Absolute distance measurement for multiple targets is required in industrial and scientific fields such as machine monitoring, detection of distortion in large structures, wafer alignment in semiconductor manufacturing, and the formation flying of satellites. Furthermore, the expansion of measurement channels is essential for the effective application of multi-target measurement. However, because measurement channels' expansion requires high power, it is difficult due to the low conversion efficiency of conventional systems that use a non-linear crystal for optical cross-correlation. In this study, for measurement channel expansion, time-of-flight based absolute laser ranging via high-efficiency dual-comb cross-correlation using a semiconductor optical amplifier is developed. The semiconductor optical amplifier acts as a cross-correlator, and it can produce a cross-correlation signal with a laser’s power of 50 µW because of its very high conversion efficiency. This method is suitable for expanding the measurement channels and measuring non-cooperative targets as it can detect low-power signals. The repeatability of the distance measurement is 4 µm at a single shot (37 µs) and 120 nm for 5 ms. The linearity is assessed by evaluating the R-square, which is equal to 1 within the range of significant figures. Moreover, the distance measurement of targets lying on the two axes was demonstrated to ensure the measurement channels' expansion. This measurement system has the potential to determine multiple distances, making it applicable to diverse fields such as semiconductor manufacturing, smart factories, plant engineering, and satellite formation flying.

Distance measurement technologies have been developed over several decades because of their fundamental requirements in both scientific and engineering fields.1,2 Distance measurement methods can be classified into continuous-wave laser interferometers and absolute distance measurement methods using mode-locked lasers.3,4 CW laser interferometers have reliable precision up to the nanometer level and have been widely used for precision metrology applications, including length and angle measurements and surface profiling. However, owing to its limitation in the non-ambiguity range (NAR) determined by the laser’s optical wavelength, it can only be utilized for displacement measurements. Absolute distance measurement was introduced with the development of a femtosecond laser to measure the distance instantaneously. Absolute distance measurements can be achieved using diverse optical techniques, such as synthetic wavelength interferometry,5–8 multi-wavelength interferometry,9–15 spectrally resolved interferometry,16–20 dual-comb interferometry,21–25 and time-of-flight.25–35 These metrology systems have high precision and linearity and are applicable to various fields, such as high-precision machinery engineering and next-generation space missions.

Among these methods, absolute distance measurement based on dual-comb time-of-flight can determine the distance of multiple targets in both the on- and off-axes by measuring the flight time of round-trip signals by time-domain expansion via optical cross-correlation (XCOR) between two femtosecond lasers. Measurement channel expansion is required for multi-axis laser ranging to measure targets with more than one degree-of-freedom, such as attitude and location. Measuring multiple degrees of freedom is essential for various tasks such as controlling the attitude of satellites,36 aligning wafers,37 and monitoring thermal vibration in large machinery.38 Using absolute distance measurements for multiple targets, the deformation of more than one component of the measured objects can be simultaneously detected by a single metrology apparatus. The system for absolute distance measurement of multiple targets consists of two femtosecond lasers with slightly different repetition rates, an XCOR module, and a real-time data processing module. As the pulses of the signal laser and local oscillator are incident on the XCOR module, overlapping with each other, the XCOR signals are produced with an intensity proportional to the amount of overlapping, resulting in time domain expansion with a scaling ratio of ∆fr/fr, where fr is the repetition rate and ∆fr is the difference in repetition rate between two lasers. This temporal scaling overcomes the photodetector’s response speed limitation, allowing direct determination of the time-of-flight via the XCOR of the dual-comb. Moreover, multiple signals, including references and targets, generated by the XCOR process can be detected simultaneously within one cycle of the repetition rate, allowing multiple targets to be measured simultaneously.

The conventional methods for dual-comb XCOR laser ranging include interferometric26,31,33 and second harmonic generation techniques,28–30,32 and recently, a method utilizing two-photon absorption34,35 has been developed. The interferometric dual-comb ranging employs the interferograms between the signal laser and local oscillator as XCOR signals, and it has high precision of measurement. Nevertheless, this method requires tight stabilization of femtosecond lasers for reading the carrier frequency in the interferogram, which increases the complexity of the system. The ranging system based on second harmonic generation adopts non-linear crystals such as type II barium borate (BBO) and periodically poled potassium titanyl phosphate (PPKTP). This technique needs only intensity information in the XCOR signal, so intuitive measurement can be achieved with high resolution. The conversion efficiency of second-harmonic generation, however, is dependent on the power of the pulse incident on the non-linear optical crystal, which indicates that, as the power of the pulse is less than several milliwatts, the generated second-harmonic pulse reaches the nanowatt level.39 Because multi-axis absolute distance measurement requires sufficient power to split the laser’s output into multiple probes, it is difficult to expand the measurement channels because of the non-linear crystal’s low conversion efficiency. Recent research on two-photon absorption dual-comb utilizes two-photon absorption in semiconductor to generate the XCOR signals. This metrology has a simple system and can measure the signals using the 1–6 mW power of the lasers. Moreover, it overcomes the frequency limit of the repetition rate, which means that it is free to select the repetition rate difference, so high-speed measurement is possible. Nonetheless, the precision and required power of the beam for signal detection by this method need to be improved for effective laser ranging applications.

To overcome the limitations, we demonstrate a dual-comb-based time-of-flight absolute distance measurement via a high-efficiency optical XCOR using a semiconductor optical amplifier (SOA). This method is based on the XCOR process occurring in a SOA using gain dynamics.40,41 XCOR using a SOA has the feature of high conversion efficiency; therefore, it does not require high power for the returning pulse. If an additional power amplifier, such as an erbium-doped fiber amplifier (EDFA), is used, it is possible to expand the number of measurement channels to 10 or 20. This measurement system has a repeatability of 4 µm at 37 µs, similar to the conventional PPKTP-based system. Furthermore, owing to its construction entirely from fiber components without any free-space elements, this system is simple to assemble, highly compact, and has a low weight, making it well-suited for use in space missions or other engineering applications. Based on these advantages, SOA-based absolute distance measurement is applicable to diverse fields, such as the monitoring of machines or large structures, the alignment of lens arrays or wafers in the semiconductor industry, and satellite formation flying.

