Solution of the task of planar geometric optics with a non-stationary source

Abstract

In the present paper a geometric model of acquisition of receiver curve in the tasks of planar geometric optics with a non-stationary emitter is proposed. The model is based on cyclographic mapping of Euclidean space on a plane and significantly differs in terms of simplicity from the existing mathematical models applied in solution of similar tasks. Furthermore, the proposed model differs in applying uniform solution algorithms for direct and inverse planar geometric optics tasks. The variety of such tasks is dictated by variety of geometric forms of the sought element of the triad “emitter-reflector-receiver” as well as the initial conditions, where a single element of the triad is unknown and sought. The results of the present paper can find application in the area of metrology for optical profile control of machined cylindrical workpieces constituting reflector of the triad.