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Table of Contents
Intro
Preface
Acknowledgements
Author biography
Christopher M Sorensen
Chapter 1 Waves
1.1 Wave concepts
1.2 Energy transport
1.3 Complex notation
1.4 Fourier analysis
1.4.1 Fourier transformation of periodic functions
1.4.2 Fourier transformation of any function
1.4.3 Fourier transform of the square pulse
1.4.4 Fourier transform of the Gaussian function
1.4.5 The convolution and the convolution theorem
1.5 Diffraction
1.5.1 Single slit diffraction
1.5.2 Convolutions and diffraction
1.5.3 Phasor description of single slit diffraction
1.5.4 Babinet's principle
1.6 Foundations of scattering
References
Chapter 2 Introduction to scattering and absorption
2.1 The total cross section
2.2 Angles and solid angles
2.3 The differential scattering cross section
2.3.1 The phase function
2.3.2 The asymmetry parameter
2.4 Extinction, albedo and the efficiencies
2.5 Attenuation by an ensemble of particles
2.6 Multiple scattering
References
Chapter 3 Polarization
3.1 Polarized light
3.2 Polarization by an oscillating electric dipole
3.3 The Stokes vector and the Mueller matrix
3.4 The scattering matrix
3.5 Polarization upon scattering
3.6 Microphysical description for the scattered light polarization for spheres
References
Chapter 4 The structure factor
4.1 A system of scatterers
4.2 The scattering wave vector
4.3 The structure factor
4.4 The structure factor as a Fourier transform squared of the density distribution function
4.5 The structure factor as a Fourier transform of the density autocorrelation function
4.6 The density autocorrelation function
4.7 And another form for the structure factor
4.8 The Guinier regime
4.9 The structure factor of the sphere.
4.10 The structure factor as diffraction: generalization to arbitrary dimension
References
Chapter 5 The scaling approach to the structure factor
5.1 The scaling approach concepts
5.2 The scaling approach rules
5.3 The scaling approach applied to various shapes
5.3.1 A uniform sphere
5.3.2 A uniform circular obstacle
5.3.3 A uniform linear obstacle
5.3.4 A long circular cylinder-orientationally averaged
5.3.5 A disk (a short circular cylinder)-orientationally averaged
5.3.6 A circular cylinder-aligned
5.3.7 A fractal aggregate
5.4 The scaling approach for single particles
5.5 The scaling approach for ensembles of particles
5.5.1 Systems with volumetric density fluctuations
5.5.2 An ensemble of particles in a scattering volume
5.5.3 Scattering from dense systems
5.6 Connections to other formulations
5.7 Assessment
References
Chapter 6 Rayleigh scattering
6.1 Dimensional analysis
6.2 The Rayleigh differential scattering cross section for a sphere: electromagnetic theory
6.3 The total Rayleigh cross section
6.4 Consequences of Rayleigh scattering
6.4.1 Blue skies, red sunsets
6.4.2 Polarization effects
6.4.3 The Tyndall effect
6.5 Rayleigh absorption
6.6 Rayleigh extinction
6.7 Rayleigh albedo
6.8 The Rayleigh ratio
6.9 Limits to the Rayleigh regime
6.10 Epilogue
References
Chapter 7 Light scattering and absorption by spherical particles
