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arXiv:2108.05998

Spectral-domain optical coherence tomography based on nonlinear interferometers

Arturo Rojas-Santana, Gerard J. Machado, Maria V. Chekhova, Dorilian Lopez-Mago, Juan P. Torres

Published Aug 12, 2021• 0 citations
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Abstract

Optical coherence tomography (OCT) is a 3D imaging technique that was introduced in 1991 [Science 254, 1178 (1991); Applied Optics 31, 919 (1992)]. Since 2018 there has been growing interest in a new type of OCT scheme based on the use of so-called nonlinear interferometers, interferometers that contain optical parametric amplifiers. Some of these OCT schemes are based on the idea of induced coherence [Physical Review A 97, 023824 (2018)], while others make use of an SU(1,1) interferometer [Quantum Science and Technology 3 025008 (2018)]. What are the differences and similarities between the output signals measured in standard OCT and in these new OCT schemes? Are there any differences between OCT schemes based on induced coherence and on an SU(1,1) interferometer? Differences can unveil potential advantages of OCT based on nonlinear interferometers when compared with conventional OCT schemes. Similarities might benefit the schemes based on nonlinear interferometers from the wealth of research and technology related to conventional OCT schemes. In all cases we will consider the scheme where the optical sectioning of the sample is obtained by measuring the output signal spectrum (spectral, or Fourier-domain OCT), since it shows better performance in terms of speed and sensitivity than its counterpart time-domain OCT.

