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Abstract
We present the development of a multi-spectral, integrated-path differential absorption (IPDA) lidar based on a dual-comb spectrometer for greenhouse gas monitoring. The system uses the lidar returns from topographic targets and does not require retroreflectors. The two frequency combs are generated by electro-optic modulation of a single continuous-wave laser diode. One of the combs is pulsed, amplified, and transmitted into the atmosphere, while the other acts as a local oscillator for coherent detection. We discuss the physical principles of the measurement, outline a performance model including speckle effects, and detail the fiber-based lidar architecture and signal processing. A maximum likelihood algorithm is used to estimate simultaneously the gas concentration and the central frequency of the comb, allowing the system to work without frequency locking. H2O (at 1544 nm) and CO2 (at 1572 nm) concentrations are monitored with a precision of 3% and 5%, respectively, using a non-cooperative target at 700 m. In addition, the measured water vapor concentrations are in excellent agreement with in-situ measurements obtained from nearby weather stations. To our knowledge, this is the first complete experimental demonstration and performance assessment of greenhouse gas monitoring with a dual-comb spectrometer using lidar echoes from topographic targets.
© 2024 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Differential absorption lidars (DIAL) have become an essential tool for environmental and atmospheric research, especially in the quest for more precise and robust remote sensing systems of greenhouse gases. When a DIAL system is used to measure the differential absorption of an atmospheric column by analyzing the backscattered signal from a distant hard target, the technique is referred to as integrated-path differential absorption (IPDA) lidar. Typically, in IPDA systems, two wavelengths are used to probe the atmosphere and estimate the average gas concentration. Yet having multiple differential absorption measurements at several wavelengths can help mitigate systematic errors in the gas concentration estimation and even provide additional information about the absorption line shape and the spatial distribution of the gas [1–4]. However, the precise knowledge and control of the emitted wavelengths can pose important technical challenges. In addition, minimizing the time delay between emitted frequencies becomes crucial for air or space-borne applications. Otherwise, the different wavelengths will be reflected by different surfaces on Earth, leading to inaccuracies in the estimated gas concentrations [5]. An additional advantage of using multiple wavelengths is a higher dynamic range in the gas measurement [6].
On the other hand, the possibility of probing gas absorption features with multiple evenly-spaced wavelengths has led to considerable interest in systems based on dual-comb spectroscopy (DCS) for remote sensing of atmospheric trace gases. When using a frequency comb emitter, all the wavelengths are sent and detected simultaneously, and their line spacing is precisely controlled. Previous works have demonstrated open-path DCS of atmospheric gases of interest using broad optical frequency combs generated by mode-locked lasers [7–10]. The technique has also been successfully implemented for multi-species gas fluxes quantification [11,12]. However, these studies used retro-reflectors placed at the end of the line-of-sight to reflect the signal back to the detector, resulting in high amplitude and speckle noise-free DCS signals with a large number of comb lines.
We aim to explore this technique for more operational scenarios from ground, air, or space-borne platforms; thus, the use of retro-reflectors must be discarded, and scattering effects from diffuse targets must be considered. DCS signals from long-distance topographic targets have very low amplitude and are affected by speckle noise. Nevertheless, by using electro-optic combs (EOC), the optical power can be concentrated in a small number of comb lines (less than 10) selected to cover the absorption feature of the target gas [13]. A previous preliminary study has reported on the deployment of an electro-optic dual-comb spectrometer for atmospheric $\text {CO}_2$ spectroscopy using natural targets [14]; however, due to various issues, gas concentration estimation was not performed in this work.
We present in this article the development of an IPDA lidar based on electro-optic DCS. Starting from the physical principles of the measurement, an inversion method based on the maximum likelihood (ML) theory is outlined and used to calculate the expected performances of the system. Subsequently, the lidar architecture is detailed, and the signal processing is explained. Finally, we present measurements of atmospheric $\text {H}_2\text {O}$ and $\text {CO}_2$ (non-simultaneous) around 1544 nm and 1572 nm, respectively, for a hard target located 700 m away from the emitter. Results are discussed and compared to the expected performances and to in-situ detectors for water vapor. As far as we know, this is the first complete experimental demonstration of dual-comb spectroscopy to monitor greenhouse gas concentrations using the lidar returns from topographic targets.
