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 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.

A big problem in low-coherence interference microscopy is the degradation of the coherence signal caused by shift of the angular and temporal spectrum gates. It limits the depth of field in confocal optical coherence microscopy and degrades images of sample inner structure in most interference microscopy techniques. To overcome this problem we propose numerical correction of the coherence gate in application to full-field swept-source interference microscopy. The proposed technique allows three-dimensional sample imaging without mechanical movement of the microscope components and is also capable of determining separately the geometrical thickness and the refractive index of the sample layers, when the sample contains a transversal pattern. The applicability of the proposed technique is verified with numerical simulation.

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