Correlation Function for a 2-D field

In summary, the speaker is looking for a way to compute a correlation function or parameter for a 2-dimensional field of values representing the heights of a surface. They have seen a similar procedure done with galaxies and are looking for guidance on how to apply it to their data. The suggested approach involves integrating over the product of two height values at different points on the surface. Searching for terms related to 2-D correlation for rough surfaces yields a lot of relevant information. It is also noted that the autocorrelation for random surfaces tends to be Gaussian.
  • #1
Miss_Astro
15
0
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?
 
Physics news on Phys.org
  • #2
That's pretty straightforward: something like

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

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.
 

1. What is a correlation function for a 2-D field?

A correlation function for a 2-D field is a mathematical tool used to measure the relationship between two variables in a 2-dimensional space. It calculates the degree to which changes in one variable are associated with changes in another variable.

2. How is a correlation function for a 2-D field calculated?

The correlation function is calculated by first determining the mean and standard deviation of the two variables. Then, for each point in the 2-D space, the product of the differences from the mean for both variables is calculated and summed. This sum is divided by the product of the standard deviations to get the correlation value for that point.

3. What does the result of a correlation function for a 2-D field indicate?

The result of a correlation function indicates the strength and direction of the relationship between the two variables. A value of 1 indicates a perfect positive correlation, while a value of -1 indicates a perfect negative correlation. A value of 0 indicates no correlation.

4. How is a correlation function for a 2-D field used in scientific research?

A correlation function is commonly used in scientific research to identify patterns and relationships between variables. It can help scientists understand the underlying mechanisms and interactions within a system, and can also be used to make predictions about future behavior.

5. Are there any limitations to using a correlation function for a 2-D field?

Yes, there are several limitations to using a correlation function. It does not indicate causation, meaning that just because two variables are correlated, does not mean that one causes the other. It also assumes a linear relationship between the variables, and may not accurately represent non-linear relationships. Additionally, it may be influenced by outliers or other factors that can impact the results.

Similar threads

  • Other Physics Topics
Replies
15
Views
3K
  • Quantum Physics
Replies
1
Views
920
  • Atomic and Condensed Matter
Replies
1
Views
680
Replies
2
Views
785
  • Quantum Interpretations and Foundations
2
Replies
54
Views
3K
Replies
1
Views
775
Replies
10
Views
1K
  • High Energy, Nuclear, Particle Physics
Replies
1
Views
1K
  • Set Theory, Logic, Probability, Statistics
Replies
5
Views
1K
Replies
1
Views
679
Back
Top