Surface-error Measurement for a Convex Aspheric Mirror Using a Double-stitching Method

A reflecting telescope consists of a concave primary mirror and a convex secondary mirror. The primary mirror is easy to measure, because it converges the beam from an interferometer, while the secondary mirror diverges the beam and so is not easy to measure, even though it is smaller than the primary mirror. In addition, the Korsch-type telescope uses the central area of the secondary mirror. so that the entire area of the secondary mirror needs to be measured, which the classical Hindle test cannot do. In this paper, we propose a double-stitching method that combines two separate area measurements: the annular area, measured using the Hindle stitching method, and the central area, measured using a spherical wave from the interferometer. We test the surface error of a convex asphere that is 202 mm in diameter, with 499 mm for its radius of curvature and -.4.613 for its conic constant. The surface error is calculated to be 19.5 +/- 1.3 nm nns, which is only 0.7 nm rms different from the commercial stitching interferometer. ASI. Also, the two results show a similar 45 degrees astigmatism aberration. Therefore, our proposed method is found to be valuable for testing the whole area of a convex asphere.