Quantum entangled photons, in which multiple photons have a quantum mechanical correlation, have been used to obtain exponential improvement of, and new functionality for, certain tasks in computation [1–3] and communication [4–6]. Recently, a wide variety of applications of entangled photons for quantum metrology and sensing has been proposed and demonstrated. For example, the classical precision limit for phase measurement can be exceeded using quantum light entangled in photon number [7–9]. It is also known that the diffraction limit can be overcome [10–14]. Correlated photons can also be used to detect weak absorption of light beyond the shot noise limit [15–20]. Furthermore, nonlinear quantum interference enables spectroscopy in the infrared wavelength region using a visible light source [21–24].

Among such techniques, quantum optical coherence tomography (QOCT), which uses two-photon interference between photon pairs entangled in frequency, is a promising approach to overcome a problem encountered with optical coherence tomography (OCT): degradation of the resolution due to dispersion within the sample. In the early 2000s, QOCT was proposed [25] and experimentally demonstrated [26]. In the first demonstration, two surfaces of a fused-silica plate were imaged one-dimensionally and it was confirmed that a resolution of 18.5 $\mathrm{\mu}$m was maintained even when a dispersive medium was placed in front of the sample. Then, the surface of a coated onion-skin cell was imaged with a depth resolution of 7.5 $\mathrm{\mu}$m [27]. Recently, full-field QOCT has been demonstrated with a depth resolution of 6 $\mathrm{\mu}$m [28]. The narrowest full width at half maximum (FWHM) for two-photon interference, 0.54 $\mathrm{\mu}$m, was realized with broadband photon pairs generated from a chirped quasi-phase-matched crystal [29], although QOCT imaging was not performed. Therefore, in the demonstration of QOCT imaging, the reported highest resolution has been limited to approximately 6 $\mathrm{\mu}$m. In addition, to the best of our knowledge, dispersion tolerance of QOCT imaging has not been demonstrated on a resolution higher than 10 $\mathrm{\mu}$m. Note that it has been shown that chirped-pulse interferometry OCT provides automatic dispersion cancellation as well as QOCT [30–33], but high-intensity light, which is required to obtain enough efficiency for the sum frequency generation process, may damage the sample. The dispersion cancellation in QOCT can be mimicked by computationally processing the interferograms obtained with a conventional OCT system at the cost of computational resources and the need for a spectrometer or wavelength-tunable laser [34–36].

In this paper, we experimentally demonstrate QOCT imaging of a dispersive material in the high-resolution regime. We achieved a depth resolution of 2.5 $\mathrm{\mu}$m, which is the highest value for QOCT imaging. We show that the QOCT image with a dispersive material remains clear whereas that of OCT is drastically degraded. We also discuss the signal-to-noise ratio (SNR) of the obtained QOCT image. These results mark a step forward for QOCT toward more advanced realizations.

Figure 1(a) shows a schematic of our experimental setup. We generated frequency-correlated photon pairs (signal photons and idler photons) through spontaneous parametric downconversion (SPDC). A 2-mm $\beta$-barium-borate (BBO) crystal cut for the Type-I non-collinear condition is pumped by a continuous wave diode laser (Cube 405-100C, COHERENT) at a wavelength of 401 nm. The black dots in Fig. 1(b) show the measured spectrum of the generated photon pairs, which has a center wavelength of 803 nm and a FWHM bandwidth of approximately 80 nm. After the pump beam is removed with a long-pass filter (LPF), the generated photons coupled to fiber couplers are transferred to the QOCT interferometer through polarization-maintaining fibers (PMFs). A sample is placed in one of the arms while a delay stage is placed in the other arm. A dispersive material (ZnSe) [not shown in Fig. 1(a)] is used to verify the dispersion cancellation of QOCT. We imaged an aluminum-coated glass substrate with a 30-$\mathrm{\mu}$m height difference. For each arm, we adopted an optical circulator based on a Michelson-type polarization interferometer [27] that has a four-fold higher transmittance than a simple and frequently used scheme consisting of a 50:50 beam splitter [26,29]. Then the signal and idler photons are guided to a non-polarizing beam splitter (BS). After two-photon interference at the beam splitter, the photons are transferred to single-photon detectors (SPD, SPCM-AQRH-14-FC, Excelitas Technologies) through PMFs. The coincidence count is measured using these two single-photon detectors. For the classical OCT experiment, we used a superluminescent diode (SLD, EBS8000, EXALOS) as a low coherence source and a power meter (PWM, PDB150A, THORLABS) as a detector [Fig. 1(a) inset]. Figure 1(c) shows the measured spectrum of the light from the SLD, which has a center wavelength of 810 nm and a FWHM bandwidth of approximately 75 nm.

