Subaperture stitching test of large steep convex spheres

Limited by the aperture and f/number of the transmission sphere (TS), large convex spheres with very small R/number (ratio of the radius of curvature to the aperture) cannot be tested in a single measurement with a standard interferometer. We present the algorithm and troubleshooting for subaperture stitching test of a half meter-class convex sphere with R/0.61. Totally 90 off-axis subapertures are arranged on 5 rings around the central one. Since the subaperture is so small, its surface error is comparable with that of the TS reference error. Hence a self-calibrated stitching algorithm is proposed to separate the reference error from the measurements. Another serious problem is the nonlinear mapping between the subaperture's local coordinates and the full aperture's global coordinates. The nonlinearity increases remarkably with the off-axis angle. As a result, we cannot directly remove power from the full aperture error map as we usually do. Otherwise incorrect spherical aberration will be generated. We therefore propose the sphericity assessment algorithm to match the stitched surface error with a best-fit sphere. The residual is true surface error which can be used for corrective figuring or for tolerance assessment. The self-calibrated stitching and troubleshooting are demonstrated experimentally.