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Письма в Журнал экспериментальной и теоретической физики

Theoretical Foundations of Quantum Spectral-Domain Optical Coherence Tomography with Frequency Scanning

Nikolai A. Ushakov, Tatiana Makovetskaya, Маркварт Александр Александрович, Лиокумович Леонид Борисович

Published Jan 15, 2023• 0 citations
Publisher

Abstract

A quantum spectral-domain optical coherence tomography technique based on the control of the joint spectral amplitude of a biphoton has been developed. An analytical expression for a quantum spectral-domain optical coherence tomography signal has been obtained in the case of a Gaussian joint spectral amplitude. The effect of the shape of the joint spectral amplitude of the biphoton on the resulting interference signal has been analyzed. The possibility of improving the quality of the interference signal by controlling the parameters of the joint spectral amplitude has been considered. It has been shown theoretically that the proposed approach provides a higher longitudinal spatial resolution than other optical coherence tomography techniques.

DOI
10.31857/s1234567823010032

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A quantum spectral-domain optical coherence tomography technique based on the control of the joint spectral amplitude of a biphoton has been developed. An analytical expression for a quantum spectral-domain optical coherence tomography signal has been obtained in the case of a Gaussian joint spectral amplitude. The effect of the shape of the joint spectral amplitude of the biphoton on the resulting interference signal has been analyzed. The possibility of improving the quality of the interference signal by controlling the parameters of the joint spectral amplitude has been considered. It has been shown theoretically that the proposed approach provides a higher longitudinal spatial resolution than other optical coherence tomography techniques.
A quantum spectral-domain optical coherence tomography technique based on the control of the joint spectral amplitude of a biphoton has been developed. An analytical expression for a quantum spectral-domain optical coherence tomography signal has been obtained in the case of a Gaussian joint spectral amplitude. The effect of the shape of the joint spectral amplitude of the biphoton on the resulting interference signal has been analyzed. The possibility of improving the quality of the interference signal by controlling the parameters of the joint spectral amplitude has been considered. It has been shown theoretically that the proposed approach provides a higher longitudinal spatial resolution than other optical coherence tomography techniques.
The aim of this work is to develop a spectral-domain quantum optical coherence tomography approach, based on the control of the joint spectral amplitude of the entangled photons. An analytical expression is obtained that describes the signal of spectral quantum optical coherence tomography. The dependence of the interference signal on the change in the difference between the central frequencies of the spectral distributions of entangled photons was demonstrated. The effect of digital processing of an interference signal on the achievable axial spatial resolution was shown. The influence of the shape of the joint spectral amplitude of the entangled photons on the final interference signal was analyzed, and the possibility of improving the quality of the interference signal by controlling the properties of the spectral amplitude was considered.
Quantum optical coherence tomography (Q-OCT) is the non-classical counterpart of optical coherence tomography (OCT), a high-resolution 3D imaging technique based on white-light interferometry. Because Q-OCT uses a source of frequency-entangled photon pairs, not only is the axial resolution not affected by dispersion mismatch in the interferometer but is also inherently improved by a factor of two. Unfortunately, practical applications of Q-OCT are hindered by image-scrambling artefacts and slow acquisition times. Here, we present a theoretical analysis of a novel approach that is free of these problems: Fourier domain Q-OCT (Fd-Q-OCT). Based on a photon pair coincidence detection as in the standard Q-OCT configuration, it also discerns each photon pair by their wavelength. We show that all the information about the internal structures of the object is encoded in the joint spectrum and can be easily retrieved through Fourier transformation. No depth scanning is required, making our technique potentially faster than standard Q-OCT. Finally, we show that the data available in the joint spectrum enables artefact removal and discuss prospective algorithms for doing so.
The paper proposes a spectral-domain version of a biphoton (Hong–Ou–Mandel) interferometry. The operation principle is based on measuring the coincidence rate of entangled photons while scanning the difference between their central frequencies. A theoretical apparatus describing the operation principle and the resolution limits of the proposed spectral-domain biphoton interferometry is developed. The analysis is based on quantum and classical Cramer–Rao bounds. It was shown that the proposed spectral-domain biphoton interferometry approach enables the mitigation of the fringe number counting errors, often encountered in classical spectral interferometry. A comparison with a conventional Hong–Ou–Mandel biphoton interferometry is also presented.
The Wiener-Khinchin theorem, the fact that the autocorrelation function of a time process has a spectral decomposition given by its power-spectrum intensity, can be used in many disciplines. However, the applications based on a quantum counterpart of the Wiener-Khinchin theorem that provides a translation between time-energy degrees of freedom of biphoton wave function still remains relatively unexplored. Here, we use a quantum Wiener-Khinchin theorem (QWKT) to state that two-photon joint spectral intensity and the cross-correlation of two-photon temporal signal can be connected by making a Fourier transform. The mathematically defined QWKT is experimentally demonstrated in frequency-entangled two-photon Hong-Ou-Mandel (HOM) interference with the assistance of spectrally resolved detection. We apply this method to spectral-domain quantum optical coherence tomography that detects thickness-induced optical delays in a transparent sample, and show that our method suffices to achieve great advantages in measurement precision within a wide dynamic range and capturing time over the conventional HOM interferometric schemes. These results may significantly facilitate the use of QWKT for quantum information processing and quantum interferometric spectroscopy.
Optical-coherence tomography (OCT) is a technique that employs light in order to measure the internal structure of semitransparent, e.g. biological, samples. It is based on the interference pattern of low-coherence light. Quantum-OCT (QOCT), instead, employs the correlation properties of entangled photon pairs, for example, generated by the process of spontaneous parametric downconversion (SPDC). The usual QOCT scheme uses photon pairs characterised by a joint-spectral amplitude with strict spectral anti-correlations. It has been shown that, in contrast with its classical counterpart, QOCT provides resolution enhancement and dispersion cancellation. In this paper, we revisit the theory of QOCT and extend the theoretical model so as to include photon pairs with arbitrary spectral correlations. We present experimental results that complement the theory and explain the physical underpinnings appearing in the interference pattern. In our experiment, we utilize a pump for the SPDC process ranging from continuous wave to pulsed in the femtosecond regime, and show that cross-correlation interference effects appearing for each pair of layers may be directly suppressed for a sufficiently large pump bandwidth. Our results provide insights and strategies that could guide practical implementations of QOCT.