Atmospheres.- 9.1 Integro-Differential Equations for the Source Function and Reflection and Transmission Coefficients.- 9.2 Method of Truncated Atmosphere for Determining Reflection and Transmission Coefficients.- 9.3 A Semi-Infinite Atmosphere.- 10. Basic Equations Defining the Radiation Field in a Vertically Inhomogeneous Layer.- 10.1 Equation for the Radiation Intensity in a Plane Layer.- 10.2 Invariance Relation for a Plane Sublayer and Some of Its Corollaries.- 10.3 On Numerical Methods to Compute Radiation Field in an Inhomogeneous Atmosphere.- 10.4 An Inhomogeneous Atmosphere Above a Reflecting Surface.- 10.4.1 The Radiation Field in an Atmosphere.- 10.4.2 The Case of a Lambertian Surface. Reflection and Transmission Coefficients.- 10.4.3 Albedo of the Atmosphere and Illumination of the Surface.- 11. Invariance Relations and Their Corollaries for a Semi-Infinite Atmosphere.- 11.1 Invariance Relations.- 11.2 Basic Equations Determining the Radiation Field.- 11.3 Two Integral Relations, Normalization of Escape Function and M Integral.- 11.4 Relationship Between the Milne Problem and the Parallel External Flux Problem.- 11.5 Some Integral Relations.- 11.6 Integrals of the Transfer Equation.- 11.7 The Concept of an Inverted Semi-Infinite Atmosphere.- 11.8 Discussion of the General Approach to the Solution of the Stated Problems.- 12. Asymptotic Properties of Radiation Fields in Inhomogeneous Atmospheres.- 12.1 Radiative Transfer in an Infinite Medium.- 12.1.1 Isotropization of Radiation. P1 Approximation.- 12.1.2 P2 Approximation.- 12.1.3 M Integral. Relationship Between y0(-?) and y0(?).- 12.2 Deep Layer Regime in a Semi-Infinite Atmosphere.- 12.3 Separation of Angular Variables in the Problem of Light Scattering in an Optically Thick Layer.- 12.4 Reflection Coefficient for a Semi-Infinite Atmosphere with Nearly Conservative Scattering.- 12.5 Escape Function, Albedo of Atmospheres and Other Quantities for Small True Absorption.- 12.6 An Inhomogeneous Atmosphere with Conservative Scattering.- 12.7 Conservatively Scattering Atmosphere Above a Reflecting Surface.- 12.8 Radiation Field in an Atmosphere with Nearly Conservative Scattering.- 12.8.1 Radiation Field in an Inverted Atmosphere and in Optically Thick Layer.- 12.8.2 Radiation Flux.- 13. Atmospheres with Exponentially Varying Characteristics.- 13.1 Coefficient of Reflection from a Semi-Infinite Atmosphere.- 13.2 Results of Calculations and an Estimation of Accuracy of Asymptotic Formulas for ?(?) = ?1e-m?.- 13.3 Algorithm for Calculating Internal Radiation Field.- 13.4 Linear Integral Equation for Intensity of Radiation Emerging from Isotropically Scattering Semi-Infinite Atmosphere.- 14. Astrophysical, Geophysical, and Other Possible Applications of the Theory.- 14.1 Effect of Inhomogeneity of a Cloudless Earth Atmosphere on the Radiation Field.- 14.2 Vertical Structure of the Venusian Atmosphere According to Data Obtained by Probes.- 14.2.1 Vertical Distribution of the Absorption Coefficient in an Atmosphere.- 14.2.2 Optical Parameters of Atmospheres in Different Spectral Regions.- 14.3 Absorption Line Formation in an Inhomogeneous Planetary Atmosphere. Basic Concepts and General Formulas.- 14.4 Absorption Line in an Optically Thick Nearly Conservatively Scattering Atmosphere.- 14.4.1 Dependence of the Observed Spectrum on the Width and Orientation of Spectrograph Slit.- 14.4.2 Profile and Equivalent Line Width for Different Models of Atmospheres.- 14.4.3 Arbitrary Model of an Atmosphere. Reduction to the Cauchy Problem.- 14.5 Effect of Inhomogeneity of Stellar Photospheres on the Continuous Spectrum.- 14.5.1 Basic Equations and Relations.- 14.5.2 Reduction to the Standard Problem.- 14.5.3 Various Methods of Solution.- 14.5.4 Isothermic Photosphere with a Density Decreasing by the Barometric Law.- 14.5.5 Asymptotic Formulas.- 14.6 Other Fields of Possible Application of the Theory.- Bibliographical Comments and Additions to Part III.- Appendix. Tables of Some Functions and Constants..- References.
