Reconstruction of Reflector Surfaces from Near-field Scattering
Data
Sergey Kochengin
Abstract:
Consider a reflector system consisting of a closed convex reflecting
surface R, a point light source O and some object T. Suppose that the
source O and the object T are inside the reflecting surface
R. Depending on the geometry of R the energy radiated by O and
reflected by R is distributed on T producing a certain illumination
pattern. We consider here the inverse problem consisting in
reconstructing the reflector R from the following data: the position
of the source O, its radiation intensity I, the screen T, the energy
pattern to be achieved on T. We show here that under the assumptions
of the geometric optics theory the problem admits a solution, provided
the total input and output energies are equal, and some other
geometric conditions are satisfied. In analytic formulation, the
problem leads to an equation of Monge-Ampere type on a unit sphere. In
this paper we formulate the problem in terms of certain associated
measures and establish existence of weak solutions.