Figure 1 shows the configuration of the multi-axis absolute distance measurement using a SOA. Two femtosecond lasers based on a semiconductor saturable absorber mirror (SESAM) with all-polarization-maintaining fibers42 are used for dual-comb ranging. The lasers consist of a SESAM for mode locking, an erbium-doped fiber (EDF) as a gain medium, a laser diode pump (LD pump) of 980 nm wavelength connected with wavelength division multiplex (WDM), a piezoelectric actuator (PZT) for repetition rate stabilization, a dielectric mirror with 90% reflection of 1550 nm wavelength and 95% transmission of 980 nm, and an isolator (Iso). Additionally, one of the lasers has a free-space collimator for adjusting the repetition rate to the all-fiber lasers. The repetition rate of the femtosecond lasers is 203.2 MHz, and the difference in repetition rate between the two lasers is 27 kHz. The output power of the lasers is ∼1 mW, and the center wavelength is 1558 nm. Before the signal laser probe, the circulator receives the returning pulses from the targets and transfers them to the SOA.

FIG. 1.

Multi-axis dual-comb-based absolute distance measurement using a semiconductor optical amplifier for detecting the low power pulse signal. (a) Absolute distance measurement system for multiple targets with measurement channels' expansion. The power of the traveling pulses from targets becomes lower due to beam separation for the expansion of the measurement channels to achieve multi-axis absolute laser ranging. (b) The limitation of the method of second harmonic generation, XCOR, due to the low conversion efficiency of the non-linear crystal. As the power of pulses is not sufficient to generate the second harmonic wave, it is difficult to achieve multi-axis absolute distance measurement. (c) High-efficiency XCOR process by gain dynamics phenomenon in a SOA. The gain in the SOA changes when a pulse is incident to the SOA and the adjacent pulse is attenuated. It occurs in the XCOR process. To overcome the limitations of PPKTP, the XCOR method with high efficiency using a SOA is demonstrated.

FIG. 1.

Multi-axis dual-comb-based absolute distance measurement using a semiconductor optical amplifier for detecting the low power pulse signal. (a) Absolute distance measurement system for multiple targets with measurement channels' expansion. The power of the traveling pulses from targets becomes lower due to beam separation for the expansion of the measurement channels to achieve multi-axis absolute laser ranging. (b) The limitation of the method of second harmonic generation, XCOR, due to the low conversion efficiency of the non-linear crystal. As the power of pulses is not sufficient to generate the second harmonic wave, it is difficult to achieve multi-axis absolute distance measurement. (c) High-efficiency XCOR process by gain dynamics phenomenon in a SOA. The gain in the SOA changes when a pulse is incident to the SOA and the adjacent pulse is attenuated. It occurs in the XCOR process. To overcome the limitations of PPKTP, the XCOR method with high efficiency using a SOA is demonstrated.

Close modal

Figure 1(a-1) shows a potential example of multi-axis absolute distance measurement for engineering applications for monitoring distortion in industrial machines, such as roll printing systems. The coarse features of XCOR at a SOA are shown in Fig. 1(c). When two laser pulses pass through a SOA, the gain in the SOA rapidly decreases for ∼1 ps40 owing to gain depletion by the first pulse, resulting in the power of the subsequent pulse remaining either constant or decreasing during the period of reduced gain. This gain dynamics leads to XCOR between two adjacent pulses by differentiating the relative intensity of the pulse so that the time-of-flight of the reference and target signals can be directly measured owing to the time-domain extension. For the XCOR of a SOA, the conversion efficiency depends only on the systematic loss in components such as the fiber connection or bandpass filter used to disguise the signal laser and local oscillator, which is sufficient to detect the XCOR signal even if the returned pulse power is less than several milliwatts. Based on this feature, the SOA-based absolute distance measurement can overcome the limitations of the system using PPKTP, as shown in Fig. 1(b).

The details of the SOA XCORs are shown in Fig. 2. The system for XCOR via a SOA consists of the same components, as shown in Fig. 1. The system using a PPKTP produces a second-harmonic generation with a wavelength of ∼780 nm, which can separate the XCOR signal from others, whereas the SOA only makes a difference in the relative intensity with the same wavelength. To distinguish between the signal laser and local oscillator, optical bandpass filters (BPFs) are connected after each laser. One of the BPFs has a bandwidth of 1555 nm and the other has a bandwidth of 1560 nm; therefore, the signal laser and local oscillator can be separated into different wavelengths. After the two laser pulses emerged into the same fiber line using a coupler, the SOA (SOA1117P, Thorlabs) underwent an XCOR process to differentiate the relative intensity of two adjacent pulses via gain dynamics. The behavior of the gain dynamics in the SOA is shown in Fig. 2(b). When a pulse is first incident on a SOA, its gain value rapidly decreases and then rapidly increases, forming a dip of approximately one picosecond. This short period is called the “fast recovery region.” After the fast recovery region, the gain is recharged for several nanoseconds or microseconds until it reaches a steady state, corresponding to the current injected into the SOA. This lengthy period is known as the “slow recovery region.” This series of processes can be interpreted by three equations derived from the photon-electron rate equations, as follows:40,43–45
dhadt=hah0τcexpha+hSHB+hCH1P(t,0),
dhSHBdt=hSHBτSHBεSHBτSHBexpha+hSHB+hCH1Pt,odhadtdhCHdt,
dhCHdt=hCHτCHεCHτCHexpha+hSHB+hCH1Pt,0,
where the first equation is called the current injection rate equation, the second one is spectral hole burning, and the last is referred to as carrier heating. The terms ha, hSHB, and hCH are the gains of each mechanism, and the total gain in the SOA is h0 = ha + hSHB + hCH. Pt,0 represents the power of the input pump pulse, and ɛSHB, ɛCH represent the gain compression factor.
FIG. 2.

