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Abstract
Precise distance metrology and measurements play an important role in many fields of scientific research and industrial manufacture. Dual-comb laser ranging combines sub-wavelength ranging precision, large non-ambiguity range, and high update rate, making it the most promising candidate in precise distance metrology and measurements. However, previous demonstrations of dual-comb ranging suffer from short working distances, limited by the decoherence of lasers in interferometric schemes or by the low sensitivity of the photodetectors in response to the sparse echo photons. Here, we propose and demonstrate time-of-flight laser ranging with dual-comb nonlinear asynchronous optical sampling and photon counting by a fractal superconducting nanowire single-photon detector, achieving ranging precision of 6.2 micrometers with an acquisition time of 100 ms and 0.9 micrometers with an acquisition time of 1 s in measuring the distance of an outdoor target approximately 298 m away.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical frequency comb (OFC) [1,2] benefits broad fields from fundamental science to industrial manufacture, such as optical atom clocks [3], spectroscopy [4], microwave photonics [5], and high-precision light detection and ranging (LiDAR) [6–14]. In particular, for LiDAR, by combining two OFCs with a slight repetition-rate difference, sub-wavelength ranging precision and kilometer non-ambiguity range have been simultaneously achieved [15]. However, in the long-distance-ranging scenario, decoherence of the laser would destroy the interferometric fringes so the reconstruction of the distance through Fourier transform or Hilbert transform would be impossible [16]. Although nonlinear asynchronous optical sampling (ASOPS) was introduced in dual-comb ranging to solve the problem of decoherence [17], the sensitivity of the photodetectors still limited the working distance. Several approaches have been proposed to increase the sensitivity of dual-comb ranging, by coherently tracking weak echo at shot-noise limit [18], and by optical sampling with cavity tuning [19]. Ranging and imaging of non-cooperative targets have been demonstrated by increasing the optical receiving aperture [20] or by electrical asynchronous sampling [21]. However, their ranging distances have been limited to a few meters. Although the ranging precision of 2.05 µm at a distance of 648 m using a conventional photodetector has been achieved with relatively high optical power (100 mW) [22], another route that does not need high optical power is to use single-photon detectors as the sensitive receivers.
Time-correlated single-photon counting (TCSPC) technique has long been used in time-of-flight (ToF) laser ranging and imaging in the faint-light regime [23–27]. Single-photon detectors provide ultimate sensitivity and high timing resolution, now becoming indispensable tools in long-distance laser ranging and imaging [28–31]. However, the timing precision of direct ToF measurements of photons by TCSPC is limited by the timing precision of the single-photon detectors and the electronics. The use of optical sampling to realize high timing precision has been investigated previously [32–34]. Recently, TCSPC has been introduced in dual-comb spectroscopy [35], dual-comb time-resolved measurement [36], and dual-comb ranging [37] and imaging [38]. In [37], a ranging precision of 2 µm for a distance of 15.6 m was achieved, but with long acquisition time of 1000 s, posing a challenge to the mutual coherence and long-term stability of the combs, since the distance was extracted from the photon-counting statistics obtained by TCSPC.
In this paper, we demonstrate laser ranging combining dual-comb nonlinear ASOPS [17,22,39] and TCSPC involving a fractal superconducting nanowire single-photon detector (SNSPD) [40–42]. Recently, the fractal SNSPDs have been demonstrated in ToF imaging [41], polarimetric measurements and imaging [43]. The use of the fractal SNSPD in a dual-comb nonlinear ASOPS setup overcomes the difficulty of maintaining long-term mutual coherence and complexity of distance determination in the dual-comb interferometric setup based on TCSPC and therefore, permits long-distance ranging. Consequently, we achieved ranging precision of 6.2 micrometer with acquisition time of 100 ms, and 0.9 micrometer with acquisition time of 1 s in measuring the distance of an outdoor target approximately 298 m away. Our work improved the performance of single-photon dual-comb ranging in terms of distance, ranging precision, acquisition time, and non-ambiguity range.
