Considerations in the evaluation and correction of mid-spatial frequency surface features

Surfaces are commonly specified with peak to valley (PV) and root-mean-square (rms) requirements for surface form and roughness, describing surface quality with a few simple numbers. These specs ignore lateral feature sizes between form and roughness (so-called mid-spatial frequencies, or MSFs), however, making them inadequate for many modern optics fabricated with advanced technologies. Specifications sensitive to the lateral feature size, such as such as slope or power-spectral density (PSD), are increasingly employed to fill this void. Having a detailed view of the surface error as a function of lateral feature size can drive fabrication decisions. For example, a large aperture tool tends to correct small features well but performs less well on large features; while subaperture tools tend to do the opposite. Therefore after each fabrication step we want to know how the surface features at different lateral sizes evolved, so that we can optimize the choice of the next fabrication step. A spec like PSD often doesn't inform the fabricator whether it's failing because of a localized error (such as edge roll), continuous texture, or an artifact of metrology or computation. So while it may indicate the need for additional fabrication steps, it is not ideal for guiding specifically which fabrication step ought to be undertaken next. We have developed analyses to help determine what surface characteristics are failing spec, and thus optimize the next fabrication step. Finally, we demonstrate an example of how we have applied these techniques to fabricate parts with demanding slope and MSF specifications.