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Abstract
Dual-comb (DC) ranging is an established method for high-precision and high-accuracy distance measurements. It is, however, restricted by an inherent length ambiguity and the requirement for complex control loops for comb stabilization. Here, we present a simple approach for expanding the ambiguity-free measurement length of DC ranging by exploiting the intrinsic intensity modulation of a single-cavity dual-color DC for simultaneous time-of-flight and DC distance measurements. This measurement approach enables the measurement of distances up to several hundred kilometers with the precision and accuracy of a DC interferometric setup while providing a high data acquisition rate ($\approx\! 2 \;{\rm{kHz}}$) and requiring only the repetition rate of one of the combs to be stabilized.
Published by The Optical Society under the terms of the Creative Commons Attribution 4.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.
Recent progress in automation and metrology in various fields of application such as industrial robotics or autonomous transportation has led to an increasing demand for precise, fast, robust, and inexpensive ranging technologies that are applicable outside the laboratory frame.
Interferometric distance-measurement techniques based on homodyne or heterodyne detection offer high precision [1]. In their most basic form, however, they require continuous tracking and unidirectional motion of the target to clearly interpret relative phase changes during the measurement. Otherwise, absolute measurements can only be obtained modulo the ambiguity-free range given by $\lambda /2$, where $\lambda$ is the optical wavelength. Alternatively, these ambiguity limitations can be overcome by using modulated or pulsed light. In these so-called time-of-flight (TOF) measurements, the distance is measured by analyzing the temporal delay between the pulse coming back from the target and the pulse that has travelled along a known reference path [2,3]. However, such systems typically lack the high resolution of an interferometric system.
Since their invention in the late 1990s, optical frequency combs (OFCs) have become an indispensable tool in optical metrology [3,4]. Initially used for counting the cycles of optical clocks, they quickly revolutionized many other fields, including applications in spectroscopy and ranging [5]. Various ranging methods based on OFCs have been reported so far, including optical cross correlation [6], synthetic-wavelength interferometry [7], and multiple wavelengths referenced to a stabilized comb [8], among others.
Dual-comb (DC) ranging systems [9] enable an ambiguity-free measurement range of $c\!/\!{f_{{\rm{rep}}}}$ (typically a few meters) in a single measurement via analysis of the beating signal between two OFCs with slightly different repetition rates, i.e., different frequency spacings of the comb lines. A first comb is sent along a known reference path and along a signal path. At the end of both paths, the light is reflected back. The signal and reference reflections are sampled with a second comb. By evaluating the temporal shift of the respective interferograms, the precision of the established TOF technique is improved by a factor of $\frac{{{f_{{{{\rm rep},2}}}}}}{{\Delta {f_{{\rm{rep}}}}}}$ [9]. Here, ${f_{{{{\rm rep},2}}}}$ is the repetition rate of the comb used for the remote sensing, and $\Delta {f_{{\rm{rep}}}}$ is the difference to the repetition rate ${f_{{\rm{rep,1}}}}$ of the local reference comb. As these systems depend on a complex light source (two phase-stable frequency combs), different methods have been presented to simplify them while further improving their accuracy and precision [10–12]. Via additional evaluation of the interferogram carrier phases, for example, it is possible to achieve wavelength resolution. A detailed review on the DC ranging technique is provided by Zhu et al. [13].
Different approaches have been reported to overcome the remaining ambiguity limitation, e.g., by using the Vernier effect [9]. The Vernier-effect method can be implemented by switching the role of the signal and reference path [9], by adjusting the repetition rate of the signal [14], or by adding an extra measurement path [15]. However, all of these approaches either introduce moving parts [9] or increase the measurement time and experimental complexity. Besides the Vernier effect, one can exploit nonlinear optics to enable absolute distance ranging [16]; however, this method demands high peak powers.
An alternative high-precision ranging technique relies on using a single-frequency comb and an electro-optical modulator (EOM) [17]. This elegant method offers high-precision and long-distance measurement, but depends on the detection of weak side-bands, requiring high reflectivity of the target.
Liu et al. used a single-cavity DC [15] to reduce the complexity of the light source. However, they could only overcome the ambiguity limitation by exploiting the Vernier effect.
This Letter presents a new approach to extend the ambiguity-free range of DC ranging based on a single-cavity dual-color DC [18] without the need to use the Vernier effect or nonlinear optics. The ambiguity-free range is increased to $c\!/\!\Delta {f_{{\rm{rep}}}}$ (150 km for the laser parameters used in the presented experiment) within a single measurement, while allowing for data acquisition in the millisecond range.