2. Measurement principle
2.1 Coherent IPDA lidars
IPDA lidars exploit the wavelength dependence of trace gas absorption. For an atmospheric column of length $l_c$, the optical depth associated with the gas of interest is given by
with $\bar {\text {X}}_{gas}$ the weighted average gas concentration in ppm and $\sigma _a$ the absorption cross section in $\text {ppm}^{-1}\text {m}^{-1}$. The integral in Eq. (1) is commonly referred to as the integrated weighting function (IWF) in units of $\text {ppm}^{-1}$ [15].By emitting two or more wavelengths and measuring its differential attenuation by the gas column, it is possible to estimate the average gas concentration by means of an inversion method [16]. Assuming that the laser beam impacts on a surface located at a distance $z$ and whose area is larger than the beam size, the optical power received by the detector is
Once the backscattered laser signal reaches the optical system, the subsequent step is to measure its power. Two detection schemes are possible: direct detection and coherent detection. Direct detection is usually preferred for DIAL lidars since coherent detection systems are limited by speckle noise [17]. Coherent detection, in contrast, allows for simultaneous wind and gas measurements that can be used to estimate gas fluxes [18–20]. Here, we will only consider the coherent configuration since it allows the detection of frequency combs.
In coherent detection, also known as heterodyne detection, the signal of interest is combined with a second optical signal called the local oscillator (LO). The two signals have a slight frequency difference $|f_0|$, achieved by frequency shifting. The combined signal is then directed to a photodetector, generating a beating of frequency $f_0$. The beating frequency typically lies in the radio frequency (RF) domain; thus, it can be easily digitized and processed. The power of the heterodyne current generated by a detector of responsivity $\mathcal {R}_{det}$ in coherent detection is
$\eta _{het}$ is called the heterodyne efficiency. It characterizes the quality of mixing between the lidar and the LO beams. The optical power of the LO, $P_{LO}$, being typically much higher than $P_{lid}$, serves as an amplifying term. An important quantity to evaluate the quality of a heterodyne signal affected by noise is the carrier-to-noise ratio (CNR). It is defined as with $i_{noise}^2$, the noise power. The angle brackets represent the expected value. Other than additive noise, the beat signal is also affected by speckle, which randomly modulates the amplitude of the heterodyne current and adds a random phase. It can be shown that, in the presence of speckle, the standard deviation of $i_{het}^2$ obeys [21]Equation (5) illustrates the limitation of coherent detection systems. The relative random error in the heterodyne current power has a threshold of 1. This means that even for a high $\text {CNR}$, the error of a single measurement cannot be further reduced. Accumulating statistically independent power measurements is the only way to improve the precision.
2.2 Electro-optic DCS for IPDA measurements
DCS can be implemented in two different architectures: the symmetric architecture (both combs probe the sample) and the asymmetric architecture (only one comb probes the sample) [22]. Since we aim to use lidar echo from diffuse hard targets, the asymmetric DCS configuration is to be privileged to reduce propagation and scattering losses [23]. In addition, incoherent averaging must be implemented since speckle noise prevents coherent averaging [24].
Thus, by means of the DCS technique, electro-optic combs can be used to conduct IPDA measurements in an entirely analogous manner to a coherent detection lidar. The difference is that instead of using a set of laser pulses of different wavelengths to probe the atmosphere, an EOC is used. Likewise, an EOC is used as a local oscillator instead of a single-wavelength LO. Therefore, our system can be regarded as a multi-heterodyne IPDA lidar with an EOC emitter or as an open-path electro-optic dual-comb spectrometer using topographic targets.
The electric field of an EOC can be written as [25]
The subindex $_x$ stands for $_{P}$ (probe comb) and $_{LO}$ (local oscillator). $\nu _{x, 0}$ is the central frequency of the EOC, and $f_{x, M}$ is its line spacing, given by the driving frequency of the electro-optic modulator. $E_{x, 0}$ is the field amplitude at the input of the modulator. We have considered only an odd number $N_l$ of comb lines. $n$ is referred to as the comb line index. $a_{x, n}$ and $\phi _{x, n}$ are, respectively, the amplitude and phase distributions of the EOC. When generating an EOC, the total output power $P_{x-out}^{tot}$ is distributed among the different comb lines according to the coefficients $a_{x, n}$. Thus, the output power of the $n$-th comb line is given by $P_{x-out}(\nu _{x, n})=a_{x, n}^2 P_{x-out}^{tot}$. For EOCs generated by pure phase modulation, which will be our case, $a_{x, n}=J_{n}(m_x)$, with $J_n$ the $n$-th order Bessel function and $m_x$ the modulation index.
