High-accuracy large-scale length measurements are becoming more demanding in a variety of scientific and industrial fields. For large-scale structure fabrication and assembly, the three-dimensional (3D) coordinate metrology at length scales of 5 to 100 m has become a routine requirement^[1]. Distributed synthetic aperture radar (SAR), which shows great potential in space-based surveillance, reconnaissance, and resource management, also relies on high-accuracy ranging and azimuth information. Typically, micrometer level ranging accuracy at a dozen meters of baseline is required^[2]. Accuracy of conventional time-of-flight (TOF) LIDARS based on direct photoelectric detection of the retroreflected nanosecond laser pulses is restricted to millimeters due to limited response time of direct photo-detection^[3]. Interferometric distance measuring techniques such as synthetic wavelength interference and multi-heterodyne interference, can also achieve absolute ranging^[4,5]. However, for 10 μm level ranging accuracy, a sophisticated laser frequency stabilization apparatus is indispensable, which limits their applications in industrial fields and in space.

In recent years, absolute distance measurements based on femtosecond laser technology have become an active research field^[6–11]. In particular, a dual-comb setup^[12–15] draws great attention due to high resolution, high update rate, as well as dead-zone free measurement. Beam combination of two tightly phase-locked optical frequency combs with slightly different repetition rates naturally undergoes asynchronous optical sampling (ASOPS)^[16], allowing precise timing determination for femtosecond laser pulses. Based on this principle, Coddington et al. achieved a ranging accuracy of 5 nm within a 1.5 m ambiguity range^[12]. In a simplified setup without complex phase lock loops, Liu et al. obtained a ranging accuracy of 2 μm in 140 μs based on only two free-running low noise mode-locked femtosecond lasers^[13]. A dual-wavelength passive mode-locked fiber laser that inherently emits dual pulse trains with an offset repetition rate was also used for absolute ranging, enabling a further simplified setup^[14]. At the same time, the impact of the optical frequency comb design on dual-comb ranging precision has also been comprehensively investigated^[17–19].

Compact and reliable femtosecond laser sources^[20–23] are essential for practical femtosecond laser ranging applications. There has been rapid progress in this field. In 2014, an Er-doped femtosecond fiber laser based on a real saturable absorber (SA) mode locker was tested in aerospace^[24]. The laser developed by South Korea operated well within a one-year in-orbit test. In order to avoid the low damage threshold and insufficient lifetime of a real SA, Germany tested an all-polarization-maintaining (PM) femtosecond fiber laser that is mode-locked by a nonlinear amplified loop mirror (NALM)^[20], which acts as an artificial SA in space and showed its potential aerospace applications for optical clock comparison^[25].

Despite the powerful all-PM NALM femtosecond laser technique and its potential for practical aerospace and industrial applications, its performance on absolute ranging has not been tested. In this Letter, we construct a simple and robust dual-comb LIDAR by employing two NALM mode-locked environmentally stable PM fiber lasers with ∼2 kHz offset repetition rate as laser sources. The absolute distance is measured through an ASOPS-based TOF method. A ranging accuracy of ±2 μm within 65 m is realized. A high update rate is maintained by using Kalman filtering for real-time data processing.

The NALM mode-locked fiber laser used for absolute ranging contains a fiber loop and a linear arm, as schematically shown in Fig. 1. The counter-propagating pulses in the fiber loop obtain asymmetrical gain, hence differential nonlinear phase. They combine at the linear arm, and the interference between two pulses introduces an intensity-dependent response, serving as a fast SA. A Faraday rotator and a quarter waveplate (QWP1) work as a nonreciprocal phase shifter, introducing an additional phase bias, which contributes to self-started mode-locking^[20]. Two output ports with tunable output power are obtained through QWP2. In this system, port 1 is used for distance measurement, while port 2 is used for monitoring.

Two home-built all-PM NALM mode-locked fiber lasers with ∼2 kHz repetition rate difference were used for the dual-comb ranging system. The optical spectra of the two lasers are shown in the inset of Fig. 1, and the output parameters are listed in Table 1.

The principle of ASOPS-based TOF measurement is shown in Fig. 2^[17]. The pulse train emitted from the signal laser (SL) with a repetition rate of fr is partly reflected by a reference mirror, and the transmitted part is then reflected by a target mirror. The collected reference-reflected and target-reflected pulse trains are combined with the pulse train from a local oscillator (LO), which has a repetition rate of fr+Δfr. The repetition rate difference between the SL and LO causes a walk-off between these pulse trains, ensuring that the LO pulse train takes a sample of the reflected SL pulse train over many repetition periods (tr). In other words, LO pulses walk through the reflected SL pulses with a step of Δt=1fr−1fr+Δfr≈Δfrfr2(1)at each repetition period. A full scan of the LO pulses across the reflected SL pulses is completed every Tupdate=1Δfr.(2)

Equivalently, the SL pulses are temporally stretched by a factor of N, where N=trΔt=frΔfr.(3)