Optical characteristics of each component for cross-correlation of semiconductor optical amplifier. (a) The schematics of two femtosecond lasers and their optical spectrum. To distinguish each laser for acquiring the XCOR signal from the SOA, two optical band-pass filters are used after the lasers, and another one is used before the photodetector. This allows for the differentiation of the optical spectrum bandwidth of each laser. (b) Theoretical behavior of gain dynamics derived from the current injection, spectral hole burning, and carrier heating equations in a SOA. It has the features of a gain dip occurred in the fast recovery region when an optical pulse is incident to the SOA and a slow recovery region that would be noise in the data. (c-1) Simulation data of the XCOR. The characteristics of gain dynamics are reflected in the XCOR with temporal domain extension. (c-2) Real data of the XCOR with temporal scaling of ∆fr/fr. The data are smoothed by a low pass filter, and the temporal characteristics are similar to the simulation data.

FIG. 2.

Optical characteristics of each component for cross-correlation of semiconductor optical amplifier. (a) The schematics of two femtosecond lasers and their optical spectrum. To distinguish each laser for acquiring the XCOR signal from the SOA, two optical band-pass filters are used after the lasers, and another one is used before the photodetector. This allows for the differentiation of the optical spectrum bandwidth of each laser. (b) Theoretical behavior of gain dynamics derived from the current injection, spectral hole burning, and carrier heating equations in a SOA. It has the features of a gain dip occurred in the fast recovery region when an optical pulse is incident to the SOA and a slow recovery region that would be noise in the data. (c-1) Simulation data of the XCOR. The characteristics of gain dynamics are reflected in the XCOR with temporal domain extension. (c-2) Real data of the XCOR with temporal scaling of ∆fr/fr. The data are smoothed by a low pass filter, and the temporal characteristics are similar to the simulation data.

Close modal

The graph in Fig. 2(b) is displayed based on the above-mentioned equations, with several incident pulses having a duration of 300 fs. The fast recovery region guides the laser pulses to the main signal of the XCOR, utilizing the gain dip during the XCOR process; however, the slow recovery region becomes noisy and deviates from the baseline. If the two pulses are far apart, they are amplified with the gain of the SOA in the steady state; however, if they are close to each other within the fast recovery region, the following pulse loses its power owing to the lack of gain reduced by the first pulse. The power difference between the amplified and attenuated pulses in the pulse train rendered an XCOR signal equivalent to the original signal pulse with temporal scaling. After the XCOR process, another BPF filters the pulses from the local oscillator, and the passed pulses enter the photodetector. An RF low-pass filter was used to smoothen the signals and extract the pulse train envelope. Figures 2(c-1) and 2(c-2) show the XCOR signal in the pulse train, the simulation data derived from the above gain dynamics equations, and the real data smoothed by the low-pass filter, respectively. The time domain of the real data is multiplied by the temporal scaling factor of ∆fr/fr. The interval of the XCOR signals is measured at about 5 ns, which corresponds to the repetition rate, and the time duration of the slow recovery region is 0.43 ns. Both sets of data were obtained at a repetition rate of 203.2 MHz and a repetition rate difference of 27 kHz. The time duration of the “fast recovery” region is ∼1 ps, considering a pulse duration of about 300 fs. This implies a limitation on fr of 1 THz, with ∆f determined tslip = ∆fr/fr2, resulting in ∆fr < 41 kHz when fr = 203.2 MHz, as per our experimental setup. Optimizing the repetition rate difference for the measurement precision, ∆fr is selected as 27 kHz.32 In contrast with fast recovery, the “slow recovery” region does not impose limitations on both fr and ∆fr because fast recovery also occurs within the duration of the slow recovery region. Despite the baseline of the XCOR signal decreasing due to insufficient gain to amplify the pulses and the steady-state of the gain not being reached when fast recovery emerges in the slow recovery region, XCOR signals can still be detected. In the simulation data, the envelope of the pulse train formed a valley similar to the gain dip from the gain dynamics. The duration of the XCOR signal was ∼15 ns, which is equivalent to 2 ps in the effective time domain scaled by the factor of ∆fr/fr. Similarly, the real XCOR data already extended with the scaling factor have temporal characteristics with a signal duration of 2.6 ps, almost equivalent to the simulation data, and a slope of falling edge of 9.5 mV/ps, which make the signal detectable.

There is another type of power amplifier such as an EDFA; however, this cannot be utilized as a cross-correlator for the distance measurement. While a SOA has a fast recovery of ∼1 ps and a slow recovery of ∼1 ns, which is able to be adopted as a cross-correlator, an EDFA has a significantly slower recovery time scale of 1∼100 µs.46,47 Therefore, it is practically impossible to use the EDFA as a fast cross-correlator for absolute distance measurement instead of SOA.

In this study, the signal laser emits an output power of 1.3 mW, while the local oscillator produces an output power of 1.2 mW. To compensate for the optical losses due to the round-trip path of the signal laser pulses to the target objects, the returning pulses are amplified to 1.2 mW. Upon combining the pulses from both lasers using an optical coupler, the integrated power was measured at 1 mW, accounting for the inner losses of the coupler. The input power to the SOA, resulting from the combination of the two laser pulses through the optical coupler, was set at 1 mW for distance measurement purposes. When an injection current of 170 mA was applied to the SOA, the output power reached 500 µW, and it increased to 700 µW with a current of 190 mA. For distance measurement, an injection current of 190 mA was utilized, resulting in a conversion efficiency of ∼70%, acting as an attenuator. The minimum input power incident to the SOA required for the detection of the XCOR signal was found to be 50 µW. In this scenario, the power from each laser entering the coupler was 50 µW. Interestingly, the SOA was capable of amplifying this low-power input to 100 µW with an injection current of 180 mA and 150 µW with 190 mA. This observation implies that the conversion efficiency of the SOA exceeded 100% at such low power levels. These findings indicate that, as long as the input power exceeds 50 µW, distance measurements can be reliably conducted, regardless of conversion efficiency. The discussion regarding the XCOR signals of low-power pulses and their measurement performance is presented in Sec. III B.

