The application of the Wiener–Khintchin theorem for determining the functions of the transversal and longitudinal spatial coherence of the optical field, depending on the parameters of the angular and temporal frequency spectra of the field, is considered. Based on the Wiener–Khintchin theorem, the possibility to derive the van Cittert–Zernike theorem for transversal and longitudinal spatial coherence of the optical field of a spatially incoherent quasi-monochromatic light source is shown. An expression for the dependence of the longitudinal coherence length of the optical field on the width of the frequency and width of the angular spectra of the field is obtained. The results of the interference experiment confirming the dependence of the longitudinal coherence length on the parameters of angular and frequency spectra of the field are presented.

We have observed the longitudinal pure spatial coherence of a light field in an interference experiment when the length of the temporal coherence is significantly smaller than the length of the longitudinal spatial coherence of the light field. We introduce into consideration new spatial and temporal scales of a light field: the length of the coherent (free) run and the coherent time (the time of life) of a wave train.

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