Comparative study of surface roughness with power spectral density and multi-fractal spectrum

This paper presents a comparative studied of surface roughness. Samples were first measured by atomic force microscope (AFM). The acquired height data was then processed to calculate their power spectral density (PSD) and multi-fractal spectrum (MFS). The calculation results indicate that MFS of different samples with same sampling length differs significantly from each other, while the MFS of the same sample with different sampling length or different sampling position is quite similar. The calculation also shows that MFS is very sensitive to particles or scratches appeared on the surface. The PSD of the same data acquired from these samples are also presented for comparison. It is clear from the calculation results that the PSD curves vary with the sampling position and sampling length, thus makes the evaluation uncertain. No quantitative index available from PSD, only qualitative information obtained. Comparatively, MFS is better in description of a surface roughness.