After recombination of the lidar signal with the local oscillator, we obtain a multi-heterodyne signal $i_m$, which can be expressed as the sum of the individual beatings, i.e., $i_m=\sum _n i_{m, n}$. We assume that $i_m$ is composed only of the useful DCS signal and that higher-order beatings are filtered [26]. In the RF domain, the measurement signal corresponds to an $N_l$-line comb, centered at $|\nu _{P, 0}-\nu _{LO, 0}|$ with a line spacing of $|f_{P, M}-f_{LO, M}|$, and that contains the absorption signature of the gas.
A reference dual-comb signal must be produced as well in order to normalize the measurement spectrum [22]. This reference signal is simply the beating of the probe comb (before interacting with the sample) with the LO comb, which can also be written as a sum, i.e., $i_{ref}=\sum _n i_{ref, n}$ . In the same way, the reference beat signal corresponds to an $N_l$-line RF comb.
The power of the individual beatings of the measurement and the reference signals can be expressed, respectively, as
$C$ is a scaling coefficient that accounts for the power in the reference interferometer relative to the output power in the measurement interferometer.
The measured total optical depth (including the lidar losses) at the probe frequencies, $\nu _{P, n}=\nu _{P, 0}+n f_{P, M}$, can be calculated from the power ratio of the heterodyne beatings as
The hat symbol represents an estimated quantity. In this study, the power of the heterodyne signals will be estimated from the power spectra in the frequency domain, as will be explained in section 3.3. From Eq. (5), it follows that the variance of a single optical depth measurement is [16]
where $\text {CNR}_{m, n}$ is the carrier-to-noise ratio of the $n$-th comb line of the measurement signal. The error contribution of the reference interferometer can be neglected, given that it is not affected by speckle or propagation losses.2.3 Inversion method
The total optical depth in Eq. (8) is related to the weighted average gas concentration $\bar {\text {X}}_{gas}$ by
where $L$ is a scalar parameter that accounts for the wavelength-independent losses between the measurement interferometer with respect to the reference interferometer. It should be noted that the IWF is evaluated at the probe frequencies $\nu _{P, n}$. Assuming that the modulation frequency $f_{P, M}$ remains stable so that the comb line spacing is constant, then by determining the central frequency $\nu _{P, 0}$, all the comb frequencies can be known. $L$ is considered as unknown since it is affected by uncontrolled and potentially time-varying parameters as $\rho$ or $T_{atm}^2$ (see Eq. (2)).Equation (10) can be inverted in order to estimate the three unknown parameters: $\bar {\text {X}}_{gas}$, $\nu _{P, 0}$, and $L$. In principle, as long as the number of comb lines $N_l \geq 3$, we can solve the inversion problem. It should be noted that only the value of the detuning relative to the center of the absorption line is needed to solve the inversion problem rather than the absolute central frequency. We will then refer to $\nu _{P, 0}$ interchangeably as the central frequency or the comb detuning. In traditional dual-wavelength IPDA systems, estimating the detuning of the lasers is not possible, and locking to a frequency reference must be done. The use of multiple wavelengths removes the need for absolute frequency control [27,28].
Different inversion techniques can be implemented in order to estimate the unknown parameters [4]. For this study, the maximum likelihood (ML) method will be used. The measured optical depth in Eq. (10) is a function of two linear parameters, $\bar {\text {X}}_{gas}$ and $L$, and one non-linear parameter, $\nu _{P, 0}$. It can be rewritten in matrix form as $\hat {\boldsymbol {\tau }}=\textbf {R}(\nu _{P, 0})\, \boldsymbol {\theta }$. Where $\hat {\boldsymbol {\tau }}$ is a column vector containing the measured optical depth and $\boldsymbol {\theta }=(\bar {\text {X}}_{gas}, \: L)^\top$ contains the unknown linear parameters. $\textbf {R}(\nu _{P, 0})=(\textbf {IWF}(\nu _{P, 0})\: \boldsymbol {1})$, where $\textbf {IWF}$ is a column vector containing the integrated weighting function at the probe frequencies, and $\boldsymbol {1}$ is a column vector of ones.
