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27.—The Zeros of Optical Coherence Functions and their Utility in the Study of Spectra

Synopsis This paper shows that the coherence function associated with a band-limited optical spectrum is expressible as an infinite product involving its zeros. Only a finite number of zeros are physically significant and these can be determined from measurements of the visibility of interference fringes; but an ambiguity remains in the sign of the imaginary part of each zero. If the spectrum is to be recovered using the visibility measurements, an auxiliary experiment is needed to supply the necessary signs, but it need not be especially accurate. If the signs are not known there is only a limited number of different spectra that are compatible with the visibility measurements. Finally it is suggested that wavelength measurements made on an asymmetric spectral line with a Michelson interferometer may yield differing results when used with long and short delays.