A brief review of techniques for measuring surface roughness and optical figure is given. One of the most promising of these techniques for measuring the roughness of optical surfaces is interferometry employing fringes of equal chromatic order (FECO). A FECO scanning interferometer is described, which has been used to determine statistics of polished surfaces having roughnesses under 100 Å rms. The scanning interferometer resolves square surface elements 2 µm on a side and statistically characterizes the surface in terms of these elements. Height- and slope-distribution functions, rms roughness, rms slope, and modified autocovariance length distributions have been measured for selected optical surfaces. Nearly all surfaces had Gaussian distributions of heights and slopes, but none had Gaussian distributions of autocovariance lengths. Surfaces such as electropolished copper, electroless nickel, and single-point diamond-machined copper were found to have smaller rms slopes than other surfaces of comparable roughness and scattered less than predicted by simple scalar scattering theory.1,2 On the other hand, heavily scratched surfaces such as polished potassium chloride had larger slopes and produced more scattering than expected from simple theory.
Jean M. Bennett, "Measurement of the rms roughness, autocovariance function and other statistical properties of optical surfaces using a FECO scanning interferometer," Appl. Opt. 15, 2705-2721 (1976)