Using the ML formalism, we can solve for $\boldsymbol {\theta }(\nu _{P, 0})$ as a function of the non-linear parameter. Then, a least squares optimization of the likelihood function provides an estimation $\hat {\nu }_{P, 0}$ of the non-linear parameter, which can then be used to obtain the estimate $\boldsymbol {\hat {\theta }}$ of the linear parameters.
The ML method provides a theoretical expression for the covariance matrix of the linear parameters. If we assume that the CNR of the different comb lines in the measurement interferometer is approximately the same, i.e., $\text {CNR}_{m, n} \approx \overline {\text {CNR}}$, then the error in the optical depth (see Eq. (9)) is the same for all the comb lines. This can be achieved by optimizing the power distributions of the EOCs. In this case, the covariance matrix of the linear parameters can be simplified [29] to
The first element of the covariance matrix in Eq. (11) gives the variance of the gas concentration estimate. For this analysis, we have neglected the error contribution of the reference signal and assumed that the speckle affecting the different comb lines is completely uncorrelated, which is the anticipated scenario for an atmospheric lidar using topographic targets [30]. Note that the error in the gas concentration estimate also has a threshold given by speckle noise that can only be overcome by averaging an increasing number $N_s$ of independent measurements. For $\overline {\text {CNR}}<1$, additive noise becomes dominant.
3. Lidar design
3.1 Lidar architecture
A DCS-based IPDA lidar has been developed according to the architecture shown in Fig. 1(a). The output (around 15 mW) of a tunable fiber-coupled laser diode (LD) is split into two arms. The probe and LO combs are generated using a pair of phase modulators (PM) with a $\text {V}_{\pi }$ of 5 V and a bandwidth of 10 GHz. A 40 MHz acousto-optic modulator (AOM) is used to frequency shift the probe comb and to generate a pulse which is subsequently amplified by an Erbium-doped fiber amplifier (EDFA). A nearly Gaussian output pulse shape is obtained by optimizing the electric signal applied to the AOM. All the fiber components are polarization-maintaining. The output of the amplifier is collimated, sent to a polarization beam splitter (PBS), and expanded using a Keplerian telescope. At the output of the telescope, we obtain a collimated beam of 56 mm in diameter (1/$e^2$).
Fig. 1. (a) Lidar architecture. LD, laser diode; PM, phase modulator; AOM, acousto-optic modulator; EDFA, Erbium-doped fiber amplifier; PBS, polarization beam splitter; QWP, quarter-wave plate; PD, photodetector; ADC, analog-to-digital converter. (b) Photo of the experimental setup.
A quarter-wave plate (QWP) is inserted between the telescope lenses in order to separate the emitted beam from the received lidar return at the level of the PBS. The lidar echo is recombined with the LO EOC in a balanced photodetector (PD) to obtain the measurement RF comb. The optical leak of the PBS is collected in a polarization-maintaining fiber, attenuated, and recombined with the LO comb in a second balanced PD to produce the reference RF comb. For both detectors, the noise equivalent power (NEP) is 9 pW/$\sqrt {\text {Hz}}$. Signals are further digitized at a sample rate of 156 MHz and processed.
The lidar prototype allows for non-simultaneous measurement of atmospheric $\text {CO}_2$ and $\text {H}_2\text {O}$. Indeed, most of the fiber components can be utilized in the C and L bands except for the laser diode and the laser amplifier. The latter, having a limited spectral coverage (in the order of 1 nm), must be selected to match the absorption feature of the target gas. Two lidar configurations (using different EDFAs) targeting $\text {H}_2\text {O}$ at 1544 nm and $\text {CO}_2$ at 1572 nm were implemented. Table 1 summarizes the lidar parameters for both configurations.
Table 1. Lidar parameters for the non-simultaneous measurement of atmospheric $\text {H}_2\text {O}$ and $\text {CO}_2$. PRF, pulse repetition frequency.
The number of comb lines is fixed according to the available laser power by adjusting the modulation indices. The line spacing is selected to provide a spectral coverage of approximately 5 GHz, which corresponds to the full-width half maximum (FWHM) of the absorption line. The RF line spacing and the AOM frequency are selected to keep the DCS signal far from low-frequency noise and below the Nyquist frequency. The LO power reaching the detector PD-1 in both configurations is about 0.5 mW. A pulse length of around 1 $\mu$s allows resolving the RF comb structure and distinguishing the lidar returns from parasitic reflections from the optics for targets located beyond 150 m, as will be discussed in section 3.3. The collimated beam diameter ensures eye-safe operation even for the highest energy configuration. The results of the measurement campaigns are given in section 4.
