Results and Discussions A ±200 V, 100 kHz square wave with a duty cycle of 0.5 is used in the experiments. The maximum update rate of a single measurement is up to 200 kHz, and the detectable range is 351 μm. The measurement accuracy reaches 16.7 nm after 4100 times of averaging (Fig. 4), and the system has been proven to have good accuracy and stability. At an update rate of 200 kHz and a static distance of 41 μm, the standard deviation of 10000 consecutive measurements is 938 nm. The standard deviation can be reduced to 100 nm after moving average of 100 points (Fig. 3). Therefore, the system has been proven to have good repeatability. In addition, multiple measurements at the same location at different Δf_r show a standard deviation of 417.2 nm after 2050 times of averaging (Fig. 5), which reflects that the system has good reproducibility. Then, the target object is moved with each step of 10 μm, and after 2050 times of averaging, the measured values are compared with the true values. The measurement accuracy of the system is within a few hundred nanometers, and the residual is within ±528 nm (Fig. 6), which indicates that the system has good accuracy. To prove the capability of the system to detect surface traces, a silicon-based micromechanical device [Fig. 7(b)] is measured. In the measurement, a ±200 V, 50 kHz square wave modulation with a duty cycle of 0.5 is applied to the EOM. The update rate is 100 kHz at this time, and the detectable range is 702 μm. Ten positions are measured with a lateral spacing of 30 μm between every two positions. The original ranging data of each position is averaged by 2050 times, and then the trench depth is calculated to be about 67.6 μm [Fig. 7(a)]. The proposed absolute distance measurement system has high accuracy and update rate, and can be applied in the 3D surface profile measurement of micromechanical structures. This system is also suitable for high-frequency mechanical vibration monitoring.

Time-of-flight distance measurement based on a dual-comb approach is widely applied in the fields of laser radar, topography scanning, and vibration measurement by using two femtosecond lasers with a small repetition frequency difference for asynchronous optical sampling (ASOPS). In this manner, the high temporal resolution, comb-shaped spectrum, and ultra-low noise performance of femtosecond lasers can be fully utilized. However, the update rate of a dual-comb ranging system based on ASOPS is limited to a few kilohertz (determined by the repetition frequency difference) so as to avoid insufficient optical sampling. Given the extremely small duty cycle determined by the ratio of the femtosecond pulse width to the millisecond sampling period, most of the sampling time during a full sampling cycle is wasted in the process of pulse walk-off. To solve this problem, an electro-optical modulator (EOM) is added to the ASOPS system to modulate the repetition frequency periodically in this work. The so-called electronically controlled optical sampling (ECOPS) approach breaks the update rate limitation in the ASOPS system and can increase the update rate to hundreds of kilohertz, further enriching the application fields of dual-comb distance measurement technology.

ECOPS uses two lasers with tightly phase-locked repetition frequency (f_r) as the light source. One is called a local laser with an EOM inserted in the cavity, and the other is called a signal laser. The EOM in the cavity is used to modulate the repetition frequency of the local laser. As a square wave is imposed on the EOM, the repetition frequency is switched between f_r-Δf_r and f_r+Δf_r, and the modulation period is determined by the square wave modulation frequency f_m. Therefore, the repetition frequency difference between the two lasers switches between -Δf_r and Δf_r at the modulation frequency f_m. Different from ASOPS with only a fixed Δf_r, the rapid switching of ±Δf_r effectively drives the output pulse of the local laser to scan back and forth on both sides of the output pulse of the signal laser, resulting in a controlled, bounded optical sampling and avoiding the unwanted pulse walk-off. The update rate is determined by the modulation frequency f_m, which breaks the limitation of the ASOPS-based measurement system where the update rate is determined by the repetition frequency difference Δf_r. In the experiment, a pair of nonlinear polarization rotation (NPR) mode-locked fiber lasers with a repetition frequency of ~158 MHz are selected as the signal laser and the local laser. In the local laser, the pulse duration is 140 fs, the spectral width is 21 nm, the central wavelength is 1569 nm and the average power is 20 mW. As for the signal laser, the pulse duration is 92 fs, the spectral width is 51 nm, the central wavelength is 1557 nm and the average power is 50 mW. Part of the output of the two lasers is combined and directed to a balanced optical cross-correlator (BOC), which detects the relative timing error between the two lasers with sub-femtosecond resolution. The error signal is fed back to the end mirror mounted on a fast piezo-actuator such that the repetition frequencies of the two fiber lasers are tightly phase-locked, and the residual timing jitter is lower than a few femtoseconds. After the phase locking of repetition frequencies is established, the main parts of the laser output are directed to the distance measurement module. A mechanical delay line is used to adjust the optical path from the output of one laser so as to make sure that the pulses from the two lasers overlap in time. As square wave modulation is applied to the EOM, the signal pulses naturally scan back and forth on both sides of the local pulses, which enables ECOPS-based distance measurement.

This paper proposes a dual-comb absolute distance measurement system based on ECOPS and selects two NPR mode-locked lasers with a repetition frequency of ~158 MHz. In the experiment, their repetition frequencies are locked by the synchronization module. After the two femtosecond pulse trains are aligned through the spatial delay line, the sampling pulse is moved back and forth on both sides of the signal pulse by adding a square wave to the EOM in the local laser, which overcomes the problem in the ASOPS approach where the update rate is limited by the repetition frequency difference. The update rate of the experimental setup can be up to 200 kHz, and the measurement accuracy can reach 16.7 nm with an average time of 20.5 ms in the measurement of an absolute distance of 41 μm. In theory, when the update rate is reduced to 40 kHz, the detectable range can reach 1.75 mm, which meets the detection requirements of trenches in most micromechanical structures, semiconductor devices, and other micro-nano devices. The experiments show that the system has good repeatability, reproducibility, stability, and accuracy. The trench depth in a micromechanical structure is measured with the designed system. The dual-comb system based on ECOPS can be widely used in micro-distance measurement, and also has potential application prospects in the fields of 3D topography scanning, such as surface profilometry and flatness analysis.