Calculation of the power spectral density from surface profile data

TLDR

The 2‑D power spectral density is the preferred metric for surface roughness in draft international standards. The study provides a correct method for computing the 1‑D PSD from discrete surface profiles and highlights pitfalls in standard FFT approaches. The authors present a method with proper normalizing factors and two variance‑reduction techniques for PSD estimation. Illustrative examples demonstrate the effectiveness of the variance‑reduction techniques.

Abstract

The power spectral density (PSD), in its two-dimensional form, has been designated as the preferred quantity for specifying surface roughness on a draft international drawing standard for surface texture. The correct calculation of the one-dimensional PSD from discrete surface profile data is given, and problems in using fast Fourier-transform routines that are given in some of the standard reference books are flagged. The method given here contains the correct normalizing factors. Two ways to reduce the variance of the PSD estimate are suggested. Examples are shown of the variance reduction possible in the PSD's.