Lecture12 - Chapter 11 The Radiative Transfer Equation with...

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1 1 Chapter 11 The Radiative Transfer Equation with Scattering 2 Scattering : The process by which particles redistribute incident EM radiation into the total solid angle surrounding the particle. Scattering requires that the refractive index of the scattering medium is different from that of the surrounding medium. Small particles (r < λ /10): Scatter almost equally in the forward and backward directions. Rayleigh Scattering Scattering intensity varies as λ -4 Gas molecules Particles with r ~ (or >) λ : More energy is scattered in forward direction, and secondary maxima and minima appear at various angles. Mie Scattering (but Mie theory can also be applied to smaller particles) Aerosols Elastic Scattering : When the incident and scattered photons have the same energy. This applies to both Rayleigh and Mie scattering. Inelastic (Raman) Scattering : Molecular scattering in which the energy of incident and scattered photons is different (energy difference corresponds to vibrational levels of scattering molecules). Multiple Scattering : When radiation is scattered more than once.
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2 3 Rayleigh vs. Raman Scattering Both are molecular or atomic scale processes Rayleigh : Scatterer transitions to “virtual” level and back down to original level; scattered radiation has same energy as input radiation. Raman : Scatterer transitions to “virtual” level and back down to level that is higher in energy (Stokes) or lower in energy (anti-Stokes) than original level. Scattered radiation has lower (Stokes) or higher (anti-Stokes) energy than input radiation. 4 What is the difference between absorption and scattering? Both processes can remove flux from the incident wave, but: Scattering redistributes energy over the total solid angle centered around the scatterer, but the internal energy states of the scatterer are not changed (except Raman). Absorption causes “permanent” change in the internal energy states: rotation, vibration, electronic. Scattering (except Raman) only causes “virtual” changes. Absorption is spectrally selective and quantized, but scattering occurs at all wavelengths. Absorption depends on the imaginary part of the index of refraction, but scattering depends on both the real and imaginary parts. Emission occurs when a molecule relaxes from a higher to a lower energy state (real, not virtual), so emission and scattering are not the same. How does scattering occur? EM wave causes electron distributions to oscillate with same frequency as electric field This oscillation causes periodic separation of charges: induced dipole moment Accelerating charges are source of EM radiation: scattering
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3 5 http://www.wyatt.com/theory/r ayleigh scattering/mass.cfm Light scattering by an induced dipole moment due to an incident EM wave Two formal theories of light scattering: Rayleigh Scattering (after Lord Rayleigh): Theory was formulated specifically for small, dielectric (non-absorbing) spherical particles.
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This note was uploaded on 01/19/2011 for the course ATOC 5235 taught by Professor Randell during the Fall '10 term at Colorado.

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Lecture12 - Chapter 11 The Radiative Transfer Equation with...

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