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Error in vertex radius of curvature extrapolation via least-squares fit

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Abstract

We assume a number of points on a possibly off-axis test segment are sampled and that the pupil coordinates of these points are known or estimated a priori. The z-coordinate (the sagitta) of each sampled point can be determined using some remote distance measuring technique. The (x,y,z) ordered triplets thus generated for each sampling point are used as data in a least-squares fit to determine the best-fit parent surface. In the case presented here, the best-fit parent is assumed to be a perfect paraboloid. Since a three dimensional paraboloid is axially symmetric, the sagittae measured at the sampling points on the test piece can be fitted (in a least-squares sense) to a two dimensional parabola that is a function of radius only. From this parabola a vertex radius of curvature is calculated. This method can be extended, with only superficial changes, to any conic of rotation.

© 2002 Optical Society of America

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