# What is "Correlation length"?

by Ariel
Tags: correlation, correlation length, roughness
 P: 2 Hi everyone, I want to know meaning of "correlation length". Correlation function is usually used in statistics, so I think correlation length also similar meaning. But some paper used correlation length to explain roughness factor. Plz, anyone reply this message who is know about correlation length meaning or useful links. Thanks a lot to read this message. :)
 Sci Advisor P: 1,549 Consider a sample with a surface that is not perfectly flat, but somewhat rough. If you want to analyze the surface roughness, you can just measure the thickness of your sample at many positions, say every micrometer. Now, you have the mean sample thickness and the deviation from the mean for every point on the surface where you did a measurement. For a real surface, the deviation from the mean will not change randomly on every micrometer, but there will be some extended "hillls" and "valleys" on your sample. So, if you check the deviation from the mean at one sample position and have a look at the deviation at an adjacent position, it is very likely that both will be similar, while it is very unlikely that one is a large positive deviation and the other is a large negative deviation. If you have a look at the deviation from the mean thickness at one end of the sample and the deviation from the mean at the other end of the sample, the two values should be completely uncorrelated. They may be large, small or zero - completely independent of each other. Now somewhere in between , there must be a typical length scale on which the deviations from the mean stop being similar. That is the correlation length. It gives you some information on how large these "hills" and "valleys" on your sample typically are. Needless to say, you can apply the same principle to other quantities as well, with applications ranging from surface roughness to the optical coherence of light fields.
 P: 2 Thanks your reply, If correlation length is short it means surface fluctuation is strong, so rough surface, otherwise fluctuation is week, so flat surface. Is my understanding correct?