Abstract

The coherence length Λ_coh of a random wave field E(x,y) is defined as the characteristic distance over which the whole field, ensemble averaged autocorrelation function μ(Δx)= <E*(x,y)E(x+Δx,y)>/<|E(x,y)|2> decays to zero [1] A natural, indeed universal interpretation is that on length scales larger than Λ_coh, different field structures such as maxima, minima, etc. are uncorrelated. Indeed, it is the apparently random distributions of positions, heights, and widths of these features that make the field appear “random”. But as is often the case, appearances can be deceiving, and we have recently found that there are literally thousands of unexpected, often highly unusual, local correlations and anticorrelations present even in that apparently most random of all wave fields, the Gaussian field (i.e. a field whose fundamental field variables obey Gaussian statistics). These local correlations tend to be paired such that correlations with μ ~ +1 in one region of the wave field are exactly canceled by anticorrelations with μ ~–1 in other regions, leading to a whole field average μ ~ 0. Many of these correlations are topological in nature, and are thus universal features of all wave fields. Knowledge of these universal correlations may prove useful in the manipulation and reconstruction of a variety of abberated fields.

© 1996 Optical Society of America