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Abstract
We present an innovative spectroscopic method based on coherent optical frequency-modulated continuous-wave (FMCW) interferometry that can realize multi-point gas detection with high spatial resolution, high sensitivity, and high selectivity. This method takes full advantage of the intrinsic capability of spatial localization of the coherent FMCW, meanwhile efficiently decodes the spectral information from the reflected optical signals. Gas sensors are deployed by adopting bus topology, i.e., distributed along a single backbone fiber in the measurement arm of the FMCW interferometer. For validation, a multi-point acetylene gas sensing system with three sensing nodes is experimentally demonstrated. The transmission spectra of the three gas sensors are accurately extracted, and their corresponding gas concentrations are efficiently retrieved with a low crosstalk below -30 dB. The demonstrated system achieves a sensitivity of 55 ppm (noise equivalent absorbance of 0.004) over a distance of 52 m, with a sensing spatial resolution of 30 cm and a spectral resolution of 0.5 GHz. Our proposed method promotes a novel way for the development of multi-point spectroscopic gas sensing systems for challenging applications such as gas leakage detection and gas emission monitoring, where spatially resolved chemical analysis over a large area is required.
© 2020 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Multi-point or quasi-distributed gas sensing is of great importance in various applications, such as detection of leakage in natural gas pipelines [1], monitoring of gas emissions from landfill sites [2], and gas monitoring in the underground utility tunnel [3]. In these applications, quantitative detection and precise localization of chemicals over an extended distance or area are required. Currently, in-situ gas detection are mostly performed using low-cost chemical gas sensors [4,5], which, however, always suffer from cross sensitivity (to other gases or humidity) and slow response. By comparison, gas sensors based on laser spectroscopic methods represented by laser absorption spectroscopy (LAS) offer advantages of high specificity, high speed, and intrinsic safety in explosive gas environment [6,7]. However, laser based gas sensors are of relatively high cost and rather less competitive for multi-point gas sensing applications.
To improve the economy and competiveness of the laser-based gas sensing system for monitoring multiple points, multiplexing techniques must be implemented to share expensive optical components such as laser sources and detectors so that the cost per sensing point can be significantly reduced. Typical multiplexing schemes having been applied to LAS-based gas sensors include spatial-division multiplexing (SDM) [2,3,8,9], time-division multiplexing (TDM) [10,11], wavelength-division multiplexing (WDM) [12,13], and frequency-division multiplexing (FDM) [14–16]. In a SDM system, the laser wavelength is swept as in a single-sensor system to obtain the gas absorption spectra, while the light source is divided and guided into multiple independent gas sensing paths, and a number of separated detectors are required to localize the different sensors [2,3]. For TDM, a wavelength-swept pulsed laser source is used, and the multiple gas sensors are distinguished according to the different time delays of the transmitted or reflected light pulse [10,11]; however, it is highly demanded for a TDM system to achieve a high spatial resolution (e.g., a spatial resolution of sub-meter requires a laser pulse less than 10 ns and a sampling rate at GHz level). The WDM are often used in combination with fiber Bragg gratings (FBGs) whose wavelengths for different sensing points are aligned with different absorption lines of the target gas, and the gas concentration at each sensing point is determined according to the rough absorption spectrum obtained by a spectrometer [12,13]; however, the number of WDM-multiplexed sensors is limited by the available absorption lines. For FDM, a most representative technique is incoherent frequency-modulated continuous-wave (FMCW) interferometry [14,15], in which the laser is modulated in intensity with a swept frequency, and the individual gas sensors are localized according to their specific beat frequencies; meanwhile, the frequency of the laser itself is scanned to obtain the gas absorption signals.
Summarizing the existed mainstream multiplexing techniques adopted for multi-point spectroscopic gas sensing, all of them employ at least two separate techniques with corresponding equipment to realize sensor localization and spectroscopic analysis. Here, we propose a novel multi-point spectroscopic gas sensing method that adopts a single technique, the coherent FMCW interferometry. The coherent FMCW is traditionally used in the field of light detection and ranging (LiDAR), having advantages of high precision, simplicity and low cost [17–19]. In fact, for coherent FMCW, when a wavelength-swept laser beam passes through the gas of interest, the absorption spectral information is inevitably encoded into the optical signal. Therefore, in principle, other than the capability of spatial localization, the coherent FMCW should intrinsically has a great potential for spectroscopic gas analysis. Recently, we have for the first time successfully mined the gas absorption spectra from the received beat signals in a coherent FMCW system, and realized identification of absorption spectra associated with different reflection positions in a multi-pass cell [20]. In this work, we demonstrate that the coherent FMCW technique also possesses the capability to perform highly sensitive, distributed spectroscopic gas analysis.