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This monograph gives a systematic presentation of the theory of light scattering in homogeneous, mulitlayered and inhomogeneous atmospheres. Simple asymptotical formulas, numerical algorithms, and example solutions of astrophysical and geophysical problems are given.
1. Basic Concepts, Equations and Problems.- 1.1 Intensity of Radiation.- 1.2 Interaction of Radiation with Matter.- 1.3 Radiative Transfer Equation.- 1.4 Radiative Transfer Equation in a Stratified Medium.- 1.5 The Parallel External Flux Problem.- 1.5.1 Azimuthal Harmonics of the Radiation Intensity.- 1.5.2 Integral Equation for the Source Function.- 1.6 The Milne Problem.- 1.7 The Problem for Two-Sided Infinity.- 1.8 Radiation Flux.- 1.9 Characteristics of Radiation at the Boundaries of an Atmosphere. The Problem of Diffuse Reflection and Diffuse Transmission of Light.- 1.10 The Flux Integral and K Integral.- 1.11 Green Function and Reciprocity Relations.- 1.12 Invariance Principles.- I. Homogeneous Atmosphere.- 2. Radiation Field in an Infinite Atmosphere.- 2.1 Conservatively Scattering Atmosphere.- 2.2 General Case.- 2.3 Characteristic Equation and Method of Its Solution.- 2.4 Normalization Constant M.- 2.5 Radiation Field with Nearly Conservative Scattering.- 3. Semi-Infinite Medium.- 3.1 Invariance Relation for the Parallel External Flux Problem.- 3.2 The Milne Problem.- 3.3 Relationship Between the Milne Problem and the Parallel External Flux Problem.- 3.4 Corollaries.- 3.5 Ambartsumian's Equation for the Reflection Coefficient and a Method for Its Solution.- 3.6 Some Integral Relations Involving Escape Functions.- 3.7 Integrals of the Transfer Equation.- 3.8 Separation of Variables. Angular Relaxation of Photons.- 3.9 Radiation Field in Deep Atmosphere Layers.- 3.10 Doubling Formula. Radiation Field in an Atmospheric Surface Layer.- 3.11 Atmosphere with Nearly Conservative Scattering.- 3.11.1 Initial Relations.- 3.11.2 Radiation Intensity at the Boundary of an Atmosphere.- 3.11.3 Asymptotic Formulas for N and C.- 3.11.4 Radiation Intensity at an Arbitrary Optical Depth.- 3.11.5 Radiation Flux and K Integral.- 3.11.6 Albedo of Atmosphere.- 3.12 Q Form of the Transfer Equation and Solution to the General Problem.- 3.12.1 Function Q( , 0,?) and Its Physical Meaning.- 3.12.2 Q Form of the Transfer Equation.- 3.12.3 Conservative Scattering.- 3.12.4 Q Representation of the Green Function for the Transfer Equation in a Plane Atmosphere.- 3.12.5 Solution to the General Problem.- 4. Atmosphere of Finite Optical Thickness.- 4.1 Invariance Relation.- 4.2 Equation for Radiation Intensity in Medium.- 4.3 Radiation Intensity at Atmosphere Boundaries.- 4.4 Further Consequences of the Basic Invariance Relation.- 4.5 Doubling Method for Calculation of Transmission and Reflection Coefficients.- 4.6 Radiation Field in a Layer.- 4.7 Integrals of the Transfer Equation for a Layer of Finite Thickness.- 4.8 Atmosphere with Large Optical Thickness.- 4.8.1 Reflection and Transmission Coefficients and Other Quantities.- 4.8.2 Conservative Scattering.- 4.8.3 Nearly Conservative Scattering in an Optically Thick Layer.- 4.8.4 Estimation of the Accuracy of Asymptotic Formulas.