Sol-gel replicated optics made from single point diamond turned masters exhibit fractal surface roughness

Deterministic optics manufacturing, notably single point diamond turning (SPDT) has matured such that the current generation of machines is capable of producing refractive and reflective optics for the visible wavelength region that are quite acceptable for many applications. However, spiral tool marks are still produced that result in unwanted diffractive scattering from grating-like features having a spatial frequency determined by the machine feed, tool radius, and other influences such as vibration and material removal effects. Such regular artifacts are the characteristic of deterministic manufacturing methods such as SPDT. The authors present some initial findings suggesting that fractal, or non-deterministic surfaces can be produced by SPDT through sol-gel replication. The key is the large isotropic shrinkage that occurs through monolithic sol-gel replication (a factor of 2.5) that results in all features, including tooling marks, being reduced by that amount. The large shrinkage itself would be a laudable-enough feature of the replication process. However, by an as-yet-not understood manner, the replication process itself seems to alter the roughness character of the replicated surface such that it appears to be fractal when analyzed using contact profilometry and the power spectrum approach