Multi-frequency differential absorption lidar incorporating a comb-referenced scanning laser for gas spectrum analysis

A multi-frequency differential absorption lidar incorporating a tunable laser and an optical frequency comb is demonstrated for precise spectrum analysis of atmospheric gas. The single frequency tunable laser is stabilized by locking to the optical frequency comb, with a standard deviation of 0.5 MHz. To achieve a high signal-to-noise ratio, a multi-mode superconducting nanowire single-photon detector with an active-area diameter of 50 μm, a quantum efficiency of 31.5%, and dark noise of 100 counts per second is implemented, which enables to avoid the need for high energy lasers. In the experiment, the range-resolved spectrum of atmospheric mixture gases (CO2 and HDO) in a region of 1572.2 1572.45 nm is obtained. Results show different partially overlapped absorption of two gases in different seasons, with a stronger influence of HDO on CO2 in summer than in winter. The interactions are taken into account by separating the mixture absorption spectrum (one CO2 line and two HDO lines) with triple-peak Voigt fitting. The retrieved concentrations over 6 km with a range resolution of 120 m and a time resolution of 10 min are compared with in-situ sensors. The uncertainties of the retrieved concentrations are as low as 6.5 μmol/mol (ppm) and 1×10−3 g/kg for CO2 and HDO, respectively. © 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement


Introduction
Long-lived greenhouse gases (GHGs) absorb the longwave radiation coming from the surface, affecting the radiation balance of the Earth [1]. Since the start of the industrial era, GHGs increases are greatly attributed to human activities [2]. Carbon dioxide (CO 2 ) and methane (CH 4 ) are the most potent GHGs after water vapor, such gases together with nitrous oxide (N 2 O) and ozone (O 3 ) related trace gases accumulate in the atmosphere thus warm the global climate, causing extreme events, glaciers melting and sea level rising [3]. It is extremely important to predict and determine the sources and sinks of these gases in the atmosphere [4,5]. In the past decades, passive and active methods have been used to track and quantify atmospheric transport and mixing of gases. The methods based on passive spectrometers [6,7] relying on sunlight are not applicable at night. While the light detection and range (lidar) is widely applied in atmospheric remote sensing for its active light source [8]. The most common differential absorption lidar (DIAL) and integrated path differential absorption (IPDA) lidar use two wavelengths. The offline wavelength is selected at a close-by region of the absorption line with negligible gas absorption, while the online wavelength is set close to a maximum of absorption [9]. These methods have been proposed to remotely sense the atmospheric gases in ground, airborne and space-borne platforms [9][10][11][12][13][14][15].
Gas absorption spectrum analysis is important for atmospheric chemistry and physics research, since spectrum results from not only gas concentration but also pressure and temperature of the atmosphere. Multi-frequency DIAL and IPDA [11,[16][17][18][19] are effective ways to obtain the broadband gas absorption spectrum for gas remote sensing. The reported light sources include multiple fixed-wavelength distributed-feedback laser diodes (DFB-LDs) [16], scanning DFB monitored by heterodyne detection [17], and injection-seeding optical parametric oscillator (OPO) [18]. With the development of frequency comb [20,21] with evenly-spaced optical modes, new opportunities are opened up for spectrum analysis methods and frequency locking systems. Dual-frequency combs have been field-deployed to monitor GHGs in open paths [22][23][24][25]. Meanwhile, a tunable laser can be locked to the comb with an absolute frequency through phase locking [26] and injection locking [27] system.
Here, an all-fiber multi-frequency DIAL incorporating a comb-referenced scanning laser is demonstrated to analyze the spectrum of CO 2 and HDO (isotopic water vapor) in the wavelength range of 1572. 22 -1572.45 nm. The optical frequency comb is contributed to realize frequency locking and mode-hop-free tuning of the tunable laser with a simple feedback loop, which restrains the frequency uncertainty (standard deviation) less than 0.5 MHz during 120 s integration time. The backscatter signal is detected by a multi-mode fiber (MMF) coupled superconducting nanowire single-photon detector (SNSPD), which provides high coupling efficiency. In the experiment, the mixed spectrum of one CO 2 line and two HDO lines are obtained by using a 400 ns pulse with energy of 40 µJ, where the range and time resolutions are 120 m and 10 min, respectively. The three absorption lines are separated by triple-peak Voigt fitting and the independent CO 2 spectra influenced by the concentration of HDO in dry (winter) and moist (summer) environments are analyzed. The lidar system has the potential to monitor GHGs in ground-based or flight-based platforms.