To present the detailed transient characteristics of the fast and slow recovery regions of the SOA, the XCOR signals are shown in Fig. 3 with different injection currents. The XCOR signal used here is attained from the signal laser, while the local oscillator is employed for inducing gain competition with the signal laser in SOA. The left panel shows a shorter temporal range of 1000 ns for the fast recovery region, while the right panel shows a longer range of 100 µs for the slow recovery region. When the injection current is lower than 130 mA, the XCOR signal cannot be detected. At an injection current of 130 mA, the XCOR signal measures with an amplitude of 30 mV, which increases to 100 mV at 150 mA. As the injection current increases, the strength of the XCOR dip drastically increases. The negative impact of the slow recovery region can be minimized at an injection current of 190 mA, which is close to SOA’s transparency current. When the injection current increases to around 190 mA, the SOA starts to function as an optical attenuator. With the current above 190 mA, the influence of the slow recovery region gets stronger, so XCOR signals start to be distorted, as demonstrated in Fig. 3 with an injection current of 270 mA. This phenomenon is because the local oscillator pulses take more energy from the SOA in the fast recovery region compared to other injection currents; consequently, the SOA’s gain becomes insufficient to amplify subsequent pulses from the signal laser. Nevertheless, it is still better to use higher injection currents when the input power to the SOA is very low because the overall signal intensity increases with a higher injection current. The pulse duration of XCOR signals is about 20 ns for injection currents between 170 and 270 mA. This duration is converted to 2.6 ps when the temporal scaling factor of ∆fr/fr is applied. The slow recovery region corresponds to 0.1–1 ns in the effective time domain, which can be minimized at the injection current of 190 mA. By considering these results, we selected than injection current of 190 mA in this study.

FIG. 3.

The changes of the XCOR signals along the injection current to the SOA from 130 to 270 mA showing the fast recovery region and the slow recovery region.

FIG. 3.

The changes of the XCOR signals along the injection current to the SOA from 130 to 270 mA showing the fast recovery region and the slow recovery region.

Close modal

Using an additional optical amplifier, such as an EDFA, the expansion of the measurement channels becomes possible, as the required power for splitting the laser output into multiple probes is fulfilled. Moreover, this method for high-efficiency XCOR only requires all the fiber components, such as couplers and BPFs; in other words, there are no bulk optics, such as lenses, half-wave plates, or bulk mounts, in the system. This feature makes it easy to build a system and measure the distance.

To determine the absolute distance through the time-of-flight signal, data processing is required, such as a timing-determination algorithm using second polynomial fitting or linear fitting of the rising edge. In the case of a SOA-based XCOR signal, a process for suppressing the slow recovery region is necessary because of its noisy behavior. Because the slow recovery region can reach the signal peak, it is an obstacle to measure the distance. Figure 4 shows the data processing procedure for determining the absolute distance between the raw and processed data. The raw data acquired from the oscilloscope (MSO8104, Rigol) included the signals of the reference and targets in the form of dips and slow recovery regions beside the signals. Its repeated cycle was 27 kHz, which is equal to the repetition rate difference and can be displayed in the time domain of microseconds. As the effective time domain is mainly of interest, the temporal expansion factor ∆fr/fr is used for multiplying with the real-time domain, and the series of signals is magnified to the nanosecond level. To suppress the slow recovery region in the data, the calculation of the correlation to the data was conducted using a function with a valley and peak, as shown in Fig. 4. The temporal duration of the correlation function was ∼8.5 ps, similar to the duration of the XCOR signal, and the ratio between the peaks and valleys was 1.2:1 for the peak-detection algorithm. Because the correlation calculation is used to extract the analogous portion between two functions, this procedure makes the XCOR signals clearer owing to their similarity with the peaks and valleys in the correlation function, while the slow recovery region is canceled out. The third graph in Fig. 4 shows the slow recovery region removed so that all signals in the data can be detected without disturbance from overshooting by the slow recovery region. After the correlation calculation, an algorithm for the timing determination of the signals is applied to measure the time-of-flight in the time domain between the reference and target signals. In this study, the peak detection from second polynomial fitting was used as the timing determination algorithm. This algorithm can be implemented using the library function in LabVIEW, and it is possible to select signals to be detected by adjusting the detection threshold. As the peak positions of the signals are specified using a peak detection algorithm, the absolute distance can be calculated as follows:
Di=mc2Nfr+c2NΔfrfrΔτi,
where m represents the ambiguity integer, c represents the speed of light, N represents the refractive index, ∆τ represents the time-of-flight between the reference and target signals, and i represents the index of the target. The resultant distance is the term with Δτi due to the NAR. If the target is located within the NAR (0.738 m in this case), m is zero. In the case of m > 0, which indicates that the distance is more than 0.738 m, the value of m can be determined by switching the repetition rate.28 Because it is possible to detect the peak positions of multiple signals, concurrent measurement of the absolute distances between multiple targets can be achieved. Using this data processing procedure, the absolute distance can be determined from the raw data acquired using an oscilloscope or digitizer without obstacles in the slow recovery region.
FIG. 4.

Data process procedure for determining the multiple absolute distance. The procedure includes temporal domain extension, correlation calculation, timing determination using the peak detection algorithm via second polynomial fitting, and distance calculation using the rime-of-flight. As the slow recovery region is similar to noise, it has to be suppressed with correlation calculations.

FIG. 4.

Data process procedure for determining the multiple absolute distance. The procedure includes temporal domain extension, correlation calculation, timing determination using the peak detection algorithm via second polynomial fitting, and distance calculation using the rime-of-flight. As the slow recovery region is similar to noise, it has to be suppressed with correlation calculations.

Close modal

When another target pulse arrives in this “fast recovery region” that was initiated by a previous target pulse, it poses a challenge. If these two pulses, which typically have optical pulse durations of 300–400 fs, are too close to each other in time, it is difficult to distinguish them. Therefore, the generated XCOR signals can be distorted in such cases, displaying two dips in a single XCOR signal. This region is named the “dead-zone” of the dual-comb range.28,48 On the contrary, when a pulse reaches the SOA within the “slow recovery region,” which corresponds to 0.1–1 ns, it can still be detected because the fast recovery of gain occurs, even if the SOA is in a state of slow recovery, which means that the dead zone does not occur in the slow recovery region. As the data process of correlation calculation effectively eliminates the negative impact of the slow recovery region, the dynamic range remains unrestricted.

