Slope error tolerances for optical surfaces

Today, most optical surfaces are assigned tolerances on power and irregularity, as well as on surface defects (scratch and dig), but usually not on surface slope error. This situation reflects concern for the types of 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 - or, at least, types of surface 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 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 can be calculated.