Design of a null compensator for steep convex secondary asphere of extremely large optical telescope

A new test for steep convex hyperboloidal secondary mirrors with large aperture and fast focus ratio is presented. It makes use of small correcting lens and an auxiliary ellipsoidal mirror that is about one point eight times as large as that of the convex mirror tested. This methord is sutable for convex secondary asphere of extremely large aperture optical telescope. Taking TMT as an example which surface is a convex shape with a 3.1m diameter, a F/1 of fast focus ratio, -1.318228 of conic constant, a null compensation system is successfully designed and optimized. The design results indicate that the surface quality of the steep convex hyperboloidal secondary mirror could be measured synchronously, in addition the aberration of the testing system is well corrected and the spot diagram is smaller than diffraction limit. Analyses of the system´s wave-front error with respect to the change in the surface parameter of optical elements are described. The test is a compensating test of excellent.