For evaluating the performance of the absolute distance measurement using a SOA, the experiment for the linearity test and repeatability is demonstrated, and its scheme and results are shown in Fig. 5. The SOA-based absolute distance measurement system and conventional interferometer with targets on the granite motorized stage are used for the linearity test, as shown in Fig. 5(a), and the two beams from each system travel to the corresponding retroreflector as the targets. A partial mirror lies on the starting point of the linear stage for the reference signal of the absolute distance. Both the signal laser and local oscillator are stabilized by adjusting the cavity length with the PZT synchronized with a rubidium atomic clock, and its stability level is ∼0.8 mHz at the averaging time of 1 s, and the relative stability of the repetition rate is 10−12. After receiving the signal laser pulses from the reference mirror and target, the SOA occurs from the XCOR and the BPF before the photodetector screens the pulses from the local oscillator for detecting both the reference and target pulses. The low pass filter smoothens the XCOR data for the distance determination process. The test distance is 2.0 m, and the interval of step motion on the stage is 0.1 m. The result of the linearity test is shown in Fig. 5(b). Removing the cosine error, the slope between the interferometer data and the absolute distance is evaluated as 1.000 000 93, and the R-square value is 1, which is within the range of significant figures. Figure 5(c) shows the Allan deviation of the absolute distance measurement at 233 mm and the residual of the linearity test vs the interferometric displacement. The Allan deviation of the absolute distance at 233 mm is ∼4 µm at 37 µs (=27 kHz) and 120 nm at 5 ms. As the repeatability of the conventional dual-comb ranging with similar conditions of repetition rate, about 200 MHz, is ∼1.5 µm at the rate of 25 kHz,32 this difference is from the photon-electron phenomenon in the SOA, while the conventional method is based on the photon–photon interaction, which has the fastest response time. It also implies that the timing jitter of the comb itself does not affect the measurement performance due to its high repetition rate and the optimized repetition rate difference. The precision of single-shot measurement can be improved to the nanometer level by increasing the repetition rate of lasers with repetition rate multiplication.49 The residual is ∼750 nm for the general distance data and 5 µm for near 750 and 1500 mm data. As the NAR is 738 mm in this system that has the lasers with a repetition rate of 203.2 MHz, this discontinuity is because of the distortion on the XCOR signals by broadening the pulses using the photodetector’s slow response time, which overlaps each other. If the XCOR pulses consisting of the local oscillation are used instead of the signal laser, the tipping point in the residual can be resolved. Figure 5(d) shows the repeatability of the absolute distance along the measured data. The data from the single-shot measurement show that the repeatability is maintained between 4 and 5 µm and implies an increasing trend in the repeatability values. The repeatability of the averaging data with 10 points is in the range of 1–2 µm, and the sub-micrometer level is 0.5 µm for the 100-point averaging data. These results indicate that the SOA-based dual-comb ranging system has high linearity and repeatability, which are applicable to diverse engineering and scientific fields such as semiconductor manufacturing and the formation flying of satellites.

FIG. 5.

Experiment setup and results for the linearity test and repeatability. (a) The setup for performance evaluation of linearity and repeatability. (b) The result of the linearity test for the measured absolute distance along the displacement from the interferometer. (c) Allan deviation of the absolute distance measurement at 233 mm and residual from the linearity test. (d) Repeatability of absolute distance measurement along the measured distance.

FIG. 5.

Experiment setup and results for the linearity test and repeatability. (a) The setup for performance evaluation of linearity and repeatability. (b) The result of the linearity test for the measured absolute distance along the displacement from the interferometer. (c) Allan deviation of the absolute distance measurement at 233 mm and residual from the linearity test. (d) Repeatability of absolute distance measurement along the measured distance.

Close modal

To investigate how pulse power and chirp affect the precision of distance measurement, we conducted distance measurements under various conditions. As the pulses traverse free space during target measurement and pass through fiber components like optical band-pass filters and couplers, they are subject to chirp and power attenuation. The tunable optical band-pass filter (TBPF) was adjusted to create differences in the optical bandwidth of the lasers, simulating the effects of chirp on the pulses and extending their duration. The TBPF differentiated the bandwidth into 4, 3, and 2 nm with the change of the pulse duration of 240, 320, and 580 fs, as shown in Fig. 6(a), while also attenuating the pulse power to 1 mW, 600 µW, and 170 µW, respectively.

FIG. 6.

Distance measurement with different bandwidths of lasers for showing the chirp effect and with low-power returning pulses. (a) The optical spectrum of the signal laser and local oscillator with different bandwidths adjusted by a tunable band pass filter into 4, 3, and 2 nm. (b) The XCOR signals with the low-power pulse. (b-1) The XCOR signals with the injection current of 190 mA. It shows only the reference signals, not detecting target signals. (b-2) The XCOR signals with the injection current of 220 mA. In this case, both the reference and target signals appear due to the amplification of the SOA. (c) The result of the distance measurement with different conditions.

FIG. 6.

Distance measurement with different bandwidths of lasers for showing the chirp effect and with low-power returning pulses. (a) The optical spectrum of the signal laser and local oscillator with different bandwidths adjusted by a tunable band pass filter into 4, 3, and 2 nm. (b) The XCOR signals with the low-power pulse. (b-1) The XCOR signals with the injection current of 190 mA. It shows only the reference signals, not detecting target signals. (b-2) The XCOR signals with the injection current of 220 mA. In this case, both the reference and target signals appear due to the amplification of the SOA. (c) The result of the distance measurement with different conditions.

Close modal

Furthermore, we conducted distance measurements with a pulse power of 50 µW to confirm the repeatability of measurements at the lowest power levels. The corresponding cross-correlated signal, obtained through an oscilloscope, is presented in Fig. 6(b). In the case of the injection current of 190 mA, only the reference signals can be observed without the target signals, whereas the XCOR signals with the injection current of 220 mA in Fig. 6(b-2) show both the reference and target signals due to the amplification at the SOA. For the effective detection of low-power signals, it is recommended to employ a higher injection current for the SOA, typically around 220–240 mA, to ensure a sufficient intensity of the cross-correlation signal, as shown in Fig. 6(b-2). The experimental results for different power and bandwidth settings are presented in Fig. 6(c). Notably, the measured distance remained consistent at 151.72 mm for all settings, with a repeatability of 6.56 µm for a bandwidth of 4 nm and a power of 1.1 mW, 4.97 µm for 3 nm and 600 µW, 6.76 µm for 2 nm and 170 µW, and 6.68 µm for 4 nm and 50 µW.

