Reconstruction of an optical surface from a given source-target map.

We propose a new method for the reconstruction of a reflecting (refracting) surface from a given source-target map defining the relationships between the directions of incident and reflected (refracted) rays. In the proposed method, the optical surface is represented as an envelope of a set of paraboloids (reflecting surface) or ellipsoids (refracting surface). This representation allows the problem of design of an optical surface to be reduced to the reconstruction of a function from its total differential.