It is worth noting that the lidar enables the emission and identification of 5 (or even more) wavelengths in a single 1 $\mu$s pulse, which is considerably faster than other IPDA lidar approaches where the different wavelengths are sent and detected one after the other over time with a typical frequency of 10 kHz [3,5].
3.2 Expected performances
Since in coherent detection, speckle fixes a threshold for the measurement error, an optimum IPDA lidar system should be limited by speckle. This can be achieved if the mean carrier-to-noise ratio $\overline {\text {CNR}}$ is larger than 1. On the other hand, in coherent lidars, the noise level is mainly determined by the LO shot noise [17]. In that case, $\overline {\text {CNR}}=\mathcal {R}_{det} \eta _{het} P_{lid}/(e B_W N_l^2)$, with $e$ the elementary charge and $B_W$ the electrical bandwidth. Note that when increasing the number of comb lines, $\overline {\text {CNR}}$ decreases according to $N_l^{-2}$ since the lidar and LO powers per line are divided by $N_l$, while the shot noise stays the same.
Figure 2(a) presents the expected mean CNR as a function of the distance to the hard target for the measurement of atmospheric $\text {CO}_2$ at 1572.02 nm. We consider normal incidence on a surface of albedo 0.1, a peak power at the output of the amplifier of 20 W, and a moderate value for the heterodyne efficiency of 5% to account for the reduced beam quality ($\text {M}^2\approx 1.5$) and turbulence effects [31]. The diameter of the receiver telescope is assumed to be 76 mm, and the one-way transmission of the whole optical system ($T_{opt}$) is fixed to 0.75. Only the contribution of shot noise of the LO is considered in a bandwidth of 2.5 MHz, which corresponds to about twice the FWHM of the individual RF comb lines. We assume a typical urban extinction coefficient of 0.1/km at 1550 nm [32]. Due to $\text {CO}_2$ absorption and aerosol scattering, the expected mean CNR slightly deviates from the $z^{-2}$ trend. However, for distances below 1 km, this effect is negligible. The shaded area represents the mean CNR range for which speckle is the dominant noise. Note that for the same total power, the maximum distance for which the measurement is still speckle-limited depends on the number of comb lines.
Fig. 2. (a) Expected mean CNR as a function of the target distance for a total output peak power of 20 W with a different number of comb lines. In the gray zone, the measurement is limited by speckle noise. (b) Relative random error in the $\text {CO}_2$ concentration as a function of the number of averages for the ideal speckle-limited case and a hard target located 700 m away. The slopes of the lines are -1/2 in log-log scale.
In order to improve the measurement precision, different measurements with statistically independent speckle noise must be averaged [17]. Figure 2(b) presents the expected relative random error in the ideal speckle-limited case for a 700 m atmospheric $\text {CO}_2$ column as a function of the number of averages, calculated by means of Eq. (11). Increasing the number of comb lines improves the measurement precision as long as the measurement remains limited by speckle. According to Fig. 2(b), for a 3-line comb probing an atmospheric column of 700 m, we expect a random error of 3.5% after averaging $10^6$ measurements. This represents 50 s of measurement at a rate of 20 kHz. For a 7-line comb, this error would be 1.5%, i.e., 6 ppm. A trade-off between the number of comb lines and the mean CNR must be found. Ideally, for a given target distance, the number of lines should be increased to the point where the measurement is still speckle-limited.
On the other hand, systematic errors in the measurement arise from poor knowledge of certain quantities involved in estimating the gas concentration. In particular, the accuracy of the gas concentration measurement relies on an accurate model of the absorption line shape, which can vary with atmospheric temperature and pressure. The spectral resolution provided by a dual-comb system could allow, in principle, to invert additional parameters, such as atmospheric temperature or pressure [10]. Additionally, if the comb probes multiple absorption lines of various gases, it is possible to identify the absorption of different species and eliminate cross-talks [12]. However, these potential advantages will not be assessed in this work.
