Surface figure test method for large convex optical surfaces

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 S2 and a rear concave spherical surface side S1, thereby transforming the test optic into a lens;
• b) specifying an (x,y) coordinate system in the pupil plane of the test optic where (xi,yj) 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 OPD1(xi,yj) for the rear concave surface S1 in which the test beam passes through a reference sphere, is reflected off the rear concave surface S1, 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 OPD2(xi,yj) for the front convex surface S2 in which the test beam transmits first through a null lens, then through the rear concave surface S1 and then reflects off the front convex surface S2, and passes back through the null lens and into an interferometer;
• e) performing an interferometric null test #4 to obtain the optical path difference data set OPD4(xi,yj) 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 S2, through the test optic substrate, through the rear surface S1, where it is then reflected back through the test optic by a spherical return mirror, back through the null lens, and into an interferometer;
• f) calculating the rear surface S1 surface figure error, h1(xi,yj), the front surface S2 surface figure error, h2(xi,yj), and the optical path difference introduced by inhomogeneity in the test optic substrate, OPDI(xi,yj), from the three optical path difference data sets, OPD1(xi,yj), OPD2(xi,yj), and OPD4(xi,yj), respectively;
• g) polishing the front convex surface S2 and the rear concave surface S1 of the test optic to reduce the surface figure errors obtained in f);
• h) iteratively testing and polishing the front convex surface S2 and the rear concave surface S1 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.