7.1 The differential scattering cross section
7.1.1 The Rayleigh-Debye-Gans limit
7.1.2 Light scattering from soft spheres
7.1.3 The limits of Mie scattering and the internal coupling parameter
7.1.4 Scattering by arbitrary spheres with real refractive index
7.1.5 The spherical particle total scattering cross section
7.2 The spherical particle absorption cross section.
7.2.1 The skin depth parameter κkR
7.2.2 Rayleigh regime absorption
7.2.3 The geometric regime when kR &
#62
1 and κkR &
#62
1 and κ <
1
7.2.4 The reflection regime when κ &
#62
3 and κkR &
#62
3
7.3 Effects of absorption on scattering
7.4 Efficiencies
7.5 The single scattering albedo
References
Chapter 8 Q-space analysis of light scattering by spherical particles
8.1 Motivation for Q-space analysis
8.2 Q-space analysis of scattering by an arbitrary sphere
8.2.1 Scattering at any angle (any q)
8.2.2 The intermediate, −2 power law regime, 1 <
qR <
1.2ρτ̔̈“«”“·
8.2.3 The large qR, −4 power law regime, qR &
#62
1.2ρτ̔̈“«”“·
8.2.4 Quasi-universality with the internal coupling parameter ρτ̔̈“«”“·
8.2.5 Summary of the Q-space analysis of scattering by a sphere: a new, general description of spherical particle light scattering
8.2.6 The story of light scattering
8.2.7 The effects of the imaginary part of the refractive index on scattering
8.2.8 The Debye series expansion
8.2.9 Diffraction and refraction
8.2.10 Comparison of Q-space and θ-space
8.3 The partial scattering cross section
8.3.1 The partial scattering efficiency
8.4 The extinction paradox
8.4.1 The Ewald-Oseen extinction theorem
8.4.2 Babinet's principle revisited
8.4.3 The extinction paradox for particles
References
Chapter 9 Light scattering and absorption by fractal aggregates
9.1 Fractals
9.2 Fractal aggregate structure
9.3 Fractal aggregate structure factor
9.4 Light scattering and absorption by fractal aggregates
9.4.1 The Rayleigh-Debye-Gans approximation for fractal aggregates
9.4.2 Light scattering by an ensemble of monodisperse aggregates
9.4.3 Light scattering by an ensemble of polydisperse aggregates.
9.4.4 The internal coupling parameter for fractal aggregates
9.4.5 Experimental examples of scattering by fractal aggregates
9.4.6 Fractal aggregate albedo
9.4.7 Validity of the Rayleigh-Debye-Gans approximation for fractal aggregate light scattering and absorption
9.5 Superaggregates
References
Chapter 10 Light scattering and absorption by particles of any shape
10.1 Experimental data
10.1.1 The Amsterdam-Granada data set
10.1.2 The Kansas state data set
10.2 The general Rayleigh method for a particle of arbitrary shape
10.2.1 Rayleigh scattering by an arbitrary shape
10.2.2 Internal coupling parameter for arbitrary shapes
10.3 Theoretical calculations of scattering by various shapes
10.3.1 Solid geometric shapes orientationally averaged
10.3.2 Gaussian random spheres
10.3.3 Irregular spheres
10.3.4 Ice crystals
10.3.5 Thickened percolation clusters
10.4 Summary and conclusions
References
Chapter
Chapter
Reference
Chapter
References
Chapter
Subject Index.