2. Ranging setup with dual-comb nonlinear ASOPS and TCSPC
Figure 1 presents the experimental setup and working principle for photon-counting dual-comb laser ranging by nonlinear ASOPS. Each light source of dual comb is a fully polarization-maintaining passively mode-locked femtosecond fiber laser, which is based on the nonlinear amplification loop mirror (NALM) mode-locked technology. There is a slight negative cavity dispersion and the laser works in a stretched pulse mode-locking regime. The polarization-maintaining erbium-doped fiber doped with rare earth ion Er$^{3+}$ is selected as the gain fiber, and the cavity shape of the reflective working mode is designed. Pumped by a 980 nm semiconductor continuous-wave laser diode, the pulses running inside the laser automatically triggered mode locking to achieve femtosecond pulse compression and output. The repetition rate, $f$, of the signal laser was 134.055560 MHz, while the repetition rate of the local oscillator was slightly lower by $\Delta f$. The length of optical cavity of the dual comb was stabilized by two feedback-controlled piezo-actuators in the phase-locking loop. Two half-wave plates (HWP) controlled the intensity ratio between the p-wave and the s-wave separated by a polarizing beamsplitter (PBS). For the signal laser [blue pulses in Fig. 1(b)], the reflected s-wave passed through a quarter-wave plate (QWP) back and forth, then changed polarization to p-wave. The p-wave from the signal laser, together with the s-wave reflected by another PBS from local oscillator [red pulses in Fig. 1(b)], were focused on a type-II periodically poled KTiOPO$_4$ (PPKTP) crystal. A silicon avalanche photodetector (Si APD; KY-APRM-50M, Kyphotonics) with a 3-dB bandwidth of 50 MHz was used to detect the up-conversion optical pulses as the reference. The transmitted s-wave of the signal laser was expanded by a 15$\times$ beam expander (GBE15-C, Thorlabs) to reduce the divergence angle of the beam. The target was a solid glass retroreflector with the diameter of 64 mm, mounted on an orientation-adjustable tripod head. The retroreflected optical pulses, with a ToF delay of $t_{\textrm {d}}$ from the pulses reflected by the reference mirror, were sampled by the transmitted pulses in s-polarization from the local oscillator. A short-pass filter (SPF; FESH0850, Thorlabs) with a cutoff wavelength of 850 nm and optical density of 5 at 1570 nm was used to block fundamental-frequency light. The up-conversion light was coupled into a step-index optical fiber with a core diameter of 200 µm. Another piece of optical fiber, with a core diameter of 9 µm, was directly connected with the 200-µm-core optical fiber, delivering the up-conversion light into a cryocooler. A fractal SNSPD [40,41] with the photon-sensitive area of 15.2 µm$\times$15.2 µm, coupled with the 9-µm-core optical fiber, was mounted on the cold head of the cryocooler with a base temperature of 2.6 K. Compared with the semiconductor single-photon avalanche diodes (SPAD), the advantages of using a fractal SNSPD include low afterpulsing probability, high counting rate, and free-running operation [40]. The current configuration of connecting the 200-µm-core optical fiber with a 9-µm-core optical fiber caused additional optical loss and reduced the overall collection efficiency for the up-conversion photons. In the future, to solve this problem, we could instead use a multimode-fiber- (MMF-) coupled fractal SNSPD with an expanded area. The electrical signals from the Si APD and the fractal SNSPD were sent to a TCSPC module (Hydraharp 400, Picoquant), and coincidences were measured. Figure 1(b) shows a schematics of the accumulated histogram of coincidence over a given acquisition time. We defined the center of the Gaussian fitting to the histogram as the stretched time of flight, $t_{\rm s}$. The absolute distance of the target, $d$, can be calculated by $d=\frac {ct_{\rm d}}{2n}=\frac {ct_{\rm s}}{2n}\frac {\Delta f}{f}$, where $c$ is the light speed in vacuum and $n$ is the refractive index of air. We used $n\equiv 1$ throughout this paper. Therefore, the ranging precision could be improved by a factor of $f/\Delta f$ by dual-comb ranging compared with the direct time-of-flight measurements, assuming the same timing precision of $t_{\rm d}$ and $t_{\rm s}$.