It is important to mention that the measurement precision showed only a slight decline of ∼1.8% when the power was reduced to 50 µW and 3% when the bandwidth was shortened. These changes were negligible in terms of measurement performance, and the mean distance remained consistent at 151.72 mm for all settings. These results imply that the SOA-based laser ranging system is resilient to chirp, and its measurement performance remains robust even with decreasing power levels. Increasing the injection current allows for the detection of low-intensity signals.

The distance measurement of targets lying on two optical axes was conducted to demonstrate the ability to expand the measurement channels by the high-efficiency optical XCOR of the SOA, as shown in Fig. 7. To split the beam into two collimators, a 2 × 1 optical coupler is used, and the power of the beam after the coupler becomes 300 µW from 1 mW. The beam power also decreased by half after receiving the round-tripped pulse because of the coupler principle. One of the collimators had a fiber ferrule of FC/PC, which had an ∼8% Fresnel reflection on the tip of the ferrule. This Fresnel-reflected beam was used as the reference signal for the distance measurement of the first axis, as indicated in Reference 1 in Fig. 7. The other collimator was attached to the FC/APC for transmission to a partial mirror. The partial mirror mentioned in Reference 2 was used as the reference signal for the second measurement axis and fixed at the base of the stage. Two retroreflective mirrors are located on the moving stage as the targets, referred to as Target 1 and Target 2, respectively. The signal data of the two-axis distance measurement after the correlation processing are shown in Fig. 7(c). The distance between Reference 1 and Target 1 on the first axis was ∼657.8 mm, and the distance on the second axis was 173.2 mm. Distance signals such as Reference 1 or Target 2 are clear to be detected even when their power is low (∼100 µW). Using additional optical amplifiers, such as an EDFA, the measurement channels can be multiplied by up to 10 or 20. Based on these performances, the SOA-based absolute distance measurement system can be applied to diverse fields, such as machinery monitoring, wafer alignment, and satellite formation flying.

FIG. 7.

Distance measurement with measurement channels expansion. (a) The scheme for the distance measurement of the multiple targets. (b) The picture of the experimental setup. (c) Data of distance measurement signals with cross-correlation. This went through a data processing procedure for suppressing the effect of the slow recovery region.

FIG. 7.

Distance measurement with measurement channels expansion. (a) The scheme for the distance measurement of the multiple targets. (b) The picture of the experimental setup. (c) Data of distance measurement signals with cross-correlation. This went through a data processing procedure for suppressing the effect of the slow recovery region.

Close modal

Time-of-flight-based absolute laser ranging with highly efficient cross-correlation in a SOA was introduced to expand the measurement channels. This system can expand the measurement channels for multi-axis laser ranging because of its cross-correlation power efficiency, which only requires 50 µW for each laser beam. The repeatability of the distance measurement is 4 µm at a single shot (37 µs) and 120 nm for 5 ms. The linearity is also evaluated using an R-square equal to 1. These performances of the measurement system are maintained even if the pulses are chirped or their power is attenuated. Additionally, a two-axis distance measurement was performed to demonstrate the expansion of the measurement channels. This measurement system can be used to determine multiple distances, making it applicable to diverse fields such as semiconductor manufacturing, smart factories, plant engineering, and satellite formation flying.

This work was supported by the National Research Foundation of the Republic of Korea (Grant Nos. NRF-2020R1A2C2102338, NRF-2021R1A4A1031660, and NRF-2022M1A3C2069728), as well as the Ministry of SMEs and Startups (Grant No. RCMS-S3207602), the Commercialization Promotion Agency for R&D Outcomes (COMPA) (RS-2023-00260002) funded by the Ministry of Science and ICT (MSIT), and the KAIST UP Program.

The authors have no conflicts to disclose.

J.J. developed the experimental setup and laser sources, performed measurements, data analysis, and numerical simulation, and wrote the original draft. S.-W.K. supported the project management. Y.-J.K. developed ideas and led the project. All authors participated in the discussion and contributed to the article’s writing.

Jaeyoung Jang: Conceptualization (lead); Data curation (lead); Methodology (lead); Writing – original draft (lead). Seung-Woo Kim: Supervision (supporting). Young-Jin Kim: Funding acquisition (lead); Project administration (lead); Supervision (lead); Writing – review & editing (lead).

The data that support the findings of this study are available from the corresponding author upon reasonable request.

