Correlation Function for a 2-D field

[Miss_Astro]

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?

 

[Andy Resnick]

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.