Limited knowledge of the path length, $l_c$, can bias the gas concentration measurement or increase the random error, as seen from Eq. (1). The lidar presented in section 3.1 works in a pulsed mode that allows simultaneous differential optical depth and time-of-flight measurements. For the measurement campaigns presented below, we assume that the path length is not modified during the experiment and average over a large number of pulses to obtain a precise time-of-flight measurement. However, in scenarios of varying path length, a fast, accurate, and precise time of flight measurement is required [3].
3.3 Signal processing
Figure 3(a, b) presents the distance spectrogram of the measurement and reference channels for a water vapor measurement using a 5-line comb and a hard target located 700 m away from the emitter. The detail of the measurement campaign is given in section 4. Signal processing involves splitting the time signals into overlapping range gates of 1.6 $\mu$s. Hamming windowing and zero-padding are applied, followed by a 2048-point Fast Fourier Transform to obtain power spectra. With a 98% overlap factor, we locate the hard target range gate (yellow box in Fig. 3(a)), and then average the power spectra at this single range gate. We also select a range gate after the lidar echo (gray box in Fig. 3(a)), whose power spectrum is averaged and subtracted from the measurement power spectrum in order to remove the integrated noise level. This processing method corresponds to the squarer estimator [33] applied to multi-heterodyne lidar returns. Note that a different detector must be utilized for the reference signal since parasitic reflections generate a signal echo at 0 m in the measurement channel, which can be appreciated in Fig. 3(a).
Fig. 3. (a) Distance spectrogram of the measurement channel. A lidar echo is observed for a target at 700 m. (b) Distance spectrogram of the reference channel. (c) Power spectra of the measurement and reference channels after processing and averaging $1.5 \times 10^5$ pulses.
The length of the lidar echo in Fig. 3(a) is given by the pulse length (see Table 1), i.e., around 250 m in distance. For the reference channel, signal processing is entirely analogous. In this case, the range gate of interest is located at 0 m (red box in Fig. 3(b)) since it corresponds to the optical leaking of the PBS. Figure 3(c) presents the measurement and reference RF combs after processing $1.5 \times 10^5$ spectra. The total optical depth is obtained from the power ratio between the measurement RF comb and the reference RF comb, as stated in Eq. (8).
4. IPDA measurements of atmospheric $\text {H}_2\text {O}$ and $\text {CO}_2$
The lidar system presented above was installed on the roof of the ONERA site in the south of Toulouse, as depicted in Fig. 4. We chose as a hard target a small forest located 700 m away from the emitter. Thanks to the wind, leaves in the trees move continuously, favoring speckle renewal during the experiment. We conducted different measurement campaigns targeting $\text {H}_2\text {O}$ at 1544.25 nm and $\text {CO}_2$ at 1572.02 nm from April to July 2023. The lidar parameters for both measurement configurations are presented in Table 1.
Fig. 4. Satellite picture indicating the location of the lidar at ONERA in the south of Toulouse, the hard target located 700 m away, and the location of two nearby weather stations (WS). Credit: © Google Images 2023. A photo of the lidar line of sight is also shown.
4.1 Water vapor
The water vapor absorption line at 1544.25 nm was selected because commercial high-gain EDFAs are available at this wavelength. The amplifier used in the setup delivered an output peak power of 125 W. We generated approximately flat RF combs with only 5 lines (as shown in Fig. 3(c)) to ensure a speckle-limited measurement. This was achieved by setting the modulation indices to $m_P=1.7$ and $m_{LO}=3.2$. Since the target was located 700 m from the emitter, the effect of gas absorption on the CNR can be neglected. Therefore, we can use Fig. 2(a) to compute the expected mean CNR for a 5-line comb and an output peak power of 125 W. We obtain an expected $\overline {\text {CNR}}$ over 20 (6 times the mean CNR for 20 W).
Experimentally, a mean CNR of around 5 was observed, as can be seen with the color bar in Fig. 3(a). This confirms that the measurement was speckle-limited as planned. However, the experimental CNR was about 4 times less than expected. This discrepancy can be attributed to multiple factors, namely, an arbitrary angle of incidence, depolarization, and non-Lambertian behavior of the tree leaves. Additionally, in practice only 70% of the noise level arose from shot noise, while the remaining 30% resulted from detector noise.