Pulse trains emitted by single-cavity dual-color lasers are known to exhibit intensity modulations with a periodicity of $\Delta {f_{{\rm{rep}}}}$ caused by intracavity pulse collisions [19,20]. We exploit this periodic modulation imprinted on the individual pulse trains as a marker to perform a secondary long-range TOF measurement, which allows us to extend the non-ambiguity range. Additionally, we use the shift of the DC interferograms to measure the distance with high precision. To the best of our knowledge, imprinting an additional intensity modulation on a frequency comb to overcome ambiguity limitations in DC ranging has not been reported so far. While such a modulation can be imprinted using an external modulator, the here presented system exploits the intrinsic effect of pulse collision inside a single-cavity dual-color laser, which further simplifies the complexity of the light source.
The system presented in this Letter is based on an all-polarization-maintaining (PM) fiber laser using Yb as a gain material and a nonlinear amplifying loop mirror in combination with a non-reciprocal phase bias for mode-locking [21,22]. For a detailed analysis of how to operate and mode-lock these lasers, see [23]. A sketch of the dual-color DC can be seen in Fig. 1.
Fig. 1. Figure nine DC of 92 MHz. WDM, wavelength division multiplexer; I, Isolator; CPBC, collimating polarization beam combiner; FR, Faraday rotator; PBS, polarizing beam splitter; G, grating; M, mirror; $\frac{\lambda}{2}$, half-wave plate; $\frac{\lambda}{4}$, quarter wave plate; PI, piezos; BM, bullet mount; PD, photodiode; Col, collimator; L, lens; PCF, photonic crystal fiber; RR, retroreflector; DBS, dichroic beam splitter; PM, polarization maintaining.
The laser source used for this experiment is similar to the system presented in [18], however, the repetition rate of the laser is increased to around 92 MHz. A tuneable mechanical spectral filter [24] allows the all-PM laser to emit two independent pulse trains with different center wavelengths and slightly different repetition rates. The output spectrum of the laser is measured using an optical spectrum analyzer (Ando AQ6315A), see Fig. 2(a). One of the two pulse trains has a center wavelength of 1010 nm (running in the normal dispersion regime), an output power of 1.5 mW, and a repetition rate of 92.455 MHz, while the other one has a center wavelength of 1085 nm (running in the anomalous dispersion regime), an output power of 2 mW, and a repetition rate of 92.457 MHz. Additionally, we analyzed the laser output using a fast photodiode (PD, Thorlabs DET08CL/M) connected to a microwave spectrum analyzer (Keysight PXA N9030B). Figure 2(b) shows a zoom into the two repetition rates of the two pulse trains operating inside the single laser cavity with $\Delta {f_{{\rm{rep}}}} \approx\! 1.95 \;{\rm{kHz}}$. We generate a spectral overlap between the two combs and thus enable a DC beating signal via amplification and nonlinear broadening: first, we amplify comb 1 inside a PM-Yb single-mode fiber amplifier to approximately 30 mW. The output of the amplifier is temporally compressed using a grating compressor consisting of two gratings (II–VI transmission grating: T-1000-1040-31.8x12.3-94) used in a double-pass configuration. The temporally compressed ($\approx\! 250\; {\rm{fs}}$) light is coupled into a highly nonlinear fiber, similar to the one used in [25], with a coupling efficiency of $\approx\! 65\%$. Inside the fiber, comb 1 is spectrally broadened to overlap with comb 2 [see Fig. 2(a)].
Fig. 2. Figure nine dual-color of 92 MHz laser state with one pulse operating in the anomalous dispersion regime (centered around 1085 nm) and one pulse in the normal dispersion regime centered around 1010 nm. (a) Optical output spectrum of the laser (blue) and spectrum of comb 1 after amplification and nonlinear broadening (black). (b) Zoom into the repetition rates of the two pulse trains.
A detailed sketch of the complete ranging experiment can be seen in Fig. 3. The cross-phase modulation signal is imprinted on both combs and is visible as an intensity modulation on both pulse trains, see Fig. 3. For the TOF measurement, only comb 2 is required. In our implementation, the distance $L$ to be measured is the path delimited by the reflective side of the partial reflector (50:50RBS, red optic in Fig. 3) and the reflective side of the end mirror (SM, blue optic in Fig. 3).
