An efficient and versatile model that describes the temporal characteristics of scattered radiation when single-scatter conditions prevail is proposed and developed. The model is based on the focal radii property of a prolate spheroid, and for an impulsive source located at one focal point and an observer at the other, it associates all scattering events occurring on a given prolate spheriodal surface with the same transit time. All interactions between the radiation and matter are classified as either elastic scattering or absorption, and expressions are obtained for the intensity and the collected energy as a function of time at the observation point. The model is applied to isotropic, Rayleigh, and Mie-type scattering; the single-scatter phase function for Mie-type scattering is approximated by the Henyey-Greenstein function. For simple source and observer geometries, closed-form expressions are obtained for the intensity in the isotropic and Rayleigh cases. Finally, the model is applied to examples which typify middle ultraviolet radiation propagating in the earth’s atmosphere.
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