1.
T.
Udem
,
R.
Holzwarth
, and
T.
Hänsch
, “
Optical frequency metrology
,”
Nature
416
,
233
237
(
2002
).
2.
S. W.
Kim
, “
Combs rule
,”
Nat. Photonics
3
,
313
314
(
2009
).
3.
G.
Berkovic
and
E.
Shafir
, “
Optical methods for distance and displacement measurements
,”
Adv. Opt. Photonics
4
,
441
471
(
2012
).
4.
W.
Gao
,
S. W.
Kim
,
H.
Bosse
,
H.
Haitjema
,
Y. L.
Chen
,
X. D.
Lu
,
W.
Knapp
,
A.
Weckenmann
,
W. T.
Estler
, and
H.
Kunzmann
, “
Measurement technologies for precision positioning
,”
CIRP Ann.
64
(
2
),
773
(
2015
).
5.
K.
Minoshima
and
H.
Matsumoto
, “
High-accuracy measurement of 240-m distance in an optical tunnel by use of a compact femtosecond laser
,”
Appl. Opt.
39
,
5512
5517
(
2000
).
6.
N. R.
Doloca
,
K.
Meiners-Hagen
,
M.
Wedde
,
F.
Pollinger
, and
A.
Abou-Zeid
,
Meas. Sci. Technol.
21
,
115302
(
2010
).
7.
K.
Minoshima
, “
High-precision absolute length metrology using fiber-based optical frequency combs
,” in
2010 International Conference on Electromagnetics in Advanced Applications
(
IEEE
,
Sydney, NSW, Australia
,
2010
), pp.
800
802
.
8.
Y.-S.
Jang
,
K.
Lee
,
S.
Han
,
J.
Lee
,
Y.-J.
Kim
, and
S.-W.
Kim
, “
Absolute distance measurement with extension of nonambiguity range using the frequency comb of a femtosecond laser
,”
Opt. Eng.
53
(
12
),
122403
(
2014
).
9.
J.
Jin
,
Y.-J.
Kim
,
Y.
Kim
,
S.-W.
Kim
, and
C.-S.
Kang
, “
Absolute length calibration of gauge blocks using optical comb of a femtosecond pulse laser
,”
Opt. Express
14
,
5968
5974
(
2006
).
10.
N.
Schuhler
,
Y.
Salvadé
,
S.
Lévêque
,
R.
Dändliker
, and
R.
Holzwarth
, “
Frequency-comb-referenced two-wavelength source for absolute distance measurement
,”
Opt. Lett.
31
,
3101
3103
(
2006
).
11.
J.
Jin
,
Y.-J.
Kim
,
Y.
Kim
, and
S.-W.
Kim
, “
Absolute distance measurements using the optical comb of a femtosecond pulse laser
,”
Int. J. Prec. Eng. Manuf.
8
,
22
26
(
2007
).
12.
Y.
Salvadé
,
N.
Schuhler
,
S.
Lévêque
, and
S.
Le Floch
, “
High-accuracy absolute distance measurement using frequency comb referenced multiwavelength source
,”
Appl. Opt.
47
,
2715
2720
(
2008
).
13.
S.
Hyun
,
Y.-J.
Kim
,
Y.
Kim
,
J.
Jin
, and
S.-W.
Kim
, “
Absolute length measurement with the frequency comb of a femtosecond laser
,”
Meas. Sci. Technol.
20
,
095302
(
2009
).
14.
S.
Hyun
,
Y.-J.
Kim
,
Y.
Kim
, and
S.-W.
Kim
, “
Absolute distance measurement using the frequency comb of a femtosecond laser
,”
CIRP Ann.
59
(
1
),
555
(
2010
).
15.
G.
Wang
,
Y.-S.
Jang
,
S.
Hyun
,
B. J.
Chun
,
H. J.
Kang
,
S.
Yan
,
S.-W.
Kim
, and
Y.-J.
Kim
, “
Absolute positioning by multi-wavelength interferometry referenced to the frequency comb of a femtosecond laser
,”
Opt. Express
23
,
9121
9129
(
2015
).
16.
Ki-N.
Joo
and
S.-W.
Kim
, “
Absolute distance measurement by dispersive interferometry using a femtosecond pulse laser
,”
Opt. Express
14
,
5954
5960
(
2006
).
17.
Ki-N.
Joo
and
S.-W.
Kim
, “
Refractive index measurement by spectrally resolved interferometry using a femtosecond pulse laser
,”
Opt. Lett.
32
,
647
649
(
2007
).
18.
Ki-N.
Joo
,
Y.
Kim
, and
S.-W.
Kim
, “
Distance measurements by combined method based on a femtosecond pulse laser
,”
Opt. Express
16
,
19799
19806
(
2008
).
19.
M.
Cui
,
M. G.
Zeitouny
,
N.
Bhattacharya
,
S. A.
van den Berg
, and
H. P.
Urbach
, “
Long distance measurement with femtosecond pulses using a dispersive interferometer
,”
Opt. Express
19
,
6549
6562
(
2011
).
20.
S. A.
van den Berg
,
S. T.
Persijn
,
G. J. P.
Kok
,
M. G.
Zeitouny
, and
N.
Bhattacharya
, “
Many-wavelength interferometry with thousands of lasers for absolute distance measurement
,”
Phys. Rev. Lett.
108
,
183901
(
2012
).
21.
I.
Coddington
,
W.
Swann
,
L.
Nenadovic
, and
N. R.
Newbury
, “
Rapid and precise absolute distance measurements at long range
,”
Nat. Photonics
3
,
351
356
(
2009
).
22.
S.
Yokoyama
,
T.
Yokoyama
,
Y.
Hagihara
,
T.
Araki
, and
T.
Yasui
, “
A distance meter using a terahertz intermode beat in an optical frequency comb
,”
Opt. Express
17
,
17324
17337
(
2009
).
23.
M.
Godbout
,
J.-D.
Deschênes
, and
J.
Genest
, “
Spectrally resolved laser ranging with frequency combs
,”
Opt. Express
18
,
15981
15989
(
2010
).
24.
J.
Lee
,
S.
Han
,
K.
Lee
,
E.
Bae
,
S.
Kim
,
S.
Lee
,
S.-W.
Kim
, and
Y.-J.
Kim
, “
Absolute distance measurement by dual-comb interferometry with adjustable synthetic wavelength
,”
Meas. Sci. Technol.
24
,
045201
(
2013
).
25.
J.
Lee
,
Y. J.
Kim
,
K.
Lee
et al
, “
Time-of-flight measurement with femtosecond light pulses
,”
Nat. Photonics
4
,
716
720
(
2010
).
26.
T.-An
Liu
,
N. R.