Fig. 3. Working principle of DC ranging based on a single-cavity DC. The single cavity is emitting two intensity-modulated frequency combs (comb 1 and comb 2) with slightly different repetition rates ($\Delta {f_{{\rm{rep}}}} \approx\! 2 \;{\rm{kHz}}$) around 92 MHz. Comb 2 is used as the remote sensing probe. Comb 1 is used to sample comb 2 for precise DC ranging by evaluating the time-delay $\Delta {t_{\rm{i}}}$ between the reference and signal interferogram recorded on photodiode 1 (PD1). PD2 and PD3 provide the signals to determine the TOF delay $\Delta {t_{{\rm{tof}}}}$ used for coarse length measurement. PBS, polarizing beam splitter; M, mirror; $\lambda /2$, half-wave plate; $\lambda /4$, quarter wave plate; 90:10, beam splitter; 50:50RBS, reference beam splitter; GF, optical band pass filter; TS, translation stage; MM1, ø50 mm silver mirror $f = {{1}}\;{\rm{m}}$; MM2, ø50 mm silver mirror flat, with hole; SM, signal mirror.
The light reflected by the 50:50RBS (starting point of $L$) is sent onto a fast PD3 (Thorlabs DET08CL/M) and used as a reference. The light reflected back by the end mirror is sent onto a second fast PD (PD2, Thorlabs DET08CL/M). The PDs are connected to an oscilloscope (Teledyne LeCroy WavePro 7Zi 6 GHz-40GS/s) to evaluate the time traces. The length is evaluated by measuring the temporal shift of the cross-phase modulation signal between the reference (PD3) and the signal (PD2). A typical measurement is shown in Fig. 4. Note that the detection of the two beams on different PDs is not strictly required, but simplifies the analysis of the two pulse trains by separating them directly. However, to compensate for the different distances of the two PDs from the reflector 50:50RBS, a separate TOF calibration measurement needs to be performed. This calibration is easily implemented by sending the reference beam onto both PDs. The accuracy of the TOF measurement must only be on the order of a single-cavity length ($\approx\! 3.2 \;{\rm{m}}$), which is easily achieved. The ambiguity-free length for this measurement is given by $c\!/\!\Delta {f_{{\rm{rep}}}}$, which corresponds to 150 km for $\Delta {f_{{\rm{rep}}}} = 2\;{\rm{kHz}}$. Hence, we use the TOF measurement to calculate the integer division factor $n = {\rm{int}}\left({\frac{L}{{{L_{\rm{c}}}}}}\right)$, where ${L_{\rm{c}}} = c\!/\!{f_{{\rm{rep},2}}}$ is the optical cavity length.
Fig. 4. TOF measurement using intensity modulation on the pulse train as a marker. The red trace (top) shows the reference measured at PD3 (Fig. 3). The dark blue trace (bottom) shows the signal measured at PD2 (Fig. 3). Due to the path length difference, the modulation is shifted. The time delay between the modulation signals is used for coarse length calculation. Note: this measurement was performed at the minimal power level ($\approx\! 50 \;\unicode{x00B5}{\rm{W}}$) necessary for the evaluation of the reflected light. The distortion of the pulse trains apart from the collision signal is caused by the low signal-to-noise ratio at this power level.
To additionally measure the distance with high precision, we simultaneously implement the DC ranging principle [9]. We use comb 1 to sample the signal beam (coming back from the end mirror, blue optic) as well as the reference beam (coming back from the partial reflector, red optic) and measure the optical beating using PD1 (Thorlabs PDA05CF2). The fact that the reference beam is also able to reach PD1 despite being vertically polarized is due to the low extinction ratio of the polarizing beam splitter (PBS) when used in reflection. To avoid optical aliasing, we filter the light in front of PD1 using a spectral filter (a grating and slit) and focus it on the PD.
Fig. 5. DC ranging measurement based on a signal trace acquired via PD1. A complete scan of $1/\Delta {f_{{\rm{rep}}}}$ is shown, corresponding to the minimum measurement time.
The signal of PD1 is electronically filtered with a 70 MHz low pass filter (to filter away the repetition rate) and analyzed using an oscilloscope. Looking at the filtered time trace, we get four signals, each signal occurring periodically with a repetition frequency of $\Delta {f_{{\rm{rep}}}}$. The signals correspond to the modulation signals occurring on pulse trains 1 and 2, the DC interferogram corresponding to the reference beam and the DC interferogram corresponding to the signal beam. A typical measurement trace is shown in Fig. 5. Since PD1 is an amplified detector, power levels of a few microwatts (µW) for the reference and signal beams are sufficient to measure the interferograms. However, PD2 and PD3 are biased detectors (low cost and high bandwidth), requiring a power of around 50 µW to achieve an adequate signal-to-noise ratio for evaluation of the time traces. The signal-to-noise ratio could be improved by using amplified fast detectors. In this case, a few µW signal would be sufficient to perform the ranging measurement, making it a promising candidate for applications outside the laboratory frame. The time trace of PD1 is evaluated by measuring the time delay between the reference and signal interferograms. The time delay between the two interferograms is given by $\Delta {t_{\rm{i}}} = \frac{{{L_{\rm{i}}}}}{c}\frac{{{f_{{\rm{rep},2}}}}}{{\Delta {f_{{\rm{rep}}}}}}$, where ${L_{\rm{i}}}$ is the short-scale measurement length as defined below. ${L_{\rm{i}}}$ depends on the temporal position of the signal interferogram relative to the reference interferogram. To identify the reference and signal interferogram, we set different power levels, i.e., different amplitudes, of the interferogram. We must distinguish between three cases:
- • Case 1: The signal is delayed compared to the reference interferogram (as in Fig. 5): ${L_{\rm{i}}} = (L\bmod {L_{\rm{c}}})$.
