Two-Mirror Systems with Spherical Reflecting Surfaces

An analysis is made of two-mirror systems consisting of spherical reflecting surfaces. Solutions are found for those systems having zero third-order spherical aberration. It is shown that no practical solution exists for the configuration resembling the Cassegrainian telescope; there are three one-parameter families of solutions. These are given by c1=(q−1)/2t0t1=(t0−f)/qc2=q/2ft0=(27f/32)sec2θq=−3[1+4cos23(θ+πr)]−1,where c1 and c2 are the two curvatures; t1 the axial separation of the two reflecting surfaces; t0 the distance from a focus to the corresponding surface; and f the focal length. The free parameter is θ and r = 0, 1, −1.