The Forward Scattering Formula Of Tam And Zardecki Evaluated By Use Of Cubic Sections Of Spherical Hypersurfaces

Konrad Altmann

doi:10.1117/12.960888

11 October 1989 The Forward Scattering Formula Of Tam And Zardecki Evaluated By Use Of Cubic Sections Of Spherical Hypersurfaces

Konrad Altmann

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Proceedings Volume 1115, Propagation Engineering; (1989) https://doi.org/10.1117/12.960888
Event: SPIE 1989 Technical Symposium on Aerospace Sensing, 1989, Orlando, FL, United States

Abstract

In order to evaluate the series expansion in scattering orders derived by Tam and Zardecki for the multiple forward scattering irradiance, the multidimensional integrals describing the contributions of the individual scattering orders n have been transformed into 1-D ones by use of a weight function Fn. The function Fn represents that section of a spherical hypersurface centered at the origin which is enclosed within the unit hypercube. For the calculation of the Fn, two approaches are proposed. The first one starts from a combinatorial consideration and yields a complete mathematical expression for the Fn in the form of multidimensional integrals which, however, can be computed recursively from one another in order of increasing n by a 1-D analytical or numerical integration. For higher n a second approach is developed yielding for the Fn an approximation in form of a function series which is used to expand the contributions of the individual scattering orders in a fast converging series in negative powers of n. This expansion also reveals general features of multiple forward scattering.

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Konrad Altmann "The Forward Scattering Formula Of Tam And Zardecki Evaluated By Use Of Cubic Sections Of Spherical Hypersurfaces", Proc. SPIE 1115, Propagation Engineering, (11 October 1989); https://doi.org/10.1117/12.960888

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