Fig. 1. Experimental setup and principle of the photon-counting dual-comb laser ranging. (a) Schematics of the experimental setup. PM SMF: polarization-maintaining single-mode fiber; HWP: half-wave plate; PBS: polarizing beamsplitter; QWP: quarter-wave plate; PPKTP: periodically poled KTiOPO$_4$; Si APD: silicon avalanche photodetector; SPF: short-pass filter; SNSPD: superconducting nanowire single-photon detector; TCSPC: time-correlated single-photon counting. (b) Principle of the time-of-flight measurement by nonlinear asynchronous optical sampling (ASOPS). The repetition-rate difference is assumed to be large enough so that only one up-conversion optical pulse is generated when the signal laser and the local oscillator overlap in the time domain. The broadened electrical pulses are due to the limited bandwidth of the Si APD and kinetic-inductance-induced recovery time of the SNSPD. $t_{\rm d}$: time of flight; $f$: repetition rate of the signal laser; $t_{\rm s}$: stretched time of flight.
The characterization of the dual-comb setup is presented in Fig. 2. The full widths at half maximum (FWHM) of the spectra are 26.4 nm and 24.9 nm for the signal laser and the local oscillator, respectively. We tested the stability of the repetition-rate difference, $\Delta f$, in the phase-locking (PL) mode by recording the drift of $\Delta f$ over 100 s using a frequency counter. As shown in Fig. 2(c), the drift of $\Delta f$ is on the order of several to tens of mHz with the gate window of 100 ms and 1 ms. $\Delta f$, measured with a shorter gate window, fluctuated on the order of several Hz [see Supplement 1, Fig. S1 (a)], because the two piezo-actuators worked at the frequency of 100 Hz. For comparison, we also recorded the fluctuation of $\Delta f$ of the dual comb in the free-running (FR) mode, as shown in Fig. 2(d) and Supplement 1, Fig. S1 (b). The stabilization of $\Delta f$ in the PL mode is critical to achieving high ranging precision, as we will present later in this paper. Figure 2(e) presents the real-time waveform of the output of the Si APD at $\overline {\Delta f}=20.006$ kHz in the PL mode. The period of the pulse sequences is set by the repetition-rate difference of the signal laser and the local oscillator. A zoom-in view of the pulse in the red dashed box in Fig. 2(e) is shown in Fig. 2(f). The start signal triggers at the rising edge of the waveform. The measured start-click rate by the TCSPC module is lower than $\overline {\Delta f}$ (see Supplement 1, Fig. S2), due, presumably, to inadequate sampling at high $\overline {\Delta f}$. The fractal SNSPD used in this work exhibited system detection efficiency (SDE) of 11% at the wavelength of 780 nm and timing jitter of 61 ps. See Supplement 1, Fig. S3 for detailed characterization of the fractal SNSPD.
Fig. 2. Characterization of the dual-comb laser. (a) Optical spectrum of the signal laser. (b) Optical spectrum of the local oscillator. (c) Measured drift of the repetition-rate difference with the gate window of 100 ms (black) and 1 s (orange) in the phase-locking (PL) mode. (d) Measured drift of the frequency difference in the free-running (FR) mode. $\Delta f$ is the real-time frequency difference in one gate window, $\overline {\Delta f}$ is the average frequency difference over 100 s. (c) and (d) are obtained at $\overline {\Delta f}$ of 20.006 kHz in the PL mode, 19.524 kHz (100 ms) and 19.501 kHz (1 s) in the FR mode, respectively. (e) Real-time waveform output from the Si APD at $\overline {\Delta f}=20.006$ kHz in the PL mode. (f) A zoom-in view of the red dashed box in (e).