- 4.9 Illumination of the Boundary and Albedo of Atmospheres of Arbitrary Optical Thickness for Nearly Conservative Scattering.- 4.10 Algorithm for Solving the General Problem.- 4.10.1 Q Form Equation for the Green Function: Conservative Scattering.- 4.10.2 Solution of the General Problem: Conservative Scattering.- 4.10.3 Solution Algorithm for Nonconservative Scattering.- 5. Atmosphere Above a Reflecting Surface.- 5.1 Radiation Field in Atmospheres.- 5.2 Reflection and Transmission Coefficients.- 5.3 The Case of a Lambertian Surface.- 5.4 Albedo of Atmospheres and Illumination of Surfaces.- 5.5 Optically Thick Atmosphere Above a Reflective Surface.- 5.5.1 The Milne Problem with Reflection.- 5.5.2 Radiation Field in Atmospheres.- 5.5.3 Atmosphere with Nearly Conservative Scattering.- Bibliographical Comments and Additions to Part I.- II. Multilayer Atmosphere.- 6. Parallel External Flux Problem and the Milne Problem.- 6.1 Formulation of the Problem.- 6.2 A Two-Layer Atmosphere.- 6.3 Choosing the Direction to Add Layers.- 6.4 Radiation Field in a Multilayer Atmosphere.- 6.5 A Semi-Infinite Multilayer Atmosphere.- 6.6 A Multilayer Atmosphere Above a Reflecting Surface.- 6.7 The Milne Problem.- 6.8 The Milne Intensity at a Large Depth in Layer n.- 6.9 Normalization of the Solution of the Milne Problem.- 6.10 Solution of the General Problem.- 7. Light Scattering in Two Adjacent Half-Spaces.- 7.1 Statement of the Problem and Main Equations.- 7.2 Radiation Intensity at the Boundary.- 7.3 Isotropic Scattering.- 7.4 Radiation Field for Nearly Conservative Scattering.- 7.5 Radiation Field Away from the Boundary.- 8. Atmosphere Consisting of Layers with Large Optical Thickness.- 8.1 Parallel External Flux Problem: General Discussion.- 8.2 Asymptotic Formulas for Intensity at a Boundary and for Transmission and Reflection Coefficients.- 8.3 Radiation Field in a Medium.- 8.4 Conservatively Scattering Atmosphere.- 8.5 The Milne Problem.- 8.6 Normalization of the Milne Problem.- 8.7 A Two-Layer Atmosphere: Basic Formulas.- 8.7.1 A Two-Layer Semi-Infinite Atmosphere.- 8.7.2 Optically Thick Layers.- 8.7.3 Conservative Scattering.- Bibliographical Comments and Additions to Part II.- III. Atmosphere with Continuously Varying Parameters.- 9. Diffuse Reflection and Transmission of Light by Atmospheres.- 9.1 Integro-Differential Equations for the Source Function and Reflection and Transmission Coefficients.- 9.2 Method of Truncated Atmosphere for Determining Reflection and Transmission Coefficients.- 9.3 A Semi-Infinite Atmosphere.- 10. Basic Equations Defining the Radiation Field in a Vertically Inhomogeneous Layer.- 10.1 Equation for the Radiation Intensity in a Plane Layer.- 10.2 Invariance Relation for a Plane Sublayer and Some of Its Corollaries.- 10.3 On Numerical Methods to Compute Radiation Field in an Inhomogeneous Atmosphere.- 10.4 An Inhomogeneous Atmosphere Above a Reflecting Surface.- 10.4.1 The Radiation Field in an Atmosphere.- 10.4.2 The Case of a Lambertian Surface. Reflection and Transmission Coefficients.- 10.4.3 Albedo of the Atmosphere and Illumination of the Surface.- 11. Invariance Relations and Their Corollaries for a Semi-Infinite Atmosphere.