Comments On The Correlation Length

E L Church

doi:10.1117/12.939599

23 March 1987 Comments On The Correlation Length

E L Church

Proceedings Volume 0680, Surface Characterization and Testing; (1987) https://doi.org/10.1117/12.939599
Event: 30th Annual Technical Symposium, 1986, San Diego, United States

Abstract

Surface finish has vertical and transverse attributes. In optics the first is characterized by the root-mean-square roughness, and it is natural to seek an analogous length parameter, or "correlation length", to characterize its transverse properties. This paper evaluates various candidates for this purpose by examining their robustness to the finite-bandwidth effects inherent in all real measurement processes. The critical consideration is the magnitude of the correlation length with respect to the range of surface wavelengths in-cluded in the measurement: When the length parameters of the surface fall outside the measurement bandwidth it is possible to get totally spurious values for the measured parameters, and when they fall inside the band-width, the measured and true values can still differ by significant factors. This sensitivity of the correlation function to bandwidth effects arises from the fact that the measurement process modifies it by convolution; in contrast to the finish power spectrum, where the modifications involve simple multiplication. The present results argue against the use of length parameters derived from the measured correlation function as precise measures of the transverse character of surface finish, although they may still be useful for compar-ative and diagnostic purposes. The most precise characterization of the combined vertical and transverse properties of surface finish are given in terms of its power spectral density.

Citation Download Citation

E L Church "Comments On The Correlation Length", Proc. SPIE 0680, Surface Characterization and Testing, (23 March 1987); https://doi.org/10.1117/12.939599

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