Spectral coherence and the concept of cross-spectral purity*

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Abstract
A new measure of correlations in optical fields, introduced in recent investigations on radiometry with partially coherent sources, is studied and applied to the analysis of interference experiments. This measure, which we call the complex degree of spectral coherence, or the spectral correlation coefficient, characterizes the correlations that exist between the spectral components at a given frequency in the light oscillations at two points in a stationary optical field. A relation between this degree of correlation and the usual degree of coherence is obtained and the role that the complex degree of spectral coherence plays in the spectral structure of a two-beam interference pattern is examined. It is also shown that the complex degree of spectral coherence provides a clear insight into the physical significance of cross-spectral purity. When the optical field at two points is cross-spectrally pure, the absolute value of the complex degree of spectral coherence at these points is found to be the same for every frequency component of the light. This fact is reflected in the visibility of the spectral components of the interference fringes formed by light from these points.

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