This paper presents a rationale for the precision measurement and characterization of surface finish using Fourier techniques. It offers a precise definition of figure and finish errors in the frequency domain and discusses particular finish statistics of importance for optical surfaces: the finish power spectral density and the mean-square finish error. Problems involved in estimating these quantities from practical measurements are discussed and illustrated. The need for an expanded data base of spectral shapes is emphasized.
E. L. Church,
"The Precision Measurement And Characterization Of Surface Finish", Proc. SPIE 0429, Precision Surface Metrology, (15 November 1983); doi: 10.1117/12.936344; https://doi.org/10.1117/12.936344