On the synthesis of axisymmetric two-mirror objectives

An analytical solution to the synthesis problem for the generatrices of the mirrors of an axisymmetric two-mirror objective, which are synthesized for a specified mapping law of the incident and reflected wave fronts, is obtained in the geometrical-optics approximation. The solution, in which the generatrix is expressed in the form of a polynomial in even powers of angle, ensures exact focusing of radiation from one system focus to the other and a specified error of the realization of the mapping function via selection of the polynomial degree. Synthesis problems for an aplanatic objective and an objective with uniform amplitude distribution in the output front are considered. It is shown that, in the first case, a sixth-degree polynomial ensures realization of the Abbe sine condition with an error of 10−5 and, in the second case, it ensures a deviation from the specified amplitude of about 0.1 dB.