Preface
Acknowledgements
Author biography
Christopher M Sorensen
Chapter 1 Waves
1.1 Wave concepts
1.2 Energy transport
1.3 Complex notation
1.4 Fourier analysis
1.4.1 Fourier transformation of periodic functions
1.4.2 Fourier transformation of any function
1.4.3 Fourier transform of the square pulse
1.4.4 Fourier transform of the Gaussian function
1.4.5 The convolution and the convolution theorem
1.5 Diffraction
1.5.1 Single slit diffraction
1.5.2 Convolutions and diffraction
1.5.3 Phasor description of single slit diffraction
1.5.4 Babinet's principle
1.6 Foundations of scattering
References
Chapter 2 Introduction to scattering and absorption
2.1 The total cross section
2.2 Angles and solid angles
2.3 The differential scattering cross section
2.3.1 The phase function
2.3.2 The asymmetry parameter
2.4 Extinction, albedo and the efficiencies
2.5 Attenuation by an ensemble of particles
2.6 Multiple scattering
References
Chapter 3 Polarization
3.1 Polarized light
3.2 Polarization by an oscillating electric dipole
3.3 The Stokes vector and the Mueller matrix
3.4 The scattering matrix
3.5 Polarization upon scattering
3.6 Microphysical description for the scattered light polarization for spheres
References
Chapter 4 The structure factor
4.1 A system of scatterers
4.2 The scattering wave vector
4.3 The structure factor
4.4 The structure factor as a Fourier transform squared of the density distribution function
4.5 The structure factor as a Fourier transform of the density autocorrelation function
4.6 The density autocorrelation function
4.7 And another form for the structure factor
4.8 The Guinier regime
4.9 The structure factor of the sphere.
4.10 The structure factor as diffraction: generalization to arbitrary dimension
References
Chapter 5 The scaling approach to the structure factor
5.1 The scaling approach concepts
5.2 The scaling approach rules
5.3 The scaling approach applied to various shapes
5.3.1 A uniform sphere
5.3.2 A uniform circular obstacle
5.3.3 A uniform linear obstacle
5.3.4 A long circular cylinder-orientationally averaged
5.3.5 A disk (a short circular cylinder)-orientationally averaged
5.3.6 A circular cylinder-aligned
5.3.7 A fractal aggregate
5.4 The scaling approach for single particles
5.5 The scaling approach for ensembles of particles
5.5.1 Systems with volumetric density fluctuations
5.5.2 An ensemble of particles in a scattering volume
5.5.3 Scattering from dense systems
5.6 Connections to other formulations
5.7 Assessment
References
Chapter 6 Rayleigh scattering
6.1 Dimensional analysis
6.2 The Rayleigh differential scattering cross section for a sphere: electromagnetic theory
6.3 The total Rayleigh cross section
6.4 Consequences of Rayleigh scattering
6.4.1 Blue skies, red sunsets
6.4.2 Polarization effects
6.4.3 The Tyndall effect
6.5 Rayleigh absorption
6.6 Rayleigh extinction
6.7 Rayleigh albedo
6.8 The Rayleigh ratio
6.9 Limits to the Rayleigh regime
6.10 Epilogue
References
Chapter 7 Light scattering and absorption by spherical particles
7.1 The differential scattering cross section
7.1.1 The Rayleigh-Debye-Gans limit
7.1.2 Light scattering from soft spheres
7.1.3 The limits of Mie scattering and the internal coupling parameter
7.1.4 Scattering by arbitrary spheres with real refractive index
7.1.5 The spherical particle total scattering cross section
7.2 The spherical particle absorption cross section.
7.2.1 The skin depth parameter κkR
7.2.2 Rayleigh regime absorption
7.2.3 The geometric regime when kR &
#62
1 and κkR &
#62
1 and κ <
1
7.2.4 The reflection regime when κ &
#62
3 and κkR &
#62
3
7.3 Effects of absorption on scattering
7.4 Efficiencies
7.5 The single scattering albedo
References
Chapter 8 Q-space analysis of light scattering by spherical particles
8.1 Motivation for Q-space analysis
8.2 Q-space analysis of scattering by an arbitrary sphere
8.2.1 Scattering at any angle (any q)
8.2.2 The intermediate, −2 power law regime, 1 <
qR <
1.2ρτ̔̈“«”“·
8.2.3 The large qR, −4 power law regime, qR &
#62
1.2ρτ̔̈“«”“·
8.2.4 Quasi-universality with the internal coupling parameter ρτ̔̈“«”“·
8.2.5 Summary of the Q-space analysis of scattering by a sphere: a new, general description of spherical particle light scattering
8.2.6 The story of light scattering
8.2.7 The effects of the imaginary part of the refractive index on scattering
8.2.8 The Debye series expansion
8.2.9 Diffraction and refraction
8.2.10 Comparison of Q-space and θ-space
8.3 The partial scattering cross section
8.3.1 The partial scattering efficiency
8.4 The extinction paradox
8.4.1 The Ewald-Oseen extinction theorem
8.4.2 Babinet's principle revisited
8.4.3 The extinction paradox for particles
References
Chapter 9 Light scattering and absorption by fractal aggregates
9.1 Fractals
9.2 Fractal aggregate structure
9.3 Fractal aggregate structure factor
9.4 Light scattering and absorption by fractal aggregates
9.4.1 The Rayleigh-Debye-Gans approximation for fractal aggregates
9.4.2 Light scattering by an ensemble of monodisperse aggregates
9.4.3 Light scattering by an ensemble of polydisperse aggregates.
9.4.4 The internal coupling parameter for fractal aggregates
9.4.5 Experimental examples of scattering by fractal aggregates
9.4.6 Fractal aggregate albedo
9.4.7 Validity of the Rayleigh-Debye-Gans approximation for fractal aggregate light scattering and absorption
9.5 Superaggregates
References
Chapter 10 Light scattering and absorption by particles of any shape
10.1 Experimental data
10.1.1 The Amsterdam-Granada data set
10.1.2 The Kansas state data set
10.2 The general Rayleigh method for a particle of arbitrary shape
10.2.1 Rayleigh scattering by an arbitrary shape
10.2.2 Internal coupling parameter for arbitrary shapes
10.3 Theoretical calculations of scattering by various shapes
10.3.1 Solid geometric shapes orientationally averaged
10.3.2 Gaussian random spheres
10.3.3 Irregular spheres
10.3.4 Ice crystals
10.3.5 Thickened percolation clusters
10.4 Summary and conclusions
References
Chapter
Chapter
Reference
Chapter
References
Chapter
Subject Index.