- 11.1 Invariance Relations.- 11.2 Basic Equations Determining the Radiation Field.- 11.3 Two Integral Relations, Normalization of Escape Function and M Integral.- 11.4 Relationship Between the Milne Problem and the Parallel External Flux Problem.- 11.5 Some Integral Relations.- 11.6 Integrals of the Transfer Equation.- 11.7 The Concept of an Inverted Semi-Infinite Atmosphere.- 11.8 Discussion of the General Approach to the Solution of the Stated Problems.- 12. Asymptotic Properties of Radiation Fields in Inhomogeneous Atmospheres.- 12.1 Radiative Transfer in an Infinite Medium.- 12.1.1 Isotropization of Radiation. P1 Approximation.- 12.1.2 P2 Approximation.- 12.1.3 M Integral. Relationship Between y0(-?) and y0(?).- 12.2 Deep Layer Regime in a Semi-Infinite Atmosphere.- 12.3 Separation of Angular Variables in the Problem of Light Scattering in an Optically Thick Layer.- 12.4 Reflection Coefficient for a Semi-Infinite Atmosphere with Nearly Conservative Scattering.- 12.5 Escape Function, Albedo of Atmospheres and Other Quantities for Small True Absorption.- 12.6 An Inhomogeneous Atmosphere with Conservative Scattering.- 12.7 Conservatively Scattering Atmosphere Above a Reflecting Surface.- 12.8 Radiation Field in an Atmosphere with Nearly Conservative Scattering.- 12.8.1 Radiation Field in an Inverted Atmosphere and in Optically Thick Layer.- 12.8.2 Radiation Flux.- 13. Atmospheres with Exponentially Varying Characteristics.- 13.1 Coefficient of Reflection from a Semi-Infinite Atmosphere.- 13.2 Results of Calculations and an Estimation of Accuracy of Asymptotic Formulas for ?(?) = ?1e-m?.- 13.3 Algorithm for Calculating Internal Radiation Field.- 13.4 Linear Integral Equation for Intensity of Radiation Emerging from Isotropically Scattering Semi-Infinite Atmosphere.- 14. Astrophysical, Geophysical, and Other Possible Applications of the Theory.- 14.1 Effect of Inhomogeneity of a Cloudless Earth Atmosphere on the Radiation Field.- 14.2 Vertical Structure of the Venusian Atmosphere According to Data Obtained by Probes.- 14.2.1 Vertical Distribution of the Absorption Coefficient in an Atmosphere.- 14.2.2 Optical Parameters of Atmospheres in Different Spectral Regions.- 14.3 Absorption Line Formation in an Inhomogeneous Planetary Atmosphere. Basic Concepts and General Formulas.- 14.4 Absorption Line in an Optically Thick Nearly Conservatively Scattering Atmosphere.- 14.4.1 Dependence of the Observed Spectrum on the Width and Orientation of Spectrograph Slit.- 14.4.2 Profile and Equivalent Line Width for Different Models of Atmospheres.- 14.4.3 Arbitrary Model of an Atmosphere. Reduction to the Cauchy Problem.- 14.5 Effect of Inhomogeneity of Stellar Photospheres on the Continuous Spectrum.- 14.5.1 Basic Equations and Relations.- 14.5.2 Reduction to the Standard Problem.- 14.5.3 Various Methods of Solution.- 14.5.4 Isothermic Photosphere with a Density Decreasing by the Barometric Law.- 14.5.5 Asymptotic Formulas.- 14.6 Other Fields of Possible Application of the Theory.- Bibliographical Comments and Additions to Part III.- Appendix. Tables of Some Functions and Constants..- References.
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