On the Diffusion Matrix of Radiative Transfer
RAND CORP SANTA MONICA CA
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The diffusion matrix, formerly derived with the stochastic model of radiative transfer, is derived using auxiliary equations in conjunction with the Milne integral equations. Also derived is the extension concerning the Neumann solution as given by Busbridge. In the case of diffuse reflection and transmission of parallel rays, the solutions are expressed in terms of a pair of scattering and transmission functions for each of the two boundaries of the atmosphere. These global functions are given by X and Y functions that are equal to those previously found by Bellman and Kalaba. Whereas the diffusion matrix formally has a somewhat similar appearance to a map yielded by Preisendorfer, the mathematical development is different. If the optical properties of the medium are constant throughout the atmosphere, the reflectance and transmittance operators reduce to those given by Sobolev.
- Quantum Theory and Relativity