The optical test for the flatness of a plane mirror in conjunction with a concave spherical mirror has been analyzed in terms of the hyperboloid to which it can be thought to be referenced. This geometrical approach renders obvious the requirement to make two tests, the second after rotating the plane mirror 90° about its normal. The expression for the separation of the astigmatic foci for a long radius of curvature, nearly flat, mirror is in agreement with previous derivations.
H. D. Polster, "The Common Test for Plane Mirrors," Appl. Opt. 9, 840-843 (1970)