Figure 5(a) presents the absorption spectrum of water vapor around 1544 nm that was used for the inversion of the IPDA measurements (blue dots). We observe an excellent agreement between the line shape obtained with HITRAN-2023 and the lidar measurement after processing $1.5 \times 10^5$ spectra. Thanks to the multi-parameter inversion, the detuning of the probe comb could be determined with a precision of about 50 MHz without frequency locking of the laser. Additionally, to identify any instrumental systematic error, we conducted an IPDA measurement outside the absorption line around 1544.76 nm (red dots), where no absorption of water vapor or other atmospheric gases is expected. Applying the same processing procedure, it was possible to measure a 5-line absorption spectrum flat up to 0.1%. This value is in very good agreement with the expected standard deviation given by Eq. (9), suggesting that systematic wavelength-dependent responses in the lidar are negligible with respect to random error.
Fig. 5. (a) Absorption spectrum of water vapor and lidar measurement on the absorption line and outside of the absorption line. The inset figure presents a zoom of the fit and the residuals. The error bars indicate the standard deviation in the measured optical depth. (b) Average water vapor concentration as a function of time for two measurement campaigns. The shaded areas represent the range of values comprised between the two weather station (WS) measurements.
On the other hand, the selected absorption line depth was found to be highly dependent on temperature, so continuous temperature monitoring was done. The temperature data was obtained from the open network $\textit {Weather Underground}$ [34]. In addition to the temperature, the network provides relative humidity measurements that were used to compute the in-situ water vapor concentration at two locations near the lidar line of sight, as depicted in Fig. 4. The weather station values were compared to the lidar measurements. Note that a direct comparison between the in-situ $\text {H}_2\text {O}$ concentrations and the lidar weighted average gas concentrations is possible because the lidar line of sight is horizontal, and the target range is limited to 700 m. This leads to an approximately constant absorption cross-section along the optical path, allowing us to associate the weighted average concentration in Eq. (1) with the average gas concentration. For longer ranges, temperature variations along the optical path might modify the absorption cross-section, thereby impacting the weighted average concentration.
Results for two measurement campaigns, conducted in significantly different humidity conditions, are shown in Fig. 5(b). Each lidar measurement represents an average over $1.5 \times 10^5$ pulses, for an effective measurement time (calculated as the ratio between the number of processed pulses and the PRF) of 15 s. The precision of each measurement was calculated by splitting the set of $1.5 \times 10^5$ averaged spectra into subgroups, applying the inversion method for each of the subgroups, and computing the standard deviation (divided by the square root of the number of subgroups) of the estimated gas concentrations. We obtained an average relative standard deviation of around 3% for the campaign with higher concentrations and 5% for the campaign with lower concentrations. The water vapor lidar measurements are in very good agreement with the concentrations obtained from the weather stations. For most of the lidar measurements, the value of the water vapor concentration lies between the values provided by the two weather stations. The maximum discrepancy between the lidar and the stations is around 5%, comparable to the mean discrepancy between the two weather stations. This difference can be attributed to spatial variations in the water vapor contents. Unfortunately, the uncertainty in the temperature and relative humidity is not provided by the weather network.
4.2 Carbon dioxide
The lidar system described in section 3.1 was modified for measuring atmospheric $\text {CO}_2$ at 1572 nm. This involved replacing the laser diode and the fiber amplifier. Due to a lower gain of Erbium at this wavelength, a continuous-wave amplifier was added at the input of the pulsed amplifier. A total peak power of 20 W was obtained at the output of the whole amplification chain. Due to the lower energy, the number of comb lines was reduced to 3 by setting the modulation indices to $m_P=0.9$ and $m_{LO}=1.9$ in order to improve the mean CNR. An experimental mean CNR of around 4 (less than half of what was expected according to Fig. 2(a)) was obtained for the same target 700 m away. On the other hand, since the absorption depth of $\text {CO}_2$ at 1572.02 nm is about half that of $\text {H}_2\text {O}$ at 1544.25 nm, the measurement random error is expected to be higher for the same number of averages. Figure 6(a) shows the absorption spectrum of carbon dioxide around 1572 nm, as well as an IPDA measurement on the absorption line (blue dots) and outside the absorption line (red dots) after processing $1.2\times 10^6$ spectra. As for the water vapor, we were capable of measuring a flat transmission spectrum better than 0.1%, but with only 3 comb lines.
Fig. 6. (a) $\text {CO}_2$ absorption spectrum and IPDA measurement. A measurement outside the absorption line is also presented. (b) Close-up of the IPDA measurement and residuals. The error bars represent the standard deviation of the measured optical depth. (c) Average carbon dioxide concentration as a function of time for two measurement campaigns. The inset figure shows the measured concentration outside the absorption line.
