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Proceedings Paper

Orthogonal polynomials and tolerancing
Author(s): John R. Rogers
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Paper Abstract

Previous papers have established the inadvisability of applying tolerances directly to power-series aspheric coefficients. The basic reason is that the individual terms are far from orthogonal. Zernike surfaces and the new Forbes surface types have certain orthogonality properties over the circle described by the "normalization radius." However, at surfaces away from the stop, the optical beam is smaller than the surface, and the polynomials are not orthogonal over the area sampled by the beam. In this paper, we investigate the breakdown of orthogonality as the surface moves away from the aperture stop, and the implications of this to tolerancing.

Paper Details

Date Published: 12 September 2011
PDF: 13 pages
Proc. SPIE 8131, Optical System Alignment, Tolerancing, and Verification V, 81310D (12 September 2011); doi: 10.1117/12.896109
Show Author Affiliations
John R. Rogers, Synopsys, Inc. (United States)

Published in SPIE Proceedings Vol. 8131:
Optical System Alignment, Tolerancing, and Verification V
José Sasián; Richard N. Youngworth, Editor(s)

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