The paper is organized as follows. In Section 2, the optical layout and system parameters are introduced. Section 3 contains two subsections. In Subsection 3.1, the frequency tuning and locking method using comb-referenced subsystem is presented. In Subsection 3.2, the experiment of range-resolved spectrum analysis in different seasons is performed and the concentration results are discussed. A summary with conclusions is provided in Section 4.

System description
The optical layout of the system involves frequency locking channel, emission channel, and receiving channel, as shown in Fig. 1. In the frequency locking channel, a home-made frequency comb is used to calibrate the frequency of the external-cavity diode lasers (ECDL). The repetition frequency and the carrier-envelope offset frequency of the comb are f r = 100 MHz and f ceo = 20 MHz respectively. Both f r and f ceo are phase locked to a microwave rubidium clock. The signal of f r is mixed with a reference and the output of the mixer is feedback to a piezo-electric transducer (PZT) which changes the cavity length of the laser oscillator for tuning the repetition frequency. The frequency stability of f r measured as the Allan deviation reach 5×10 −12 and 8.5×10 −14 at an integration time of 1 s and 1000 s, respectively. The carrier-envelope offset frequency f ceo is generated from a nonlinear f −2f interferometer [28] with octave-spanning spectrum generation. The locking scheme for f ceo is the same as that for f r , except that the error signal is feedback to the current of the pump diode of the laser oscillator. The frequency stability of f ceo reaches 1.2×10 −9 and 2.4×10 −11 at an integration time of 1 s and 1000 s, respectively. The ECDL (Toptica CTL 1550) covering 1530 ∼ 1620 nm is served as a seed laser, and 1% part of the output light is combined with the comb to perform heterodyne detection. The beat frequency enters a balanced detector (BD) and is further filtered by a low pass filter (LPF) to restrain the beat frequency within 48 MHz. Then, the beat frequency is read by a frequency counter. By performing a feedback locking loop based on the beat frequency, the optical frequency of the seed laser can be locked to any preset value.
The emission channel utilizes the 99% part of the seed laser. The seed laser is chopped into a pulse train by using an acoustic optical modulator (AOM) with a pulse repetition of 20 kHz and a pulse width of 400 ns. Then the energy of laser pulse is amplified to 40 µJ by using an erbium-doped and ytterbium-doped fiber amplifier (EYDFA, Leisheng EYDFA) with an output fiber diameter of 20 µm and numerical aperture of 0.08. The amplified laser pulses are collimated and sent to the atmosphere through a collimator with a diameter of 100 mm and a divergence angle of 40 µrad. Then, the pulses with different wavelengths go through varying degrees of gas absorption, which is stronger near the line center and weaker along the two sides.
In the receiving channel, the backscatter signals from the atmosphere are coupled into MMF with a core diameter of 50 µm and numerical aperture of 0.22 through a telescope with a diameter of 256 mm and a field of view (FOV) of 90 µrad. A flattop filter (Optizone, MMF1572) centered at 1572.335 nm with bandwidth of ±0.15 nm and a peak transmission of 85% is mounted outside the Dewar of the SNSPD to suppress the solar background noise, so that daytime measurement can be realized. Considering the influence of the atmospheric turbulence, an SNSPD with large active diameter of 50 µm is manufactured instead of using the commercially available SNSPD coupled with single-mode fiber (active diameter of 9 µm) [29]. The SNSPD is operated in a 2.2-K compact Gifford-McMahon (G-M) cryocooler. To improve the maximum count rates of the detector, the large active area is divided into 9 pixels and each pixel consists of serially connected two superconducting nanowire avalanche photodetectors (SC-2SNAP) [30]. The SNSPD array is biased and read out by nine homemade electrical modules, the amplified output signals are fed to a multi-channel scaler. The measured total system detection efficiency of our SNSPD array is 31.5% at 1572 nm, and the system dark count rate (DCR) is 100 counts per second. Due to the multi-pixel layout and SC-2SNAP structure, the maximum count rate of the detector is above 30 MHz. Here, low DCR of the MMF coupled SNSPD is realized by using optical filter inside the G-M cryocooler [31], achieving a low noise equivalent power of about 5.7×10 −18 W/Hz 1/2 [32].
