This article describes the method of mathematically stitching together a plurality of overlapping individual annular sub-aperture maps to yield the full-aperture map of an asphero-diffractive surface. The unknown step height and relative position of each zone causes some ambiguity when the individual sub-apertures are combined into a full aperture map. The uncertainty is mainly caused by alignment error and noise during the measurements of individual sub-aperture maps and step height. The optimization and merit function works to minimize the discrepancy between multiple data sets by including components related to various alignment errors and noise during the measurements of individual sub-aperture maps and step height. The stitching coefficients which minimize the mean square difference between any overlapping values can be found through iterative constrained optimization. The full aperture wave-front is reconstructed by stitching sub-apertures with the stitching coefficients within meaningful bounds.

Date Published: 6 March 2015
PDF: 4 pages
Proc. SPIE 9446, Ninth International Symposium on Precision Engineering Measurement and Instrumentation, 94463K (6 March 2015); doi: 10.1117/12.2181386

Published in SPIE Proceedings Vol. 9446:
Ninth International Symposium on Precision Engineering Measurement and Instrumentation
Junning Cui; Jiubin Tan; Xianfang Wen, Editor(s)