Thin lens formulas are given for the focal length, longitudinal chromatic aberration, spherical aberration, and coma of a Mangin mirror, consisting of two lenses cemented together with the second surface of the second lens silvered. Application of these yields a rough solution for a spherically and chromatically corrected Mangin mirror. Methods of correction are discussed. Ten glass combinations, making coma correction possible, together with design details of thirty achromatic aplanatic cemented doublet Mangin mirrors using these combinations, are given.
N. v. d. W. Lessing, "Considerations on Cemented Doublet Mangin Mirrors," Appl. Opt. 8, 979-983 (1969)