Roughness Power Spectral Density

If the surface (i.e., the best fit plane) is in the x—y plane, and Z x,y) is the surface height variation (surface roughness) relative to that plane, the power spectral density is given by... 

Although the power spectral density contains information about the surface roughness, it is often convenient to describe the surface roughness in terms of a single number or quantity. The most commonly used surface-finish parameter is the root-mean-squared (rms) roughness a. The rms roughness is given in terms of the instrument s band width and modulation transfer function, M(p, q) as... 

Other roughness indices have also been introduced, such as moving average, power spectral density, half roughness index. Mays response meter, root-mean-square acceleration, root-mean-square vertical acceleration, Texas MO and Brazil Ql, to name a few (Sayers and Karamihas 1996). 

Our approach to derive a quantitative criterion for the roughness characteristics of ultra-hydrophobic surfaces with stochastic roughness properties is based on roughness analysis by power spectral density (PSD) functions and subsequent data reduction algorithm [11]. 

A stochastically rough surface with a large diversity of spatial frequencies can be quantitatively described by Power Spectral Density (PSD) functions [9, 10]. The PSD function provides the relative strength of the individual roughness components as a function of the spatial frequencies f and f in... 

A. Duparre, J. Ferr -Borrull, S. Chech, G. Notni, J. Steinert, and J. M. Bennett, Surface characterization techniques for determining rms roughness and power spectral densities of optical components, App/. Opt. 41,154-171 (2002). 

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