Patent ID: 8576408

Claim:
A method for producing a convex mirror having a desired surface figure quality wherein the substrate of the mirror under test, the test optic, is treated as a lens prior to applying a reflective coating to the convex surface of the test optic substrate, the method comprising the steps of: a) choosing a material for the test optic substrate that is transmissive at a chosen coherent test beam wavelength, the test optic having a front convex surface side S 2 and a rear concave spherical surface side S 1 , thereby transforming the test optic into a lens; b) specifying an (x,y) coordinate system in the pupil plane of the test optic where (x i ,y j ) refers to a set of point locations in the pupil plane, and where i and j are integers ranging from i=1 . . . N and j=1 . . . M and N and M are large numbers typically between 100 and 1000; c) performing an interferometric test # 1 to obtain the optical path difference data set OPD 1 (x i ,y j ) for the rear concave surface S 1 in which the test beam passes through a reference sphere, is reflected off the rear concave surface S 1 , passes back through the reference sphere and into an interferometer; d) performing an interferometric null test # 2 to obtain the optical path difference data set OPD 2 (x i ,y j ) for the front convex surface S 2 in which the test beam transmits first through a null lens, then through the rear concave surface S 1 and then reflects off the front convex surface S 2 , and passes back through the null lens into an interferometer; e) performing an interferometric null test # 3 to obtain the optical path difference data set OPD 3 (x i ,y j ) introduced by inhomogeneity in the test optic substrate in which the test beam transmits first through a null lens, then through the front convex surface S 2 and reflects off the rear concave surface S 1 , and passes back through the null lens into an interferometer f) calculating the rear surface S 1 surface figure error, h 1 (x i ,y j ), the front surface S 2 surface figure error, h 2 (x i ,y j ), and the optical path difference introduced by inhomogeneity in the test optic substrate, OPDI(x i ,y j ), from the three optical path difference data sets, OPD 1 (x i ,y j ), OPD 2 (x i ,y j ), and OPD 3 (x i ,y j ), respectively; g) polishing the front convex surface S 2 and the rear concave surface S 1 of the test optic to reduce the surface figure errors obtained in f); h) iteratively testing and polishing the front convex surface S 2 and the rear concave surface S 1 of the test optic until a desired front convex surface figure is obtained; and i) coating the convex surface with a reflective material once the desired convex surface is obtained to thereby produce the desired convex mirror.