A modified stitching algorithm for testing rotationally symmetric aspherical surfaces with annular sub-apertures

Abstract

Annular sub-aperture stitching technique has been developed for low cost and flexible testing rotationally symmetric aspherical surfaces, of which combining accurately the sub-aperture measurement data corrupted by misalignments into a complete surface figure is the key problem. An existed stitching algorithm of annular sub-apertures can convert sub-aperture Zernike coefficients into full-aperture Zernike coefficients, in which use of Zernike circle polynomials represents sub-aperture data over both circle and annular domain. Since Zernike circle polynomials are not orthogonal over annular dominion, the fitting results may give wrong results. In this paper, the Zernike polynomials and existed stitching algorithm have been reviewed, and a modified stitching algorithm with Zernike annular polynomials is provided. The performances of a modified algorithm on the reconstruction precision are studied by comparing with the algorithm existed. The results of computer simulation show that the sub-aperture data reduction with the modified algorithm is more accurate than that obtained with the existed algorithm based on Zernike circle polynomials, and the undergoing matrix manipulation is simpler.