Anton A. Grebenyuk

Wiener–Khintchin theorem for spatial coherence of optical wave field

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.

Numerically focused full-field swept-source optical coherence microscopy with low spatial coherence illumination

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.

An off-axis digital holographic microscope with quasimonochromatic partially spatially coherent illumination in transmission

We propose an off-axis imaging approach for digital holographic microscopy (DHM) with quasimonochromatic partially spatially coherent illumination in transmission, which is intended to provide the advantages of off-axis partially coherent DHM imaging with a comparatively simple optical scheme. This approach does not require a diffraction grating for creating the off-axis modality and also allows for convenient control of the spatial frequency of carrier interference fringes for hologram sampling optimization. Theoretical analysis of the off-axis imaging process in this microscope is performed. An off-axis DHM based on the proposed approach is built and quantitative phase imaging of test objects is performed with suppressed coherent noise.

Coherence effects of thick objects imaging in interference microscopy

In this paper we present a model of interference microscope image formation, which allows for analysis on unified basis of imaging different types of samples with different interference microscope modalities. The applicability of the proposed model to analysis of the coherence effects, arising in confocal and full-field interference microscopes, when imaging in depth of a layered sample, is shown. The effect of sample transversal structure on the coherence signal is also analyzed, showing that in this case the interference microscope can not be characterized by a single effective aperture and both illuminating and imaging apertures are important.

Numerical correction of coherence gate in full-field swept-source interference microscopy

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.

Digital image correlation with fast Fourier transform for large displacement measurement

Digital image correlation is an effective non-contact optical tool for full-field displacement and strain measurements. It is used for objects testing, elastic parameters evaluation, flows control, etc. One of the main challenges of practical realization of DIC is the computation time. In this paper a method of computing digital image correlation with fast Fourier transform algorithm is proposed. Unlike the usual FFT cross correlation algorithm, the proposed method allows for reduction the computation time of large displacements DIC measurements with retaining the accuracy of spatial domain correlation.

Numerical focusing in digital holographic microscopy with partially spatially coherent illumination in transmission

Digital holographic microscopy (DHM) combines the possibility of high resolution quantitative phase imaging with numerical focusing and in transmission mode is widely used for live cell imaging. The use of partially spatially coherent illumination in DHM provides some advantages over the conventional spatially coherent illumination, but modifies the signal properties and requires detailed investigation, especially in the part of numerical focusing. In this paper we present theoretical analysis of the effects of partially spatially coherent illumination in transmission-mode DHM on its impulse response and numerical focusing possibilities. Further, we propose a method of providing high quality impulse response (as by the spatially low-coherent illumination), preserving large maximum distance of numerical focusing.

Numerical reconstruction of volumetric image in swept-source interference microscopy

Theory of image formation in a full-field swept-source interference microscope is derived and numerical processing technique for volumetric image reconstruction is proposed. This technique allows reconstruction of sample volumetric image without the need for mechanical shifting of the interference microscope components and provides the possibility of separate determination of the sample layers thicknesses and refractive indices, if the sample contains transversal pattern.

Theoretical analysis of stratified media imaging in low-coherence interference microscopy

Theoretical analysis of stratified media imaging with a Linnik-type low-coherence interference microscope is presented. Expressions describing the interference microscope image formation in the case of arbitrary coherence properties of illumination are derived. The particular case of spatially incoherent illumination is further analyzed and the effects of numerical aperture size and spectral properties of illumination are shown. The derived theory can be useful for determination of optimal parameters of the interference microscope system for the object fine structure visualization. The theory can also be applied for analysis of other types of interference microscopes.

Digital off-axis holography: Reconstruction from undersampled pattern

Possibility of reconstruction of object image from undersampled holographic pattern has been experimentally verified. Influence of undersampling and of digital sensor fill factor on the quality of the reconstructed image has been studied experimentally and by means of computer simulation.