Residual surface roughness of diamond-turned optics

TLDR

Diamond‑turned optics exhibit residual surface roughness with significant periodic components, and measurements probe the two‑dimensional power spectral density across scales from the wavelength to the beam spot diameter. The study explores the optical properties of these surfaces using Rayleigh‑Rice vector scattering theory for periodic roughness with sub‑wavelength vertical amplitudes. The authors provide expressions for interpreting differential‑scatter, total‑integrated‑scatter, reflectometry, and ellipsometric data in the limit of a highly conducting surface. The derived information can aid practical characterization of mirror surfaces.

Abstract

The residual surface roughness of diamond-turned optics is expected to contain significant periodic components. The optical properties of such surfaces are explored as a special case of Rayleigh-Rice vector scattering theory applied to periodic roughness with vertical amplitudes much smaller than the wavelength of light. Expressions are given for the interpretation of differential-scatter, total-integrated-scatter, reflectometry, and ellipsometric measurements in the limit of a highly conducting, surface. In general, such measurements give varying degrees of information about the two-dimensional power spectral density of the surface roughness within the nominal range from the wavelength of light to the diameter of the probing beam spot. Such information may be useful for the practical characterization of mirror surfaces.