Radiative transfer : an introduction to exact and asymptotic methods / / Hélène Frisch

• Autore: Frisch H (Hélène)
• Pubblicazione: Cham, Switzerland : , : Springer International Publishing, , [2022]; ©2022
• Descrizione fisica: 1 online resource (611 pages)
• Disciplina: 530.138
• Soggetto topico: Radiative transfer; Radiative transfer - Data processing
• Nota di contenuto: Intro -- Preface -- References -- Contents -- List of Figures -- List of Tables -- 1 An Overview of the Content -- 1.1 Part I: Scalar Radiative Transfer Equations -- 1.2 Part II: Scattering Polarization -- 1.3 Part III: Asymptotic Properties of Multiple Scattering -- References -- Part I Scalar Radiative Transfer Equations -- 2 Radiative Transfer Equations -- 2.1 The Integro-Differential Radiative Transfer Equations -- 2.1.1 Monochromatic Scattering -- 2.1.2 Complete Frequency Redistribution -- 2.1.3 The Diffuse Radiation Field -- 2.2 Integral Equations for the Source Function -- 2.2.1 Monochromatic Scattering -- 2.2.2 The Milne Problem -- 2.2.3 Complete Frequency Redistribution -- 2.3 Neumann Series Expansion -- 2.4 The Green Function and Associated Functions -- 2.4.1 Some Definitions -- 2.4.2 A Lemma on Wiener-Hopf Equations -- 2.4.3 The Source Function and the Resolvent Function -- 2.4.4 Some Properties of the Green Function -- References -- 3 Exact Methods of Solution: A Brief Survey -- 3.1 The Infinite Medium and the Dispersion Function -- 3.2 Exact Methods for a Semi-Infinite Medium -- 3.2.1 The Wiener-Hopf Method -- 3.2.2 Traditional Real-Space Methods -- 3.2.3 The Singular Integral Equation Approach -- References -- 4 Singular Integral Equations -- 4.1 The Inverse Laplace Transformation -- 4.1.1 The Half-Space Case -- 4.1.2 The Full-Space Case -- 4.2 The Direct Laplace Transformation -- 4.3 The Hilbert Transform Method of Solution -- 4.3.1 A Special Case -- 4.3.2 The General Case -- 4.3.3 Application to Radiative Transfer -- Appendix A: Hilbert Transforms -- A.1 Definition and Properties -- A.2 The Plemelj Formulae -- A.3 The Plemelj Formulae for a Dirac Distribution -- References -- 5 The Scattering Kernel and Associated Auxiliary Functions -- 5.1 The Kernel and Its Inverse Laplace Transform -- 5.2 The Dispersion Function. ; 5.2.1 Symmetries and Analyticity Properties -- 5.2.2 The Zeroes of the Dispersion Function -- 5.2.3 The Index κ -- 5.3 The Half-Space Auxiliary Function X(z) -- 5.4 Some Properties of X(z) -- 5.4.1 Complete Frequency Redistribution -- 5.4.2 Monochromatic Scattering -- 5.4.3 Some Properties of the H-Function -- Appendix B: Properties of the Half-Space Auxiliary Function -- B.1 Factorization Relation -- B.2 Identities for the Boundary Values of X(z) -- B.3 Integral Equations for X(z) -- B.4 Values of X(z) and H(z) -- B.5 Moments of X(z) and H(z) -- References -- 6 The Surface Green Function and the Resolvent Function -- 6.1 Infinite Medium -- 6.1.1 The Fourier Transform Method -- 6.1.1.1 Complete Frequency Redistribution -- 6.1.1.2 Monochromatic Scattering -- 6.1.2 The Inverse Laplace Transform Method -- 6.2 Semi-infinite Medium. The Inverse Laplace Transform Method -- 6.2.1 Complete Frequency Redistribution -- 6.2.2 Monochromatic Scattering -- 6.3 The H-Function -- Appendix C: The Direct Laplace Transform Method -- C.1 Complete Frequency Redistribution -- C.2 Monochromatic