Synthesis of a Three-Mirror System with Specified Shape of the Main Mirror Using Phase Front and Mapping Law

Abstract

Ray-optic approximation is used to derive an analytical solution to the problem of synthesis of mirrors that form an axisymmetric three-mirror system with predetermined main mirror. Such a system provides transformation a spherical front of a source into an arbitrary front with the desired mapping law. The generatrix of an auxiliary mirror is represented as a polynomial in terms of even powers of angle. The solution can be used to exactly implement the output front and obtain the desired error of mapping law. The synthesis of a three-mirror telescope in which either parabolic or spherical mirror serves as the main mirror is considered.