Scattering Matrix and Doubling Equations for the Scattering and Transmission Functions

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  • 1 Dept. of Electrical Engineering, University of Southern California, Los Angeles 90007
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Abstract

In a series of papers given by Redheffer, Peebles and Plesset, Wang, Aronson and Yarmush, Grant and Hunt, the scattering matrix method has been applied to the solution of the linearized Boltzmann equation. On the other hand, the doubling equations for the scattering and transmission functions in a homogeneous anisotropically scattered atmosphere have been found by van de Hulst and successfully extended by Hansen and Hansen and by Hovenier with the aid of the invariance principles. In the present paper we show how to derive the doubling equations for the scattering and transmission functions in a homogeneous anisotropically scattering atmosphere by using the scattering matrix.

Abstract

In a series of papers given by Redheffer, Peebles and Plesset, Wang, Aronson and Yarmush, Grant and Hunt, the scattering matrix method has been applied to the solution of the linearized Boltzmann equation. On the other hand, the doubling equations for the scattering and transmission functions in a homogeneous anisotropically scattered atmosphere have been found by van de Hulst and successfully extended by Hansen and Hansen and by Hovenier with the aid of the invariance principles. In the present paper we show how to derive the doubling equations for the scattering and transmission functions in a homogeneous anisotropically scattering atmosphere by using the scattering matrix.

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