DOI
10.48550/arxiv.2108.05998

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Optical coherence tomography (OCT) is a 3D imaging technique that was introduced in 1991 [Science 254, 1178 (1991); Applied Optics 31, 919 (1992)]. Since 2018 there has been growing interest in a new type of OCT scheme based on the use of so-called nonlinear interferometers, interferometers that contain optical parametric amplifiers. Some of these OCT schemes are based on the idea of induced coherence [Physical Review A 97, 023824 (2018)], while others make use of an SU(1,1) interferometer [Quantum Science and Technology 3 025008 (2018)]. What are the differences and similarities between the output signals measured in standard OCT and in these new OCT schemes? Are there any differences between OCT schemes based on induced coherence and on an SU(1,1) interferometer? Differences can unveil potential advantages of OCT based on nonlinear interferometers when compared with conventional OCT schemes. Similarities might benefit the schemes based on nonlinear interferometers from the wealth of research and technology related to conventional OCT schemes. In all cases we will consider the scheme where the optical sectioning of the sample is obtained by measuring the output signal spectrum (spectral, or Fourier-domain OCT), since it shows better performance in terms of speed and sensitivity than its counterpart time-domain OCT.
(English) This thesis, mostly experimental, is based on two fundamental pillars: nonlinear interferometers and Optical Coherence Tomography (OCT). Nonlinear interferometers are a class of interferometers that exhibit nonclassical phenomena brought on by nonlinear elements, such as optical parametric amplifiers and parametric down-conversion (PDC) nonlinear crystals. OCT is a non-invasive imaging technique that allows to obtain images with high axial and cross-sectional resolution of a wide variety of samples. The first novel contribution of this thesis is an experimental scheme that combines the two ideas: an OCT scheme based on a nonlinear interferometer. In these new approach the reflectivity of the sample translates in a loss of first-order coherence between two beams, that is the variable that is measured. In addition, it allows probing the sample with a wavelength different from the one that is measured. In this way, the penetration depth in the sample can be enhanced using longer wavelengths while using light at the optimal wavelength for detection. We present and implement two different experimental configurations. The first is a nonlinear interferometer based on induced coherence, or Mandel-type interferometer, that works in the low parametric gain regime of parametric down-conversion (PDC). The results presented here are a proof-of-concept, that can potentially offer new applications for OCT, but that are not meant to substitute traditional OCT systems. The second OCT scheme overcomes some of the limitations of the first scheme discussed above. It is an SU(1,1), or Yurke-type interferometer, that operates in the high parametric gain regime of parametric down-conversion. In addition to taking advantage of the salutary features of this new approach, it also enables obtaining values of power and axial resolution comparable to those of conventional OCT. The second novel contribution of this thesis is related to fundamental aspects at the heart of nonlinear interferometers. We discuss two experiments that study two important concepts behind the idea of induced coherence: quantum distinguishability and parametric amplification (stimulated emission). In the first experiment we propose a new experimental measure of quantum distinguishability and derive a complementarity relation between distinguishability and first-order coherence. In the second experiment, we contribute to the ongoing debate about the true role of quantum distinguishability and stimulated emission in explaining the induced coherence effect. Finally, we put forward theoretically a new scheme to retrieve transverse spatial information of a sample using a nonlinear interferometer, based on projecting the outgoing photons in selected spatial modes. We call this new proposal spatial spectroscopy, and it does not require a physical mechanical scan of the sample. We demonstrate the feasibility of the technique with a simple example. This last contribution constitutes a future proposal to be carried out with nonlinear interferometers, evidencing their great versatility and potential applications in new areas. (Català) Aquesta tesi, majoritàriament experimental, està basada en dos pilars fonamentals: els interferòmetres nolineals i la Tomografia de Coherència Òptica (OCT). Els interferòmetres nolineals són un tipus d'interferòmetres en els que tenen lloc fenòmens no-clàssics generats per la presència d'elements nolineals, com amplificadors òptics paramètrics i cristalls de conversió paramètrica descendent. OCT és una tècnica interferomètrica no-invasiva per obtenir imatges 3D amb alta resolució axial d'una gran varietat de mostres. La primera contribució original d'aquesta tesi és un esquema experimental que combina dues idees: un esquema d'OCT basat en un interferòmetre nolineal. En aquesta nova proposta, la reflectivitat de la mostra es tradueix en una pèrdua de coherència entre dos feixos de llum, que és la quantitat mesurada. A més a més, permet il·luminar la mostra amb una longitud d'ona diferent a la mesurada. D'aquesta manera, podem guanyar penetració a la mostra mentre utilitzem llum a la longitud d'ona òptima per la detecció. En aquest sentit, presentem i implementem dues configuracions experimentals diferents. La primera es tracta d'un interferòmetre nolineal basat en el concepte de coherència induïda, o també anomenat interferòmetre de Mandel, que opera en el règim de baix guany de conversió paramètrica descendent. Els resultats presentats constitueixen una prova del principi de funcionament, que poden suposar noves aplicacions per OCT, però no estan enfocats a substituir els sistemes convencionals d'OCT. El segon esquema d'OCT que proposem millora algunes de les limitacions de l'anterior proposta. Es tracta d'un SU(1,1), o interferòmetre de Yurke, que opera en el règim d'alt guany de conversió paramètrica descendent. A més d'aprofitar les característiques beneficioses d'aquests nous esquemes, també permet obtenir valors de potència i resolució axial comparables als dels sistemes d'OCT tradicionals. La segona contribució original d'aquesta tesi està relacionada amb aspectes fonamentals que estan rere els interferòmetres nolineals. Presentem dos experiments que estudien dos conceptes importants que expliquen la idea de coherència induïda: la distingibilitat quàntica i l'amplificació paramètrica (o emissió estimulada). En el primer experiment proposem una nova mesura de la distingibilitat quàntica i derivem una relació entre la distingibilitat i la coherència. En el segon experiment, contribuïm al debat vigent sobre el rol de la distingibilitat quàntica i l'emissió estimulada per explicar el concepte de la coherència induïda. Finalment, presentem les bases teòriques d'un nou esquema per obtenir informació espacial d'una mostra utilitzant un interferòmetre nolineal, basat en la projecció dels fotons en uns modes espacials de llum concrets. Anomenen aquesta nova proposta espectroscòpia espacial, i no requereix un escaneig físic-mecànic de la mostra. Demostrem la viabilitat de la tècnica amb un exemple senzill. Aquesta última contribució constitueix una proposta de futur a realitzar amb els interferòmetres nolineals, evidenciant la seva gran versatilitat i potencials aplicaciones en noves àrees.
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.
We describe a resolution-improved spectral-domain (SD) optical coherence tomography (OCT) based on classical intensity correlations as a counterpart of the recently proposed intensity-based time-domain OCT. Similarly to quantum OCT, the setup employs the Hong-Ou-Mandel interferometer at the output of the conventional SD-OCT. It is shown theoretically that a factor-of-√2 improvement in axial resolution is obtained with this arrangement. Some unique and useful features of our proposed system are addressed.
Using spectrally correlated photon pairs instead of classical laser light and coincidence detection instead of light intensity detection, Quantum Optical Coherence Tomography (Q-OCT) outperforms classical OCT in several experimental terms. It provides twice better axial resolution with the same spectral bandwidth and it is immune to even-order chromatic dispersion, including Group Velocity Dispersion responsible for the bulk of axial resolution degradation in the OCT images. Q-OCT has been performed in the time domain configuration, where one line of the two-dimensional image is acquired by axially translating the mirror in the interferometer's reference arm and measuring the coincidence rate of photons arriving at two single-photon-sensitive detectors. Although successful at producing resolution-doubled and dispersion-cancelled images, it is still relatively slow and cannot compete with its classical counterpart. Here, we experimentally demonstrate Q-OCT in a much faster Fourier-domain configuration, theoretically proposed in 2020, where the reference mirror is fixed and the joint spectrum is acquired by inserting long fibre spools in front of the detectors. We propose two joint spectrum pre-processing algorithms, aimed at compensating resolution-degrading effects within the setup. While the first one targets fibre spool dispersion, an effect specific to this configuration, the other one removes the effects leading to the weakening of even-order dispersion cancellation, the latter impossible to be mitigated in the time-domain alternative. Being additionally contrasted with both the time-domain approach and the conventional OCT in terms of axial resolution, imaging range and multilayer-object imaging, Fourier-domain Q-OCT is shown to be a significant step forward towards a practical and competitive solution in the OCT arena.