 

Fig. 1. (a) Schematic of the experimental setup. The inset shows the OCT setup. LD, laser diode; HWP, half-wave plate; BBO, $\beta$-barium-borate; PMF, polarization-maintaining fiber; PBS, polarizing beam splitter; QWP, quarter-wave plate; BS, beam splitter; SPD, single-photon detector; SLD, superluminescent diode; PWM, power meter. (b) Frequency spectrum of light generated through spontaneous parametric downconversion. (c) Frequency spectrum of light emitted from SLD.

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First, we observed the interferograms with the OCT and QOCT setups when a mirror was placed as a sample. Figures 2(a) and 2(e) show the obtained OCT and QOCT interferograms, respectively, without the dispersive material. The FWHM of the OCT interferogram is 4.6 $\pm$ 0.2 $\mathrm{\mu}$m, which corresponds to the resolution of OCT and agrees with the value of 4.1 $\mathrm{\mu}$m obtained from the theoretically simulated interferogram shown in Fig. 2(b) considering the spectrum of the SLD. However, the FWHM of the QOCT interferogram is $2.2 \pm 0.1 \mathrm{\mu}$m, which corresponds to the resolution of QOCT and agrees well with the value of 1.9 $\mathrm{\mu}$m obtained from the theoretically simulated interferogram shown in Fig. 2(f) considering the spectrum of the SPDC source. We can see that the FWHM of the QOCT interferogram is almost half that of the OCT interferogram, which is known as one of the features of QOCT [37].

 

Fig. 2. Interferograms observed using the OCT system (a) without dispersive material and (c) with dispersive material, and using the QOCT system (e) without dispersive material and (g) with dispersive material. (b), (d), (f), and (h) Theoretical plots corresponding to panels (a), (c), (e), and (g), respectively. The insets in panels (c) and (d) show the whole interferogram. The red dots are the data points. The red lines connecting the data points are a guide to the eye.

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Figure 2(c) shows the OCT interferogram when a ZnSe window with a thickness of 1 mm is inserted in the optical path. Due to the group velocity dispersion (GVD) of the ZnSe window, the interference fringe becomes much broader, resulting in the FWHM of the OCT interferogram becoming 63 $\pm$ 2 $\mathrm{\mu}$m, which is more than 13 times larger than that without the ZnSe window. The double bump shape of the observed interferogram agrees well with the theoretically simulated interferogram considering the dispersion of the ZnSe window and the spectrum of the SLD source, as shown in Fig. 2(d). However, even when the ZnSe window is inserted, the QOCT interferogram maintains the narrow FWHM of $3.1 \pm 0.2 \mathrm{\mu}$m as shown in Fig. 2(g). The slight degradation in resolution is also observed in the theoretically simulated interferogram shown in Fig. 2(h) with the FWHM of $2.2\,\mathrm{\mu}$m which is larger than the $1.9\,\mathrm{\mu}$m obtained from the interferogram simulated without the dispersion [Fig. 2(f)]. In this simulation, the dispersion of the ZeSe window up to the third order was considered. The fluctuations in the coincidence counts of the experimental data may prevent observing the small peak in the theoretical interferogram. The degradation of the visibility of the QOCT interferogram can be explained by the loss and the third-order dispersion in the ZnSe window.

