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
Emil Wolf, "New theory of partial coherence in the space-frequency domain. Part I: spectra and cross spectra of steady-state sources," J. Opt. Soc. Am. 72, 343-351 (1982)