An overview of the system parameters compared to the reported works is given in Table 1. Usually, the injection-seed OPOs are used [9,18,33] to amplify the pulse energy to a certain value for high SNR, with a limited frequency tuning range of the laser. In this work, the pulse energy is amplified by an EYDFA conveniently. The multi-IPDA technique retrieves path integral gas concentration, which lacks range resolution. While the multi-DIAL technique retrieves range-resolved spectra along the optical path. Here, an optical frequency comb is used to stabilize the frequency of tunable laser with an improved frequency uncertainty. A multi-mode SNSPD with high quantum efficiency and lower dark noise is applied to achieve high SNR.  Figure 2 shows the principle of the frequency tuning and locking process. For atmospheric CO 2 spectrum scanning, the frequency span of the seed laser is adapted to its absorption cross-section in Fig. 2(a). The seed laser beats with an optical frequency comb with uniform spaced optical lines. As shown in Fig. 2(b), the beat frequency f b depends on the difference frequency between the seed laser and the nearest n th comb tooth, where the frequency is f n = n·f r + f ceo (n = 1, 2, 3. . . ). The corresponding specific optical frequency of the seed laser can be described as f e = f n ± f b , which is tuned by controlling its PZT. With the tuning of f e , the optical frequency increases with time and presents a slope in Fig. 2(c). Meanwhile, f b moves in the increasing and decreasing directions alternately, which is regarded as a triangular wave with a peak value of 50 MHz in Fig. 2(d). Once f e is tuned to a sampling value, a feedback loop is activated by comparing the current f b with a preset locking value. Then, PZT is back and forth controlled to prevent the current f b drift away from the preset value. In the locking process, both f e and f b keep stable, which present as flat steps in Figs. 2(c) and 2(d). The PZT of the seed laser will go through a sudden stop from the tuning process to the locking process during the spectrum scanning. Under the circumstance, an optical frequency drift is introduced by the inertial position drift of the PZT. To evaluate the frequency stability of the locking technique, the beat frequency drift with and without locking are compared from the end of a tuning process, as shown in Figs. 3(a) and 3(b), respectively. The unlocking one presents a rapid drift of 150 MHz that the frequency is no longer the value expected. After rapid drift, the beat frequency begins to drift slowly over time by approximately 40 MHz. The overall drift during 120 s is nearly 190 MHz. As for the locking one, the preset locking value of the initial beat frequency is 25 MHz. Then, the beat frequency at this moment is fed and controlled immediately. By using the locking mechanism mentioned above, the frequency drift is restrained. In the whole measured period, the statistical of the locked beat frequency is centered at 25 MHz with a standard deviation of 0.5 MHz. For a pressure broadened absorption spectrum, the stability of the locked frequency can meet the spectrum scanning requirement [35]. To evaluate the background and dark count rate, the raw backscatter signal in daytime and nighttime is shown in Fig. 4. The outgoing laser beam is pointed to a tall building at 6.4 km to block the laser, preventing the backscatter signal from overlapping with nearby pulses due to the pulse repetition of 20 kHz and ambiguous distance of 7.5 km. At daytime, the background noise is dominated by the solar radiation, whose count rate is over 30 kHz and depends on the weather condition. At nighttime, the bandpass filter is removed to reduce the insertion loss. The background noise mainly involves the SNSPD dark noise and the radiation from the neon lights of the city, with a total count rate of about 1 kHz. The spectra scanning in the atmosphere with and without frequency locking technique was performed at 22:00 local time on October 9, 2020. The experiment was measured horizontally at an altitude of 50 m on the roof of a building. The sampling number is set as 30, which is sufficient to cover the entire spectrum and takes appropriate processing time. The frequency spacing is non-uniform for sampling more points at the high slope of the spectrum and improve the detection sensitivity [11,36]. Both sampling number and sampling spacing are programmable for different sampling requirements. The locking time at each frequency is 16 s and the scanning time per step is 4 s, leading to a time resolution of 10 min. Figure 5(a) shows one of the backscatter signals at a distance over 6 km when the emitted frequencies are scanned in succession. The main source of random noise is shot noise. As Poisson shot noise is presumed and dominated in the detection, the SNR at each wavelength can be evaluated by the root-mean-square of photon counts. The absorption coefficient at the center frequency is greater than that at the wings and the absorption depth increases versus distance. The optical depth spectrum can be extracted from the backscatter signal. The pulse width is 400 ns that corresponds to a 60 m range resolution. To improve the SNR, an average of 120 m is performed. Figures 5(b) and 5(c) represent two experiment results of the optical depth spectra at 4 km (differential optical depth spectra from 3.94 to 4.06 km) with a range resolution of 120 m and a time resolution of 10 min. It shows that the unlocked spectrum fluctuates obviously while the locked spectrum remains robust. In comparison, the measured spectrum without locking will gradually deviate from the actual line shape due to the free drift of sampling frequencies over the scanning process. By performing a Voigt fitting, the spectrum area fitting errors of the two are 2.3% and 1.3%, respectively. The precision of CO 2 concentration relating to the spectrum area fitting error (see Eq. (3)) is improved by applying the locking technique.

