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New theory of partial coherence in the space–frequency domain. Part I: spectra and cross spectra of steady-state sources

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Abstract

It is shown that, under very general conditions, the cross-spectral density of a steady-state source of any state of coherence may be expressed in terms of certain new modes of oscillations, each of which represents a completely spatially coherent elementary excitation. Making use of this result, a statistical ensemble of strictly monochromatic oscillations, all of the same temporal frequency, is then introduced that yields the cross-spectral density as a correlation function in the space–frequency domain. From these results two new expressions for the Wiener–Khintchine spectrum of the source and also a new mode representation of the cross-correlation function of the source follow at once.

© 1982 Optical Society of America

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