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14 May 2007 Slope error tolerances for optical surfaces
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Today, most optical surfaces are assigned tolerances on power and irregularity, as well as on surface defects (scratch and dig), but usually not on peak surface slope error. This situation reflects concern for the types of error that typically occur with the classical, grind-and-polish method of fabricating lenses. Sometimes, RMS tolerance types are used to control the difference between a surface and the intended, ideal surface. With the propagation of new fabrication methods, new types of surface error - or, at least, types of surface error that were not previously prevalent - are increasing in importance. In particular, this is true for processes such as diamond turning and computer-controlled, local polishing, both of which are used for the fabrication of aspheric surfaces and aspheric mold inserts. In this paper, we examine the use of "peak slope error" as a criterion for specifying optical surface. In the first part of the paper, we look into cases in which the traditional tolerance types for form error are insufficient, and examine when and where surface slope errors (as opposed to surface height errors) are important In the second part of the paper, we look at how tolerances for slope error can be calculated.
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John R. Rogers "Slope error tolerances for optical surfaces", Proc. SPIE 10316, Optifab 2007: Technical Digest, 1031605 (14 May 2007);

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