Diffuse transmission of light from a central source through an inhomogeneous spherical shell with isotropic scattering

by Richard Ernest Bellman, H. H. Natsuyama, Robert E. Kalaba, S. Ueno


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A partial integral equation is derived for the angular distribution of the radiation that is diffusely transmitted through an inhomogeneous, isotropically scattering, spherical shell when there is a constant net flux of radiation normally incident on the inner surface. An equation is also derived for the strength of the diffusely reflected radiation when the shell is illuminated at each point on the outer surface by constant isotropic incident radiation. As far as is known the equations are new and exact and appear to lend themselves well to numerical solution. 18 pp.

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