3. Ranging results
Time-of-flight information of the echo photons was extracted by photon statistics in our experiment. We first placed the retroreflector at approximately 2.8 m away and measured the ranging precision of the dual-comb setup. The TCSPC module recorded the time tags in the Start channel and the Stop channel individually. The target was stationary during the measurements. We measured the ranging precision at several conditions to select the working point. The results are shown in Supplement 1, Fig. S4. Ranging precision was improved by phase-locking the two combs. Then, we fixed the working points, $\overline {\Delta f}=20.006$ kHz in the PL mode and the bias current of the fractal SNSPD at 18.5 µA to perform the measurements. The measurements repeated 55 times, each time with an acquisition time of 1 s. Data with shorter acquisition time was taken from this data set. We analyzed the correlation between the two channels with the bin size of 100 ps. One resulting ToF histogram at $\overline {\Delta f}=20.006$ kHz in the PL mode is shown in Fig. 3(a). The coincidence peak can clearly be distinguished from base noise. Note that the coincidences in base noise were mainly from the up-conversion photons only from the local oscillator, due to the limited polarization extinction ratio of the PBS. Although up-conversion photons only from the local oscillator collected by the optical fiber and detected were dominant, which were unwanted noise, the coincidence of the nonlinear ASOPS signals can still be distinguished by temporal filtering because the repetition rate of the up-conversion photons of the local oscillator was much larger than that of the nonlinear ASOPS signal, $f\gg \Delta f$. We used a Gaussian function to fit the highest peak, as shown by the inset of Fig. 3(a). The standard deviation (SD) of the Gaussian fitting is 405 ps for this particular histogram. The averaged fitted SD over 55 measurements is 398$\pm$10 ps. The center of the Gaussian fitting was regarded as $t_{\rm s}$. See Supplement 1, Fig. S5 for measured distances with acquisition time of 1, 10, and 100 ms. We calculated the number of detected photons in the coincidence peak by summing all the events in 5 ns around $t_{\rm s}$ and subtracting the base noise. The results are shown in Fig. 3(b). Figure 3(c) presents the measured Allan deviation versus acquisition time at $\overline {\Delta f}=20.006$ kHz in the PL mode. At a given acquisition time ($\tau$), Allan deviation [44] ($\sigma _{\rm d}$) was calculated by
where $M$ is the sample size. With an acquisition time of 1 s, Allan deviation reached 170$\pm$20 nm. The corresponding number of detected photons in the coincidence peak was 2500 on average. At shorter acquisition time of 1 ms, the number of detected photons was only 2.4 on average, while Allan deviation was 9.8$\pm$0.1 µm. Note that we did not adaptively correct the drift of $\Delta f$ throughout this paper. The achieved ranging precision by the combination of the dual comb and the fractal SNSPD is equivalent to a direct single-shot ToF measurement with a 56-fs timing resolution, which is calculated by $2\sigma _{\rm d}\sqrt {N}/c$, where $N$ is the number of detected photons in the coincidence peak. On the other hand, we can estimate the ranging precision by $c\sigma _{\rm e}/(2\sqrt {N})\times \Delta f /f$, where $\sigma _{\rm e}$ is the overall timing jitter in the stretched time scale. The calculated $\sigma _{\rm e}$ is 515 ps in SD, including the timing jitter of the Si APD ($\sigma _1 =64$ ps), of the fractal SNSPD ($\sigma _2 =29$ ps), and of the two combs ($\sigma _3 =361$ ps) (see Supplement 1, Sec. IV). The estimated ranging precision is 230 nm at the acquisition time of 1 s ($N=2500$), which should be compared with the experimental value, 170$\pm$20 nm. The analysis of timing jitter (Supplement 1, Sec. IV) leads us to conclude that the dominant limiting factors of the ranging precision in our setup are the timing jitter of the two combs [39] and the number of detected photons for a given acquisition time.Fig. 3. Time-of-flight measurement for the target approximately 2.8 m away by time-correlated single-photon counting. (a) One representative time-of-flight histogram. The bin size of the histogram is 100 ps. The inset shows the zoom-in view of the coincidence peak. The red curve is the Gaussian fitting to the peak, centering at $t_{\rm s}$ with the standard deviation (SD) of 405 ps. (b) Number of detected photons in the coincidence peak versus acquisition time. (c) Allan deviation versus acquisition time. Error range is calculated from the Allan deviation divided by the square root of the sample size. The results are obtained at $\overline {\Delta f}=20.006$ kHz in the phase-locking mode.
