In previous chapters, we developed the invariant imbedding technique for multiple scattering in a vertically stratified plane parallel medium. Many advantages of this technique have been discussed. The purpose of this chapter is to extend invariant imbedding techniques by introducing scattering matrix analysis. The scattering matrix relates inputs to outputs. Such an extension gives us a physical understanding of complex multiple scattering. This approach provides a more solid mathematical structure. This also provides us with a new tool to solve more complicated problems such as time-dependent radiative transfer. Scattering matrix analysis lays the foundation of computational methods, several as presented in this chapter. It also leads us naturally to discuss and solve the inverse problems which are used in other chapters.
KeywordsRadiative Transfer Star Product Sweep Method Reflection Operator Thin Medium
Unable to display preview. Download preview PDF.
- 3.R. Redheffer, “On the Relation of Transmission Line Theory to Scattering and Transfer,” J. Mathematics and Physics, Vol. XLI, No. 1, March 1962, pp. 1–41.Google Scholar
- 4.S. Chandrasekhar, Radiative Transfer, Dover Publications, Inc., New York, 1960.Google Scholar
- 8.S.A. Kaplan, “On the Theory of Light Scattering in a Non-steady-state Medium,” Astron. J. U.S.S.R., Vol. 39, 1962, pp. 702–709.Google Scholar
- 11.R. M. Redheffer and A. P. Wang, “Formal Properties of Time-Dependent Scattering Processes,” J. Math. and Mechanics, Vol. 19, No. 9, 1970, pp. 765–781.Google Scholar