Roughness of surface decorated with randomly distributed pillars

We have presented a quantitative analysis of roughness of planar surfaces decorated with randomly distributed, cylindrical pillars, disks, or cavities. We have described the roughness in terms of the surface power spectral density (PSD). First, we have derived a general equation for the PSD of such surfaces. Then, we have found the PSD for the special case of statistically isotropic, circular areas. We have demonstrated that the PSD provides quantitative information on the radius of the circular area, dimensions of the pillar, and surface coverage. We have also discussed the numerical method of extracting the parameters from experimental PSD data obtained from discrete Fourier transform of surface scanning measurements.