Scattering Matrix

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.