Scattering -- References -- 7 The Emergent Intensity and the Source Function -- 7.1 The Emergent Intensity -- 7.2 The Source Function -- 7.2.1 Complete Frequency Redistribution -- 7.2.1.1 Inverse Laplace Transform Method -- 7.2.1.2 Direct Laplace Transform Method -- 7.2.2 Monochromatic Scattering. A Fourier Inversion -- 7.3 Some Standard Results -- 7.3.1 Uniform Primary Source Term -- 7.3.2 Exponential Primary Source Term -- 7.3.3 Diffuse Reflection -- Appendix D: The Monochromatic Source Function -- D.1 The Inverse Laplace Transform Method -- D.2 The Direct Laplace Transform Method -- References -- 8 Spectral Line with Continuous Absorption -- 8.1 The Radiative Transfer Equation -- 8.2 Properties of the Auxiliary Functions -- 8.2.1 The Dispersion Function. ; 8.2.2 The Half-Space Auxiliary Function -- 8.3 Some Exact Results -- 8.3.1 The Resolvent Function -- 8.3.2 The Line Source Function -- 8.3.3 The Emergent Intensity -- Appendix E: Kernels for Spectral Lines with a Continuous Absorption -- References -- 9 Conservative Scattering: The Milne Problem -- 9.1 The Monochromatic Milne Problem -- 9.1.1 The Auxiliary Functions -- 9.1.2 The Source Function and the Emergent Intensity -- 9.1.3 The Hopf Function -- 9.2 The Milne Problem for a Spectral Line -- Appendix F: The Conservative Auxiliary Functions. Complete Frequency Redistribution -- F.1 Asymptotic Behavior of the Kernel -- F.2 The Dispersion Function and the Half-Space Auxiliary Function Near the Origin -- Appendix G: The Milne Problem with the Inverse Laplace Transform Method -- References -- 10 The Case Eigenfunction Expansion Method -- 10.1 The Eigenfunctions and Eigenvalues -- 10.1.1 Monochromatic Scattering -- 10.1.1.1 Discrete Spectrum -- 10.1.1.2 Continuous Spectrum -- 10.1.2 Complete Frequency Redistribution -- 10.2 The Diffuse Reflection Problem -- 10.2.1 Monochromatic Scattering -- 10.2.1.1 The Expansion Coefficients -- 10.2.1.2 The Emergent Intensity -- 10.2.2 Complete Frequency Redistribution -- 10.3 Further Applications of the Case Method -- 10.3.1 A Complete Redistribution Full-Space Problem -- 10.3.2 A Half-Space Problem with Internal Sources -- References -- 11 The ε-law and the Nonlinear H-Equation -- 11.1 The ε-law -- 11.1.1 A Quadratic Approach -- 11.1.2 A Green Function Approach -- 11.2 Construction of the Nonlinear H-Equation -- 11.2.1 Scattering Coefficient Method -- 11.2.2 Exponential Primary Source Method -- 11.3 Some Properties of the H-Equation -- 11.3.1 A Factorization Relation -- 11.3.2 Uniqueness and Alternative Nonlinear H-Equations -- Appendix H: An Elementary Construction of the H-Function -- References. ; 12 The Wiener-Hopf Method -- 12.1 An Overview of the Wiener-Hopf Method -- 12.2 Full Description of the Wiener-Hopf Method -- 12.2.1 Decomposition Formula -- 12.2.2 Analyticity of Complex Fourier Transforms -- 12.2.3 Properties of the Dispersion Function V(z) -- 12.2.4 Factorization of the Dispersion Function -- 12.2.5 Decomposition of the Inhomogeneous Term -- 12.2.6 Fourier Transform of the Source Function -- 12.3 The Resolvent Function -- 12.4 The Milne Problem -- 12.5 The Wiener-Hopf Method for Spectral Lines -- 12.5.1 Factorization of V(z) -- 12.5.2 The Fourier Transform of the Source Function -- 12.5.3 The Emergent Intensity -- 12.6 The Sommerfeld Half-Plane Diffraction Problem -- Appendix I: The Auxiliary Function Vu(z) -- I.1 Explicit Expression of Vu(z) -- I.2 The Auxiliary Functions Vu(z) and X(z) -- References -- Part II Scattering Polarization -- 13 The Scattering of Polarized Radiation -- 13.1 Description of a Polarized Radiation -- 13.2 The Rayleigh Scattering Phase Matrix -- 13.2.1 The Scattering of a Collimated Radiation Beam -- 13.2.2 The Rayleigh Phase Matrix in a Fixed Reference Frame -- 13.2.2.1 A Standard Expression -- 13.2.2.2 The Spherical Tensors Representation -- 13.2.2.3 The Coherency Matrix -- 13.3 Resonance Scattering of Spectral Lines -- 13.3.1 Populations and Coherences -- 13.3.2 The Scattering Phase Matrix -- 13.4 The Hanle Effect -- 13.4.1 Some General Properties -- 13.4.2 The Hanle Phase Matrix -- 13.4.2.1 Magnetic Reference Frame -- 13.4.2.2 Atmospheric Reference Frame -- Appendix J: Spectral Details of Resonance Scattering -- Appendix K: Spectral Details of the Hanle Effect -- K.1 Magnetic Field Reference Frame -- K.2 Atmospheric Reference Frame -- K.3 Approximations for the Redistribution Matrix -- Appendix L: The Hanle Effect with the Classical Harmonic Oscillator Model -- L.1 The Harmonic Oscillator Model. ; L.2 Polarization Direction and Polarization Rate -- L.3 Frequency Redistribution -- References -- 14 Polarized Radiative Transfer Equations -- 14.1 Rayleigh Scattering. The Radiative Transfer Equation -- 14.2 Conservative Rayleigh Scattering -- 14.2.1 The Polarized Milne Problem -- 14.2.2 The Diffuse Reflection Problem -- 14.3 Rayleigh Scattering. A (KQ) Expansion of the Stokes Parameters -- 14.3.1 Cylindrically Symmetric Radiation Field -- 14.3.2 Azimuthally Dependent Radiation Field -- 14.4 Resonance Polarization of Spectral Lines -- 14.4.1 One-Dimensional Medium -- 14.4.2 Multi-Dimensional Medium -- 14.5 The Hanle Effect -- 14.5.1 The Hanle Redistribution Matrix -- 14.5.2 One-Dimensional Medium -- 14.5.3 Multi-Dimensional Medium -- References -- 15 The ε-Law, the Nonlinear H-Equation, and Matrix Singular Integral Equations -- 15.1 The Source Vector: Its Derivative and Matrix Representation -- 15.2 The ε-Law -- 15.2.1 Rayleigh Scattering and Resonance Polarization -- 15.2.2 The Hanle Effect -- 15.3 The Green Matrix and the Resolvent Matrix -- 15.3.1 Rayleigh Scattering and Resonance Polarization -- 15.3.2 The Hanle Effect -- 15.4 Construction of the H-Equation -- 15.4.1 Rayleigh Scattering and Resonance Polarization -- 15.4.2 The Hanle Effect -- 15.5 Alternative Definitions of the H-Matrix -- 15.5.1 Exponential Primary Source -- 15.5.2 Uniform Primary Source -- 15.6 Singular Integral Equations -- 15.6.1 Rayleigh Scattering and Resonance Polarization -- 15.6.2 The Hanle Effect -- 15.7 Factorization Relations and the ε-Law -- References -- 16 Conservative Rayleigh Scattering: Exact Solutions -- 16.1 Radiative Transfer Equations -- 16.2 The Dispersion Matrix -- 16.3 Construction of the Auxiliary X-matrix -- 16.4 The Resolvent Matrix -- 16.5 The H-matrix -- 16.6 The Polarized Milne Problem -- 16.6.1 Some Physical Properties -- 16.6.2 The Source Vector. ; 16.6.3 The Generalized Hopf Functions.
• Titolo autorizzato: Radiative transfer
• ISBN: 9783030952471; 9783030952464
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Lingua di pubblicazione: Inglese
• Record Nr.: 996475870303316
• Lo trovi qui: Univ. di Salerno