An inverse problem of reflection

AbstractThis paper developed an analytic method to solve the inverse problem of reflection. The direct problem is to determine the reflection at the top of a known stratified medium bounded below by a reflector. The inverse problem is to determine the reflection of a reflector from the measured reflection at the top of the medium. The main results are based on the iteration of solutions of two initial value differential equations. They are suitable for numerical computation. A mathematical model is constructed on an abstract space for broad applications which include radiative transfer with inhomogeneous and anisotropic scattering. The solution is general is not unique. A condition has been established for a unique solution. Non-unique solutions are also constructed