We then performed long-distance laser ranging with the dual-comb setup. The retroreflector was placed by a lake on Weijin Road Campus of Tianjin University. On the other side of the lake, the dual-comb setup was placed on the seventh floor of a building. We first measured a rough distance of 298.3 m by using a commercial laser rangefinder with an accuracy of 0.3 m. A two-axis rotational stage held the dual-comb optics to find the target. The output average optical power was 11.6 mW from the beam expander. The count rate, excluding the dark-count rate, of the fractal SNSPD was $2.1\times 10^6$ cps, corresponding to an averaged detected optical power of 4.8 pW. We preformed 55 measurements on the distance of the stationary target at a windy night, each with an acquisition time of 1 s, in a similar way we did for the indoor measurements. The total measurements took approximately 4 minutes. The absolute distance of the target was calculated, as the ranging accuracy of the commercial laser rangefinder is within the non-ambiguity range of our ranging setup, by $\lfloor 298.3/(c/2f)\rfloor c/2f+ct_{\rm s}\Delta f/(2f)$, where $\lfloor \cdot \rfloor$ represents the round-down integer. In principle, we do not need the prior knowledge of the distance provided by the rangefinder, if the absolute distance is within an extended non-ambiguity range of dual-comb ranging, $c/(2\Delta f)\approx 7.5$ km, by swapping the roles of the two combs and by repeating the ranging measurements [15]. The measured distances with acquisition time of 100 ms, 500 ms, and 1 s are shown in Fig. 4(a). Ranging with even shorter acquisition time than 100 ms failed due to the degraded signal-to-noise ratio (SNR) of the ToF histograms. The averaged distance is 297.843038 m with an acquisition time of 1 s. The statistics of the measured distances in Fig. 4(a) is presented in Fig. 4(b). Gaussian fittings to the histograms result in SD of 2.6, 1.0, and 0.8 µm, for the acquisition time of 100 ms, 500 ms, and 1 s, respectively. Allan deviation of the measured distances is presented in Fig. 5, reaching 0.9$\pm$0.1 µm with acquisition time of 0.9 s and 1 s, which is consistent with SD of Gaussian fitting in Fig. 4(b3). Allan deviations with acquisition time of 100 ms and 500 ms are 6.2$\pm$0.3 µm and 1.6$\pm$0.2 µm, respectively, deviating from SD at shorter acquisition time, because the occasional distance errors increase Allan deviation, but have less influence on Gaussian fitting. In terms of ranging precision, the technical limitations for the current approach are the overall timing jitter of our setup, $\sigma _{\rm e}$, and the number of detected photons, $N$, for a given acquisition time. Additionally, the fluctuation of the refractive index of air and the weather condition could also affect the ranging precision, especially for long acquisition time [22]. In terms of working distance, the technical limitation for the current approach is SNR of the ToF histograms, which is also related to $N$. In our setup, the dominant limitation factors of $\sigma _{\rm e}$ and $N$ are the timing jitter of the two combs and the overall collection efficiency for the up-conversion photons from the free space to the 200-µm-core optical fiber and then to the 9-µm-core optical fiber, respectively. In the future, the problem of low coupling efficiency from the 200-µm-core optical fiber to the 9-µm-core optical fiber could be addressed by using a MMF-coupled fractal SNSPD with an expanded photosensitive area.
Fig. 4. Ranging results at the distance of approximate 298 m. (a) Ranging results with acquisition time of 100 ms (a1), 500 ms (a2), and 1 s (a3) at $\overline {\Delta f}=20.006$ kHz in the phase-locking mode. The black dashed lines indicate the average distance. (b) Statistics of the ranging results with the acquisition time of 100 ms (b1), 500 ms (b2), and 1 s (b3). SD represents the standard deviation of the Gaussian fitting to the histograms.
Fig. 5. Allan deviation versus acquisition time for the target approximately 298 m away. The results are obtained at $\overline {\Delta f}=20.006$ kHz in the phase-locking mode. Error range is calculated from the Allan deviation divided by the square root of the sample size.
4. Conclusions
In conclusion, we demonstrate precise laser ranging with dual-comb nonlinear ASOPS and TCSPC involving a fractal SNSPD. Allan deviation of 6.2 µm with an acquisition time of 100 ms and 0.9 µm with acquisition time of 1 s were achieved in measuring the distance of an outdoor target approximately 298 m away. This demonstration may find direct applications in land surveying [45], aircraft manufacturing [46], and formation-flying satellites [47,48]. Although a cooperative target was used in this demonstration, further improvement of the collection and detection efficiency of echo photons may allow us to measure the distance of remote non-cooperative targets in the future. In the long term, fully on-chip integration of the laser sources [9,10,49,50] and SNSPDs [51,52] would make the system more compact and stable, and might revolutionize the time and distance metrology.
Funding
Innovation Program for Quantum Science and Technology (2023ZD0300100); National Natural Science Foundation of China (62071322).
Acknowledgments
The authors thank Prof. Val Zwiller for providing NbTiN films for fabricating the SNSPDs. Portions of this work were submitted to OFC 2024.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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