Next, we performed QOCT imaging with the constructed setup. We used an aluminum-coated glass substrate with a 30-$\mathrm{\mu}$m step as a sample. Figure 3(a) shows the detailed structure of the sample. The axial depth scans were taken by moving the delay mirror and recording the detection signal every 0.5 $\mathrm{\mu}$m over a range of 65 $\mathrm{\mu}$m. The axial depth scanning speed was set to 12.5 $\mathrm{\mu}$m/s. The transverse scans were taken by moving the sample stage through a 15-mm range in 100-$\mathrm{\mu}$m steps. Figures 3(b) and 3(d) show the OCT and QOCT images, respectively. Note that for the OCT images, the envelope of each interferogram is extracted and shown. Because the resolution of QOCT is approximately two times higher than that of OCT for the same bandwidth as shown in Fig. 2, the step in the sample is clearly seen in Fig. 3(d), whereas it is obscure in Fig. 3(b). At transverse distances of approximately 3.0 mm and approximately 10 mm in Figs. 3(d) and 3(e), steps that do not exist are visible at the middle of the two steps. In QOCT, such artefacts appear between the two reflecting surfaces. In our experiment, when the beam spans the two steps, the photons are in a superposition state between the two partial reflections from each step, causing the artefacts seen in Figs. 3(d) and 3(e). To demonstrate the dispersion-cancellation capability of our QOCT imaging system, the ZnSe window with the thickness of 1 mm was placed in front of the sample. Figure 3(c) shows the OCT image with the ZnSe window. The GVD of the ZnSe window drastically degrades the quality of the image. Each step is asymmetrically broadened in the depth direction by the GVD, which can be explained by the two bumps in the interferogram shown in Fig. 2(b). However, the QOCT image with the ZnSe window remains clear, as seen in Fig. 3(e).

 

Fig. 3. OCT and QOCT images. (a) Detailed structure of the aluminum-coated glass sample. OCT images (b) without and (c) with the ZnSe window. QOCT images (d) without and (e) with the ZnSe window. Gradual temperature drift in the depth distance is compensated.

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Finally, we discuss the SNR of the QOCT image. For a single QOCT interferogram, the SNR is defined as follows:

In conclusion, we have experimentally demonstrated QOCT imaging with dispersion cancellation in the high-resolution regime. A high depth resolution of 2.5 $\mathrm{\mu}$m was achieved. The QOCT image was maintained in the presence of dispersive material, whereas the OCT image was drastically degraded. We also discussed the SNR of the obtained QOCT images. The average SNR of the QOCT image without dispersive material was $20 \pm 2$ with a scanning speed of 12.5 $\mathrm{\mu}$m/s. When the dispersive material was inserted, the QOCT image had an SNR of $10 \pm 1$ because of the loss caused by the ZnSe dispersive material. There is a trade-off between the scanning speed and the SNR. Thus, for instance, if the SNR needs to be improved and a longer measurement time is allowed, the scanning speed must be reduced. The long measurement time of QOCT imaging could be an obstacle for some applications. Bright entangled photon sources [38] and technical improvements for the efficient use of photons [39] may enable practical speed QOCT imaging in the future. In QOCT images, the artefacts, as observed in Figs. 3(d) and 3(e), appear for each pair of sample layers and may also prevent the practical applications of QOCT. To overcome this problem, some potential solutions have been proposed and demonstrated [40–43].

Our results imply that QOCT imaging in the high-resolution regime may have a potential advantage over OCT imaging in terms of the observation of water samples because the dispersion of a sample in water medium with several millimeters of thickness can prevent OCT from reaching the high-resolution regime. A promising direction may be three-dimensional high-resolution QOCT where the transverse resolution is improved so as to be comparable to the depth resolution by using a dispersion-compensated lens.