Spectrum analysis in different seasons
According to lidar equation, the range resolved optical depth at range R can be calculated as [18] α(R, where Q is the photon counts of lidar signal, subscript i indicates different frequencies, Q0 is chosen as the offline point with α(R, f 30 ) = 0. R 1 and R 2 are two ranges before and after R, respectively. The range resolution is ∆R = R 2 -R 1 . The line shape of the optical depth can be represented as a Voigt function [37,38], which is expressed as where x = (4 ln 2) 1/2 (f − f 0 )/ω G and y = (ln 2) 1/2 ω L /ω G are given for simplicity. A is the Voigt area, f 0 is the center frequency, ω L is the Lorentzian full-width at half-maximum (FWHM), and ω G is the Gaussian FWHM. ω L and ω G are broadened due to the molecular interaction, which can be determined by ω L = 2Pγ 0 (T 0 /T) n air and ω G = f 0 (8kT ln 2/mc 2 ) 1/2 . Here, P is the gas pressure, γ 0 is the broadened Lorentzian half-width at half-maximum (HWHM) at 1 atm and T 0 = 296 K, and T is the measured temperature, n air is the temperature exponent for the air-broadened HWHM, k = 1.38 ×10 −23 J/K is Boltzmann constant, m is molecular mass, c = 2.998 ×10 8 m/s is the speed of light. Considering the mixture spectrum, a multi-peak Voigt fitting is performed [39]. The fitting model can be expressed as V = b 0 + V 1 +V 2 +V 3 +. . . , where b 0 is the baseline, V 1 , V 2 , and V 3 are Voigt line functions for different gases from Eq. (2). By calculating the Lorentzian and Gaussian FWHM, and relative spacing of the center frequencies of these lines, the calculated optical depths α(R, fi) are fitted to the multi-peak Voigt line model. Finally, the Voigt area and baseline can be retrieved. The area can also be expressed from Lambert-Beer's law as In this expression, S(T) is the line strength, N is the number density, ∆R is the length of a range cell. So that the concentration can be calculated from N using the ideal-gas equation. The R16 line of CO 2 has been widely used for atmospheric CO 2 measurement due to its high absorption strength and low temperature sensitivity. Table 2 illustrates the spectroscopic parameters of several gases located in the scanning range of 1572.2 -1572.45 nm. It shows that this R16 line mainly contains the absorption of three gases, namely CO 2 , H 2 O, and HDO. The line intensity S 0 in Table 2 is obtained from HITRAN 2016 [40], with its value multiplied by natural abundance. However, when considering the interaction of three gases, the value of S 0 should be corrected to S 0 ' according to natural abundance. After the correction, the S 0 ' of H 2 O is five orders of magnitude lower than that of CO 2 so that the interference can be almost neglected. But the line intensity of two HDO lines possess nearly the same order of magnitude with CO 2 , thus the interfering should be further discussed.  )): line intensity, multiplied by isotopologue abundance at 296 K; S' (cm −1 /(molec·cm −2 )): corrected line intensity; γ air (cm −1 ·atm −1 ): air-broadened Lorentzian half-width at half-maximum (HWHM) at 1 atm and 296 K; γ self (cm −1 ·atm −1 ): self-broadened HWHM at 1 atm pressure and 296 K; E'' (cm −1 ): lower state energy; n air : temperature exponent for the air-broadened HWHM.