- • Case 2: The reference is delayed compared to the signal interferogram: ${L_{\rm{i}}} = {L_{\rm{c}}} - (L\bmod {L_{\rm{c}}})$.
- • Case 3: The reference is exactly at the same position as the signal interferogram: ${L_{\rm{i}}} = 0$.
The total length of the distance measured is then given by
To achieve sufficient accuracy, ${f_{{\rm{{\rm rep},2}}}}$ and $\Delta {f_{{\rm{{\rm rep},2}}}}$ can either be tracked or stabilized. Here, we stabilized ${f_{{\rm{rep},2}}}$ (by stabilizing the 15th harmonic ${f_{{{{\rm rep},2}}}} \approx\! 1.386 \;{\rm{GHz}}$) to a frequency generator (Rohde&Schwarz SMF 100A) using a piezo-controlled end mirror inside the laser resonator, and we tracked $\Delta {f_{{\rm{rep}}}}$ by measuring the periodicity of the cross-phase modulation signal in the time trace. The long-term stability of the measurement depends on the stabilization of the repetition rate of the probe comb. Hence, on the stability of the reference.We verified the capability of our system to perform single-shot measurements over a large ambiguity-free range by measuring the path lengths of different multi-pass cell configurations. We varied the measurement distance $2L$ (to the end mirror and back) from less than a single-cavity length to more than 24 cavity lengths, see Fig. 6. Using the presented approach, we were able to measure the different distances without any ambiguity in a single sweep (${\rm{measurement \;time}} = 1/\Delta {f_{{\rm{rep}}}} = 500 \; \unicode{x00B5}{\rm{s}}$). In each configuration we changed the path length in increments of 2 mm (by scanning the end mirror in 1 mm steps using a translation stage). For each measurement point, we took 15 measurements and got an error of $\sigma \lt 100\,\,\unicode{x00B5}{\rm m}$. This precision is limited by the DC parameters. However, it can be significantly improved by increasing ${f_{{\rm{rep}}}}$ while decreasing $\Delta {f_{{\rm{rep}}}}$ at the expense of an increase in measurement time.
Fig. 6. Evaluation of the combined TOF and DC measurements. Using both signals, we are not limited by the ambiguity range of traditional DC ranging. The dark blue section (measurement 1) is measured at a starting distance ${L_1}$ within a single-cavity length (${L_{\rm{c}}} = c\!/\!{f_{{\rm{rep}}}}$), which is the maximum ambiguity range for conventional DC ranging. The light blue section (measurement 2) is measured with a distance that is ${L_2} \gt 9{L_{\rm{c}}}$, and the turquoise section (measurement 3) is measured with a distance ${L_3} \gt 24{L_{\rm{c}}}$. To verify the precision of the measurement, we changed the end-mirror position using a micrometer translation stage.
The presented measurement principle enables single-shot high-precision absolute-distance ranging over an ambiguity-free measurement range of around 150 km by combining the advantages of TOF measurements and DC ranging. The system is based on a single light source with much less stringent requirements on stabilization (only ${f_{{{{\rm rep},2}}}}$ needs to be either stabilized or continuously measured) compared to two mutually phase-stable (locked) frequency combs. In addition, the measurement does not rely on nonlinear processes. Hence, it only needs µW-level reflected powers returning to the sensor. The high-precision, large ambiguity-free measurement range and fast data acquisition in combination with the high sensitivity, make the presented measurement approach an ideal system for field applications.
Funding
Austrian Science Fund (M2561-N36, P 33680 Einzelprojekte); Christian Doppler Forschungsgesellschaft; Österreichische Nationalstiftung für Forschung, Technologie und Entwicklung; Bundesministerium für Digitalisierung und Wirtschaftsstandort; Fundacja na rzecz Nauki Polskiej (First TEAM/2017-4/39).
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.
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