Correlation Function for a 2-D field

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SUMMARY

The discussion focuses on computing a correlation function for a 2-dimensional field representing surface heights. The proposed mathematical formulation involves the integral of the product of height values at different coordinates, specifically expressed as ∫ dα dβ [z(x,y)z(x−α,y−β)]. Participants suggest searching for terms like "rough surface" and "2-D correlation metrology scattering" to find relevant information. It is established that the autocorrelation for random surfaces typically follows a Gaussian distribution.

PREREQUISITES
  • Understanding of 2-dimensional correlation functions
  • Familiarity with integral calculus
  • Knowledge of Gaussian distributions
  • Basic concepts of surface metrology
NEXT STEPS
  • Research "2-D correlation functions in surface metrology"
  • Explore "Gaussian autocorrelation in random surfaces"
  • Study techniques for measuring surface heights
  • Investigate software tools for statistical analysis of 2-D data
USEFUL FOR

Researchers in surface metrology, data analysts working with 2-D spatial data, and mathematicians interested in correlation functions.

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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