The mixture spectra of CO 2 and HDO in two different atmospheric environments are simulated according to the Eq. (2) and the spectroscopic parameters in Table 2. One case is for relatively low absolute humidity of dry air while the other case is the reverse for moist air (H 2 O: 4 g/m 3 , CO 2 : 400 ppm for case 1 and H 2 O: 16 g/m 3 , CO 2 : 400 ppm for case 2). Figure 6 presents two simulated mixture models with a temperature of 296 K and a pressure of 1 atm. The models show that the mixture spectra are the superposition of three absorption lines. Under the circumstances, the line intensity of CO 2 is approximately 17 and 4.25 times stronger than that of HDO, respectively, with a deeper absorption depth in Fig. 6(b) than in Fig. 6(a). Thus different concentrations of HDO have different influences on the mixture absorption, which can roughly correspond to different seasons. Namely, the HDO mass per unit volume becomes less in winter with a minuscule effect on CO 2 measurement while a high content of HDO in summer presents a more obvious interaction. The spectra in different seasons are investigated to experimentally analyze the influence of HDO on independent CO 2 spectrum measurement. The experiments were performed on January 3, 2020 for the winter case and August 19, 2020 for the summer case, with the same sampling number and the spacing as Fig. 5. The absolute humidity of the two measurements are close to 3 g/m 3 and 20 g/m 3 for winter and summer measurements, provided by an in-situ sensor (Vaisala windcap WMT52). Figure 7 shows the measured optical depth spectra in two cases at 4 km with a range resolution of 120 m, respectively. Both results are consistent with the theoretical model. By applying a three-peak Voigt fitting, the CO 2 line and HDO lines can be separated. Here, the two HDO lines are fitted with a fixed ratio of the two peaks. In winter, the fitted CO 2 line is close to the mixture line in Fig. 7(a), thus the R16 line of CO 2 can be considered as minimal interference for CO 2 measurement. While in summer, the relatively high absorption of two HDO lines is shown in Fig. 7(b), with a non-negligible influence of HDO.  Figure 8 shows the measured concentrations of CO 2 and HDO from September 25 to September 26, 2020 over 6 km. For comparison purposes, gas concentrations from in-situ sensors are also plotted. In the experiment, two in-situ sensors (Thermo Scientific 410i and Vaisala windcap WMT52) were placed at 4 km in the optical path for CO 2 and H 2 O measurements, respectively. The concentration of H 2 O is converted into HDO by using the relative natural abundance in Table 2. The retrieved concentrations from lidar are based on the differential optical depth spectra from 3.94 to 4.06 km with time resolutions of 10 min and 30 min for CO 2 and HDO, respectively. And the comparisons of the retrievals and in-situ sensors measurements vs. time in Figs. 8(a) and The measurement precisions are 6.5 µmol/mol (ppm) and 1×10 −3 g/kg for CO 2 and HDO which are near 1.5% and 15% of the ambient levels, respectively. The low precision of HDO is due to its weak absorption and sparse sampling data.

Conclusion
We have demonstrated a wide-band gas analysis lidar incorporating a comb-referenced scanning laser for CO 2 spectrum scanning. The locking performance is evaluated, which effectively restrains the frequency drift of the laser with an uncertainty of 0.5 MHz. The atmospheric CO 2 spectrum scanning experiment is carried out with a range resolution of 120 m and a time resolution of 10 min. The interactions of CO 2 and HDO are investigated by measuring the R16 line of CO 2 in winter and summer, which is further corrected by triple-peak Voigt fitting. The concentration of CO 2 and HDO are retrieved with a measurement precision of 1.5% for CO 2 and 15% for HDO. Future studies of the improved system can be adapted to measurements of other gases, such as H 2 O, NH 3 , H 2 S, etc., whose absorption spectrum locates in the range of the tunable laser and the frequency comb. The promising applications of the system involve isotopic ratio measurement, gas monitoring, leakage warning and atmospheric composition, and plume emission of stacks.
Note that the atmospheric turbulence is usually an issue in measurement over long horizontal path, which degrades the spatial coherence of the propagating beam and affects the coupling efficiency of telescope from space to the fiber [41]. Here, the turbulence effect is suppressed by using the SNSPD with large active diameter of 50 µm [42,43]. In the near future, we plan to add a reference laser at offline wavelength using time-domain-multiplexing technique, emitting alternatively with the probe laser to compensate the signal fluctuation due to turbulence.
Funding. National Ten Thousand Talent Program.
Disclosures. The authors declare that there are no conflicts of interest related to this article. Data availability. Data underlying the results presented in this paper can be obtained from the authors upon reasonable request.