Newbury
, and
I.
Coddington
, “
Sub-micron absolute distance measurements in sub-millisecond times with dual free-running femtosecond Er fiber-lasers
,”
Opt. Express
19
,
18501
18509
(
2011
).
27.
J.
Lee
,
K.
Lee
,
S.
Lee
,
S. W.
Kim
, and
Y. J.
Kim
, “
High precision laser ranging by time-of-flight measurement of femtosecond pulses
,”
Meas. Sci. Technol.
23
,
065203
(
2012
).
28.
H.
Zhang
,
H.
Wei
,
X.
Wu
,
H.
Yang
, and
Y.
Li
, “
Absolute distance measurement by dual-comb nonlinear asynchronous optical sampling
,”
Opt. Express
22
,
6597
6604
(
2014
).
29.
S.
Han
,
Y.-J.
Kim
, and
S.-W.
Kim
, “
Parallel determination of absolute distances to multiple targets by time-of-flight measurement using femtosecond light pulses
,”
Opt. Express
23
,
25874
25882
(
2015
).
30.
H.
Shi
,
Y.
Song
,
R.
Li
,
Y.
Li
,
H.
Cao
,
H.
Tian
,
B.
Liu
,
L.
Chai
, and
M.
Hu
, “
Review of low timing jitter mode-locked fiber lasers and applications in dual-comb absolute distance measurement
,”
Nanotechnol. Precis. Eng.
1
(
4
),
205
217
(
2018
).
31.
Z.
Zhu
and
G.
Wu
, “
Dual-comb ranging
,”
Engineering
4
(
6
),
772
(
2018
).
32.
W.
Kim
,
J.
Jang
,
S.
Han
,
S.
Kim
,
J. S.
Oh
,
B. S.
Kim
,
Y.-J.
Kim
, and
S.-W.
Kim
, “
Absolute laser ranging by time-of-flight measurement of ultrashort light pulses [invited]
,”
J. Opt. Soc. Am. A
37
,
B27
B35
(
2020
).
33.
D.
Hu
,
Z.
Wu
,
H.
Cao
,
Y.
Shi
,
R.
Li
,
H.
Tian
,
Y.
Song
, and
M.
Hu
, “
Dual-comb absolute distance measurement of non-cooperative targets with a single free-running mode-locked fiber laser
,”
Opt. Commun.
482
,
126566
(
2021
).
34.
H.
Wright
,
J.
Sun
,
D.
McKendrick
,
N.
Weston
, and
D. T.
Reid
, “
Two-photon dual-comb LiDAR
,”
Opt. Express
29
,
37037
37047
(
2021
).
35.
H.
Wright
,
A. J. M.
Nelmes
,
N. J.
Weston
, and
D. T.
Reid
, “
Multi-target two-photon dual-comb LiDAR
,”
Opt. Express
31
,
22497
22506
(
2023
).
36.
C.
Fridlund
, “
Darwin—The infrared space interferometry mission
,”
ESA Bull.
103
,
20
25
(
2000
).
37.
T.
Yao
,
A.
Duenner
, and
M.
Cullinan
, “
In-line dimensional metrology in nanomanufacturing systems enabled by a passive semiconductor wafer alignment mechanism
,”
J. Micro Nano-Manuf.
5
(
1
),
011001
(
2017
).
38.
J.
Mayr
,
J.
Jedrzejewski
,
E.
Uhlmann
,
M.
Alkan Donmez
,
W.
Knapp
,
F.
Härtig
,
K.
Wendt
,
T.
Moriwaki
,
P.
Shore
,
R.
Schmitt
,
C.
Brecher
,
T.
Würz
, and
K.
Wegener
, “
Thermal issues in machine tools
,”
CIRP Ann.
61
(
2
),
771
791
(
2012
).
39.
J.
Kim
,
J.
Chen
,
Z.
Zhang
,
F. N. C.
Wong
,
F. X.
Kärtner
,
F.
Loehl
, and
H.
Schlarb
, “
Long-term femtosecond timing link stabilization using a single-crystal balanced cross correlator
,”
Opt. Lett.
32
,
1044
1046
(
2007
).
40.
N. K.
Dutta
and
Q.
Wang
,
Semiconductor Optical Amplifiers
(
World Scientific Publishing Co. Pte. Ltd.
,
2006
), Chap. 6.
41.
X.
Zhao
,
Z.
Zheng
,
L.
Liu
,
Qi
Wang
,
H.
Chen
, and
J.
Liu
, “
Fast, long-scan-range pump-probe measurement based on asynchronous sampling using a dual-wavelength mode-locked fiber laser
,”
Opt. Express
20
,
25584
25589
(
2012
).
42.
H.
Jang
,
Y.-S.
Jang
,
S.
Kim
,
K.
Lee
,
S.
Han
,
Y.-J.
Kim
, and
S.-W.
Kim
, “
Polarization maintaining linear cavity Er-doped fiber femtosecond laser
,”
Laser Phys. Lett.
12
(
10
),
105102
(
2015
).
43.
A.
Mecozzi
and
J.
Mork
, “
Saturation effects in nondegenerate four-wave mixing between short optical pulses in semiconductor laser amplifiers
,”
IEEE J. Sel. Top. Quantum Electron.
3
(
5
),
1190
1207
(
1997
).
44.
A.
Mecozzi
and
J.
Mørk
, “
Saturation induced by picosecond pulses in semiconductor optical amplifiers
,”
J. Opt. Soc. Am. B
14
,
761
770
(
1997
).
45.
J. M.
Tang
and
K. A.
Shore
, “
Analysis of the characteristics of TOADs subject to frequency-detuned control and signal picosecond pulses
,”
IEEE J. Quantum Electron.
35
(
11
),
1704
1712
(
1999
).
46.
K. Y.
Ko
,
M. S.
Demokan
, and
H. Y.
Tam
, “
Transient analysis of erbium-doped fiber amplifiers
,”
IEEE Photonics Technol. Lett.
6
(
12
),
1436
1438
(
1994
).
47.
C.
Tian
and
S.
Kinoshita
, “
Analysis and control of transient dynamics of EDFA pumped by 1480- and 980-nm lasers
,”
J. Lightwave Technol.
21
(
8
),
1728
1734
(
2003
).
48.
R.
Liu
,
H.
Yu
,
Y.
Wang
,
Y.
Li
,
X.
Liu
,
P.
Zhang
,
Q.
Zhou
, and
K.
Ni
, “
Extending non-ambiguity range of dual-comb ranging for a mobile target based on FPGA
,”
Sensors
22
(
18
),
6830
(
2022
).
49.
J.
Lee
,
S.-W.
Kim
, and
Y.-J.
Kim
, “
Repetition rate multiplication of femtosecond light pulses using a phase-locked all-pass fiber resonator
,”
Opt. Express
23
,
10117
10125
(
2015
).