Temporal van Cittert-Zernike theorem and its application to the measurement of chromatic dispersion

A time-domain equivalent of the van Cittert–Zernike theorem is formulated. The two-time correlation function of an incoherent source after temporal gating and chromatic dispersion is derived. Significant spectral dispersion establishes partial temporal coherence, in a way similar to the establishment of partial spatial coherence in the far field for a spatially incoherent source after propagation through an aperture and diffraction. It is shown theoretically and experimentally that the temporal degree of coherence of the source after temporal gating and dispersive propagation is related to the modulus of the Fourier transform of the temporal transmission of the gate. The derivation of the two-time correlation function of such a source is applied to an interferometric measurement of chromatic dispersion that uses a time-gated incoherent source.