Mirror Anastigmat with Two Concentric Spherical Surfaces

There is given a description of a two-mirror system suitable for imaging a small polychromatic light source at finite distance. The system consists of two-concentric spherical surfaces, convex and concave, respectively. Third-order, spherical aberration, coma, and astigmatism are cancelled. Fifth-order aberrations are calculated explicitly to permit the computation of construction parameters and mounting tolerances according to the image quality required. A numerical example is given.The following theorem is proved: if two of the third-order aberrations, coma, spherical aberration, and astigmatism, of a two-mirror system with spherical surfaces vanish, so does the third. The theorem is applied to the special case of the monocentric system described, but it is proved for heterocentric systems.