To this end, the time interval of reflected reference and target pulses tf can be obtained through fast data acquisition electronics. The target distance is simply L=c2ng·tf=c2ng·(TdN+mtr),(4)where ng is the group refractive index of air, Td is the obtained time interval between the adjacent target and reference pulses in the stretched time window, and m is an integer that accounts for ranging ambiguity. Instead of directly measuring N, we determine the distance by using L=c2ng·1fr·(Ttar−Tref1Tref2−Tref1+m),(5)where Ttar is the timing of the target pulse, and Tref1 and Tref2 represent timing of two successive reference pulses, all measured in the stretched time window. There is a ∼0.5 mm dead zone caused by the overlap of the reference pulse and target pulse in the vicinity of each integer non-ambiguous range. This small dead zone can be avoided by detecting the reference and measurement pulses separately^[7].

The experimental setup of the femtosecond LIDAR system is shown in Fig. 3. The SL and LO in Fig. 3 are as aforementioned free-running all-PM NALM fiber lasers. For compactness and robustness, the free-space outputs from port 1 of the two lasers are coupled into fiber through a space coupler, which contains an isolator, a half-waveplate, and a collimator.

A reference mirror, telescope, and target mirror are placed after port 2 of a fiber circulator. Note that the 4% Fresnel reflection from the end face of a ferrule connector/physical contact (FC/PC) connector acts as the reference mirror. A telescope (Thorlabs, C80APC-C) with adjustable focus length is used to collimate the beam for long-distance ranging. The target mirror is a hollow retroreflector installed at an 80 m granite rail at the National Institute of Metrology, China (NIM). The reflected pulses of the SL laser are combined with the LO pulses through a polarization beam splitter (PBS). Then, the reflected SL pulses are sampled by the LO via sum frequency generation in a type-II periodically poled KTiOPO4 (PPKTP) crystal, thus completing the ASOPS process. Finally, the intensity cross-correlation trace is detected by a low noise avalanche photo-detector (Thorlabs, APD120 A). After a low pass filter (30 MHz), the trace is digitized and stored by a data acquisition card (NI PXIe-5122). The repetition rate of the SL pulse train is real-time monitored by a 12 bit frequency counter (Agilent, 53220 A) at 1 s gate time, which is used as an external signal clock for the data acquisition card.

The absolute distance between the reference and target mirror is retrieved from the time interval between adjacent reference and target pulses in a stretched window, which is obtained by extracting the interval between peaks of the Gaussian fitted cross-correlation trace. The meter level non-ambiguity range can be resolved by non-ambiguity range extension approaches^[12,26], or simply by a number of coarse measurement methods. Here, we determine m by gauge readings on the granite rail. The absolute distance measurement results of this LIDAR system are compared with the 80 m laser comparator at NIM, as shown in Fig. 4(a). The residuals and standard deviations of the ranging results are depicted in Fig. 4(b). The absolute values of the residuals are within 2 μm with standard deviations less than 4 μm over the full 65 m measurement range at an averaging time of 500 ms. The Allan deviation of the results at two selected positions of 30 and 60 m are shown in Fig. 5. At the minimum acquisition time of 5 ms (set by the data processing module), the standard deviations are 4.1 μm at 30 m and 9.6 μm at 60 m, respectively. The precision drops below 1 μm when the averaging time is increased to 1 s.

Allan deviation in Fig. 5 indicates a white noise timing fluctuation during TOF determination. A number of advanced data processing techniques can be used to reduce white noise besides simple multiple averaging, which secures a high measurement precision by sacrificing the update rate. Here, we utilized the Kalman filter^[27] to reduce the measurement precision loss introduced by the stochastic process and maintain a high measurement update rate. Kalman filtering has been frequently used to filter noisy signals in dynamic systems. Here, the procedure of Kalman filtering establishes a space model to calculate the optimal state estimation of the absolute distance measurement results. The specific procedure of applying the Kalman filtering algorithm for processing distance signals obtained by the dual-comb absolute ranging system can be found in our earlier publication^[28]. The acquired distance data are processed by Kalman filtering during measurement, and the results are depicted in Fig. 6. The residuals and standard deviation are of the same level as those in Fig. 4, while a 200 Hz update rate is maintained.

In conclusion, a robust dual-comb LIDAR system based on all-PM femtosecond fiber lasers is demonstrated. Large-scale absolute distance measurement is conducted at an 80 m granite rail at the NIM. The measurement residuals are less than 2 μm, and deviations are less than 6 μm with 500 ms averaging time over 65 m distance. Through the Kalman filter in data processing, the update rate increases to 200 Hz, while the micrometer accuracy is maintained. The all-PM fiber, high accuracy, and high update rate femtosecond LIDAR system shows great promise for various space-based large-scale measurement applications, such as distributed SAR remote sensing, gravitational wave detection, and a satellite formation flying-based astronomical telescope.