Correlation Function for a 2-D field

AI Thread Summary
To compute a correlation function for a 2-dimensional field of surface heights, one can use an integral approach involving the product of height values at different points. The suggested formula includes integrating over displacement parameters to analyze spatial correlations. Research indicates that for random surfaces, the autocorrelation function typically follows a Gaussian distribution. While specific resources may be scarce, searching for terms related to "rough surface" and "2-D correlation metrology" can yield useful information. Understanding these principles is essential for accurately modeling the correlation of surface heights.
Miss_Astro
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I have a 2-dimensional field of values (they are actually heights of a surface) and I want to compute a correlation function or some sort of correlation parameter. I have seen something similar done with galaxies and you end up with something like the probability of finding a galaxy at a certain distance from another galaxy.

So yes, I want to do something similar for heights, does anyone have a cluse where I might start or how to do this?
 
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That's pretty straightforward: something like

\int d\alpha d\beta [z(x,y)z(x-\alpha,y-\beta)]

I didn't find a concise website, but searching for "rough surface" 2-D correlation metrology scattering (not all at once) pulls of a lot of information.

Generally, for random surfaces, the autocorrelation is Gaussian.
 
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