# Radially averaged surface roughness/topograph​y power spectrum (PSD)

Version 1.2.0.0 (3.49 KB) by
Calculates radially averaged 2D power spectrum for a surface roughness/topography
Updated 19 Dec 2016

In surface roughness analysis, one of the powerful tools for roughness characterization is surface roughness power spectrum. If the surface under study has isotropic roughness characteristics, then one can do a radial average on the calculated discrete Fourier transform of the surface topography and obtain its 2D power spectrum, namely, 2D PSD.
With this function you can calculate 2D PSD of a surface topography, which the topography is normally obtained by any 3D profilometry techniques, such as AFM (Atomic Force Microscopy), WLI (White Light Interferometry) and many other optical profilers.
As inputs, you first need to have a matrix (n by m) of your height values (z). Second, you need to know you PixelWidth (spatial resolution) which is obtained easily by dividing you image length to the number of pixels in length, i.e. :

PixelWidth = Lx / m; % in SI units

In order to plot the output:
loglog(q,C)

In order to check 2D FFT of your topography:
imagesc(1+log10(abs(PSD.Hm)))

An extended version of this code, calculates the surface roughness power spectrum only for a portion of the top or bottom part of the surface roughness/topography. This has been uploaded in here:

Radially averaged surface roughness power spectrum (PSD) only on top or bottom part of a topography

To calculate 1-dimensional suface roughness power spectrum, refer to:

1-Dimensional surface roughness power spectrum of a profile or topography
http://se.mathworks.com/matlabcentral/fileexchange/54315-psd-1d-z--pixelwidth--dim-

To generate an artificial randomly rough surface/topography to try these codes, refer to:

Surface generator: artificial randomly rough surfaces
http://se.mathworks.com/matlabcentral/fileexchange/60817-surface-generator--artificial-randomly-rough-surfaces

### Cite As

Mona Mahboob Kanafi (2024). Radially averaged surface roughness/topography power spectrum (PSD) (https://www.mathworks.com/matlabcentral/fileexchange/54297-radially-averaged-surface-roughness-topography-power-spectrum-psd), MATLAB Central File Exchange. Retrieved .

##### MATLAB Release Compatibility
Created with R2016a
Compatible with any release
##### Platform Compatibility
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Version Published Release Notes
1.2.0.0