The specific intensities of nonparallel light in the direction of a stellar source, such as the sun, resulting from multiple scattering and diffuse ground reflection of a unit flux of parallel radiation incident on a plane parallel, Rayleigh atmosphere, equivalent to the Earth’s atmosphere in composition and density, are evaluated following S. Chandrasekhar's extension of the Rayleigh theory. Values are given as a function of direction of the source and normal optical thickness covering the visible and near ultra violet spectrum.
It is shown that the flux resulting from such nonparallel radiation, for a sufficiently small solid angle (10-3 radian) around the source, when the latter is within 50° or less of the vertical, is of the order of 10-5 of the reduced flux of the direct solar beam, for radiation within the visible range. The relative importance of the scattered light increases with normal optical thickness and zenith distance of the source.
It is pointed out that certain observations of apparent atmospheric transmissions of solar radiation in the blue end of the visible spectrum exceed in magnitude significantly the values obtained from the exact Rayleigh scattering theory, and it is suggested that this anomaly may be due to non-Rayleigh particles existing in the high atmosphere, with strong forward scattering characteristics.
DIRAN DEIRMENDJIAN and ZDENĚK SEKERA, "Quantitative Evaluation of Multiply Scattered and Diffusely Reflected Light in the Direction of a Stellar Source in a Rayleigh Atmosphere," J. Opt. Soc. Am. 43, 1158-1165 (1953)