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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The physical conditions for observing the longitudinal spatial coherence of light of an extended thermal source in interference experiments are defined. For experimental verification of these conditions a Michelson interferometer with a longitudinal scanning mirror was used. The influence of the longitudinal spatial coherence of thermal light on a fringe envelope is demonstrated experimentally.

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We propose a 3D imaging technique based on the combination of full-field swept-source optical coherence microscopy (FF-SSOCM) with low spatial coherence illumination and a special numerical processing that allows for numerically focused coherent-noise-free imaging without mechanical scanning in longitudinal or transversal directions. We show, both theoretically and experimentally, that the blurring effects arising in FF-SSOCM due to defocus can be corrected by appropriate numerical processing even when low spatial coherence illumination is used. A FF-SSOCM system was built for testing the performance of this technique. Coherent-noise-free imaging of a sample with longitudinal extent exceeding the optical depth of field is demonstrated without displacement of the sample or any optical element.

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