Non-approximate method for designing annular field of two-mirror concentric system

Annular field aberrations of a three-reflection concentric system,which are composed of two spherical mirrors,are analyzed.An annular field with a high level of aberration correction exists near the position where the principal ray is perpendicular to the object-image plane.Aberrations are determined by the object height and aperture angle.In this letter,the general expression of the system aberration is derived using the geometric method,and the non-approximate design method is proposed to calculate the radii of the annular fields that have minimum aberrations under different aperture angles.The closer to 0.5（the ratio of the radius of convex mirror to the radius of concave mirror）is,the smaller the system aberration is.The examples analyzed by LABVIEW indicate that the annular field designed by the proposed method has the smallest aberration in a given system.