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Orthogonal polynomials and tolerancing

机译：正交多项式和公差

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摘要

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.
机译：先前的论文已经确定了将公差直接应用于幂级非球面系数的不明智性。根本原因是各个术语都不正交。Zernike曲面和新的福布斯曲面类型在“归一化半径”所描述的圆上具有某些正交性。然而，在远离光阑的表面上，光束小于表面，并且多项式在光束采样的区域上不正交。本文研究了当表面远离孔径移动时正交性的分解停止，这对宽容的含义。

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