2. Basic principle
The basic configuration of the coherent FMCW system for multi-point spectroscopic gas sensing is based on a Mach–Zehnder interferometer, as shown in Fig. 1(a). A wavelength-swept laser is split into reference and measurement paths. In the measurement arm, gas cells are distributed along the fiber adopting bus topology with reflectors equipped at their terminals. Due to the difference of time delay (τ), the reflected laser light from different gas cells would generate beat signals of different frequencies (f), as shown in Fig. 1(b). Thereby, the multiple gas sensors can be distinguished and multiplexed via frequency division.
Fig. 1. Basic principle for coherent-FMCW-based multi-point spectroscopic gas sensing method. (a) The configuration based on a Mach–Zehnder interferometer. (b) The principle of frequency-division multiplexing of gas sensors. (c) The data processing procedure for the retrieval of the transmission spectra of the multi-point gas sensors.
The data processing procedure for the coherent-FMCW-based spectroscopic gas sensing method is illustrated in Fig. 1(c), which has been detailed in [20]. Briefly, it involves twice Fourier transforms (FTs). First, being the same as the traditional FMCW LiDAR, the collected raw data containing beat signals of multiple gas sensors in frequency (spectral) domain are transformed into time domain (spatial domain), so that signals belonging to different reflection positions can be separated according to their respective flight time of light. Then, by an inverse FT, the signals of interest in the spatial domain are selected and transformed back to spectral domain, obtaining the individual transmission spectrum of each gas sensor.
3. Simulations
3.1. Retrieval of transmission spectra
We first simulate the retrieval of transmission spectra of multiple gas sensors to validate the multiplexing capability of the proposed method. The simulation is based on the configuration shown in Fig. 1(a), and simulation results are shown in Fig. 2. In the simulation, the laser frequency is linearly swept from 6577.26 cm−1 to 6579.86 cm−1 (1519.79–1520.39 nm) at a sweeping rate of 173.13 cm−1/s (∼40 nm/s), covering the strongest R(9) line in the ν1+ν2 band of acetylene [21]. The data sampling rate is set to 5.08 MHz, and the refractive index of the optical fiber is 1.468. Three 30-cm-long gas cells are located at positions of 2 m, 4 m and 6 m, filled with acetylene at atmospheric pressure with concentrations of 1000 ppm (parts per million), 0 ppm, and 2000 ppm, respectively. The transmission spectra of the three gas sensors are calculated according to the Beer-Lambert law and HITRAN database [21].
Fig. 2. Simulation procedure of the retrieval of multi-point transmission spectra of acetylene. (a) Simulated beat signals generated by three acetylene gas sensors in frequency domain. (b) DFT results of the original signals, capable of distinguishing the three sensors. (c) Transmission signals of the three sensors obtained by applying inverse DFT to the individual reflection peaks with a window width of 20 cm. (d) Retrieved transmission spectra of the three acetylene gas sensors.
Figure 2(a) shows the simulated original signals in frequency (spectral) domain, containing the beat signals from the three sensors. By applying discrete FT (DFT), the beat signals are transformed into time domain (spatial domain), and the reflection peaks due to the three gas sensors can be clearly identified in Fig. 2(b). The distance is unified in the space in fiber. The spatial resolution of the FMCW system, which is determined by
where c is the speed of light in vacuum, n is the refractive index of the fiber, ΔF is the tuning range of the laser frequency, is calculated to be 1.3 mm. This high spatial resolution is sufficient to resolve the distributed sensors and provide enough effective data points for data processing. If N data points within a window width dW in spatial domain is selected for spectrum retrieval, the effective spatial resolution will be determined by For each individual reflection peak signal, 152 data points within a window of 20 cm (the setting of window width will be discussed in the next subsection) are selected and transformed back into frequency domain, obtaining the transmission signal, as shown in Fig. 2(c). By normalization of the light intensity, the transmission spectra of the three gas sensors are successfully retrieved, which is shown in Fig. 2(d). Thereby, the capability of the proposed method for distributed spectroscopic gas analysis is in principle validated.3.2. Evaluation of spectral resolution
For spectroscopic gas analysis, a high spectral resolution is required to guarantee the sensing specificity and accuracy. In the proposed system, the spectral resolution is determined by
According to Eqs. (1)–(3), the relationship between the spectral resolution and the window width can be expressed by Equation (4) indicates that the spectral resolution is almost only determined by the window width for data selection in spatial domain. As an example, Fig. 3(a) shows the retrieved transmission spectra of sensor S3 in Fig. 2 in the cases of different window widths, clearly showing the improved spectral resolution as the increase of the window width.Fig. 3. Dependence of (a) spectral resolution and (b) transmittance error on the window width of data selection in spatial domain.
