An understanding of correlation singularities is fundamentally important in imaging science. Until now spatial coherence studies have examined a two-dimensional projection of the four-dimensional correlation function, finding so-called correlation vortices or correlation ring dislocations in a given transverse plane. Here we describe the properties and symmetries of the full four-dimensional correlation function. The general solution is found to be a hyperbola in two reduced dimensions. For perfect coherence this reduces to crossed straight lines, whereas in the incoherent limit it reduces to parallel lines. These results elucidate a number of previous experimental and theoretical observations regarding correlation singularities and suggest other behaviors of such singularities.
Department, Program, or Center
Chester F. Carlson Center for Imaging Science (COS)
Journal of the Optical Society of America, Optical Society of America, vol. 25, no. 09, September 2008
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