Figure 6(c) presents the average $\text {CO}_2$ concentration during two measurement campaigns. Each point corresponds to an average of $1.2\times 10^6$ pulses, i.e., an effective measurement time of 60 s. For both measurement campaigns, an average precision of around 5% (20 ppm) was obtained, which is over 1% higher than expected for a speckle-limited 3-line system (see Fig. 2(b)). This discrepancy arises because the shot noise error contribution is not entirely negligible. For some measurements, the relative standard deviation exceeded 5%. This can be explained by the fact that, due to the large amount of data, pulses were not acquired continuously but in subgroups; which resulted in a total measurement time of about 30 minutes (including data transfer and storage time) for each point. Thus, during this total measurement time, local $\text {CO}_2$ concentrations can vary, increasing the standard deviation of the measurement. To illustrate the stability of the instrument, we measured the transmission profile outside the absorption line during 2 h; the inverted profiles were centered around 0 ppm with a standard deviation of about 20 ppm, as shown in Fig. 6(c)-inset.
We did not have any in-situ instrument to compare our results with. However, data can be interpreted in terms of atmospheric dynamics. For both measurement campaigns, we observed a slow decrease in the $\text {CO}_2$ concentrations from more than 480 ppm to about 420 ppm. This can be attributed to a rise in the altitude of the boundary layer due to important temperature increases in the summer mornings. Indeed, a temperature increment of about $10^{\circ }$C was observed from the weather stations during both measurement campaigns. Similar trends were reported in Paris (France) and the Jiangsu province (China) in peri-urban areas, as is the case for our experiment [19,35]. The observed gradient was more pronounced for the campaign conducted on July 7 since the measurement campaign started earlier. More data would be required to establish a trend in the $\text {CO}_2$ concentrations in this zone of Toulouse. However, these experiments demonstrate the capability of the lidar system to monitor greenhouse gases using the lidar returns from non-cooperative targets.
5. Conclusion and perspectives
We presented the development of a greenhouse gas IPDA lidar based on a dual-comb spectrometer. Frequency combs were generated by phase modulation of a laser diode. Energies of 100 $\mu$J at 1544 nm for water vapor sensing and 20 $\mu$J at 1572 nm for carbon dioxide were obtained using commercial pulsed EDFAs. Non-simultaneous IPDA measurements of atmospheric $\text {H}_2\text {O}$ and $\text {CO}_2$ were conducted using 5-line and 3-line combs, respectively. A performance assessment of the system was presented and compared to experimental results. A precision of 3% (15 s of measurement) was achieved for $\text {H}_2\text {O}$ and 5% for $\text {CO}_2$ (60 s of measurement). The measurement precision was slightly worse than that expected for an ideal speckle-limited scenario due to an experimental carrier-to-noise ratio smaller than anticipated.
Perspectives for this work include generalizing the inversion method in order to infer additional parameters, such as the atmospheric temperature. In principle, this can be achieved if the number of comb lines is larger than the number of unknown parameters. By increasing the laser power, it would be possible to probe longer atmospheric columns and even conduct simultaneous range-resolved and wind measurements by focusing the laser. Additionally, if the probe comb covers two absorption features of different gases that are close enough (for example, $\text {H}_2\text {O}$ and $\text {CO}_2$ around 1578 nm), it would be possible to perform simultaneous multi-species gas measurements. On the other hand, since the lidar is fiber-based, it is expected to be robust to mechanical vibrations. Thus, conducting vertical IPDA measurements from an air-borne platform can be foreseen after power scaling and evaluation of precision requirements. Finally, the system has an increased dynamic range compared to traditional dual-wavelength DIALs, which makes it ideal for industrial applications where the gas concentrations can be significantly higher and unpredictable than in the atmosphere.
Funding
Office National d'études et de Recherches Aérospatiales (51/19282, TELEMAC); Centre National d’Etudes Spatiales (51/19282); Agence Nationale de la Recherche (EUR TESS N°ANR-18-EURE-0018).
Acknowledgments
We gratefully acknowledge Philippe Hébert for his valuable suggestions, Béatrice Augère and Didier Goular for their contributions to the lidar design, and François Lemaître for his advice and encouragement.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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