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Article

K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures

by
Alexander L. Matveyev
,
Lev A. Matveev
,
Grigory V. Gelikonov
and
Vladimir Y. Zaitsev
*
A.V. Gaponov-Grekhov Institute of Applied Physics RAS, Nizhny Novgorod 603950, Russia
*
Author to whom correspondence should be addressed.
Sensors 2024, 24(9), 2931; https://doi.org/10.3390/s24092931
Submission received: 6 February 2024 / Revised: 23 April 2024 / Accepted: 29 April 2024 / Published: 5 May 2024

Abstract

For the most popular method of scan formation in Optical Coherence Tomography (OCT) based on plane-parallel scanning of the illuminating beam, we present a compact but rigorous K-space description in which the spectral representation is used to describe both the axial and lateral structure of the illuminating/received OCT signals. Along with the majority of descriptions of OCT-image formation, the discussed approach relies on the basic principle of OCT operation, in which ballistic backscattering of the illuminating light is assumed. This single-scattering assumption is the main limitation, whereas in other aspects, the presented approach is rather general. In particular, it is applicable to arbitrary beam shapes without the need for paraxial approximation or the assumption of Gaussian beams. The main result of this study is the use of the proposed K-space description to analytically derive a filtering function that allows one to digitally transform the initial 3D set of complex-valued OCT data into a desired (target) dataset of a rather general form. An essential feature of the proposed filtering procedures is the utilization of both phase and amplitude transformations, unlike conventionally discussed phase-only transformations. To illustrate the efficiency and generality of the proposed filtering function, the latter is applied to the mutual transformation of non-Gaussian beams and to the digital elimination of arbitrary aberrations at the illuminating/receiving aperture. As another example, in addition to the conventionally discussed digital refocusing enabling depth-independent lateral resolution the same as in the physical focus, we use the derived filtering function to perform digital “super-refocusing.” The latter does not yet overcome the diffraction limit but readily enables lateral resolution several times better than in the initial physical focus.
Keywords: optical coherence tomography; K-space representation; angular spectrum; digital refocusing; digital image transformation; non-paraxial approximation; non-Gaussian beams; aberration correction optical coherence tomography; K-space representation; angular spectrum; digital refocusing; digital image transformation; non-paraxial approximation; non-Gaussian beams; aberration correction

Share and Cite

MDPI and ACS Style

Matveyev, A.L.; Matveev, L.A.; Gelikonov, G.V.; Zaitsev, V.Y. K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures. Sensors 2024, 24, 2931. https://doi.org/10.3390/s24092931

AMA Style

Matveyev AL, Matveev LA, Gelikonov GV, Zaitsev VY. K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures. Sensors. 2024; 24(9):2931. https://doi.org/10.3390/s24092931

Chicago/Turabian Style

Matveyev, Alexander L., Lev A. Matveev, Grigory V. Gelikonov, and Vladimir Y. Zaitsev. 2024. "K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures" Sensors 24, no. 9: 2931. https://doi.org/10.3390/s24092931

APA Style

Matveyev, A. L., Matveev, L. A., Gelikonov, G. V., & Zaitsev, V. Y. (2024). K-Space Approach in Optical Coherence Tomography: Rigorous Digital Transformation of Arbitrary-Shape Beams, Aberration Elimination and Super-Refocusing beyond Conventional Phase Correction Procedures. Sensors, 24(9), 2931. https://doi.org/10.3390/s24092931

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