An insufficient spectral resolution would overestimate the transmission amplitude and worsen the measurement accuracy. Figure 3(b) shows the transmittance error at absorption peak plotted as a function of the window width. When the window width is more than 10 cm, the transmittance error will less than 10−4, a noise level of a typical LAS gas sensor [6,7]. A 10-cm window width corresponds to a spectral resolution of 1.02 GHz, which is much less than the Lorenzian linewidth of the acetylene absorption at atmospheric pressure (∼5.1 GHz), so that the spectral error is negligible when dW>10 cm. Since the window width is directly related to the sensing spatial resolution, there would be a tradeoff between the spectral resolution and the sensing spatial resolution. However, for LAS, the typical length of a gas cell is tens of centimeters; thus, in practical applications, the sensing spatial resolution would be more likely limited by the cell length rather than the required window width. When the length of the gas cell is more than 15 cm (corresponding to >10 cm in fiber), it would be better to make the window width match the cell length to achieve a high spectral resolution. In principle, a longer gas cell can lead to a better measurement sensitivity and a higher spectral resolution. However, a long gas cell would degrade the sensing spatial resolution, and the improvement of the spectral accuracy is much slight when dW>10 cm. In the simulation and the latter experiments, the window width is set to 20 cm (matching the 30-cm gas cell) corresponding to a spectral resolution of 0.51 GHz, which makes the spectral error almost completely negligible and will hardly affect the sensing specificity.
3.3. Spectral noise induced by spectral leakage
When analyzing time-discrete spectra by DFT, spectral leakage occurs if the number of periods in the sampled data set is not an integer [22]. In a FMCW system, when the sampling time is an integral multiple of the beat period, the beat frequency is an integral multiple of the frequency resolution, and the distance is an integral multiple of the spatial resolution. So there will exist spectral leakage if the distance is not an integral multiple of the spatial resolution. We still take the transmission spectrum of sensor S3 in Fig. 2 as an example to simulate the spectral leakage and the noise it induces. Figure 4(a) shows the reflection peaks of the sensor S3 with three different distance offsets within a spatial resolution. The corresponding retrieved transmission spectra are shown in Fig. 4(b). It illustrates that a distance offset of half the spatial resolution (0.5Δd) would cause the largest spectral leakage. Spectral leakage can lead to severe oscillations in the transmission spectrum, and worsen the sensitivity of gas detection.
Fig. 4. Spectral noise induced by spectral leakage. (a) Reflection peaks in spatial domain and (b) the corresponding retrieved transmission spectra of sensor S3 with three different distance offsets. (c) The most seriously affected transmission spectrum smoothed by the SG filter, compared with the one without spectral leakage.
Spectral leakage can be avoided by coherent sampling, i.e., in spatial domain making the distance an integral number of the spatial resolution. However, it is not practical to finely adjust the distance for all channels in a gas sensing system having a high spatial resolution at mm level. Considering that the spectrum oscillation caused by spectral leakage is highly periodic, it should be in principle not difficult to reduce. We therefore explore the algorithm of Savitzky-Golay (SG) smoothing [23], a widely used denoising method for spectrum analysis, to counter the effects of spectral leakage. The transmission spectrum at the worst case (offset = 0.5Δd) presented in Fig. 4(b) is processed by a SG filter. The polynomial order of the SG filter is set to 2, and the frame length is about 3 times the spectral resolution. Figure 4(c) shows the filtered transmission spectrum, and also the one without spectral leakage. Clearly the spectrum can be efficiently smoothed by the SG filter except for its start and end, so 20% of the spectral data at both ends of the spectrum are cut away. The remaining filtered spectrum (spanning 2.08 cm−1) is compared with the one with no spectral leakage. The standard deviation of the residuals is at a low level of 10−4, which indicates that the SG filter can efficiently remove the spectral noise caused by spectral leakage. Hence, in practical applications, there would be no need to make the sensing distance an integral number of the spatial resolution of the FMCW system.
3.4. Inter-channel crosstalk caused by spectral leakage
Essentially, the spectral leakage is energy leakage, which can definitely cause crosstalk between neighboring sensing channels. The transmission spectrum of sensor S3 in Fig. 2 is also took as an example to perform the simulation. In the simulation, the sensing distance of sensor S3 is set to be an integral number of the spectral resolution, so that there is no spectral leakage for sensor S3 itself. Meanwhile, a sensor with severe spectral leakage (distance offset = 0.5Δd) is placed nearby with three different intervals. The smallest interval is set to 20 cm, which is the window width for spectrum retrieval. Figures 5(a) and 5(b) show the simulated results of reflection peaks in spatial domain and retrieved transmission spectra in spectral domain. As expected, the inter-channel crosstalk is reduced with the increase of channel interval. We also explore the SG filter to smooth the spectrum with the largest crosstalk noise and compare it with the one without crosstalk, which is shown in Fig. 5(c). The low level of the standard deviation of the residuals (10−4) further validate the efficiency of the SG filter for suppressing crosstalk noise. It means that the problems caused by spectral leakage can be resolved to a large extent by the SG smoothing algorithm.
Fig. 5. Inter-channel crosstalk induced by spectral leakage. (a) Reflection peaks in spatial domain and (b) the corresponding retrieved transmission spectra of sensor S3 interfered by a neighboring sensor with three different intervals. (c) The most seriously interfered transmission spectrum smoothed by the SG filter, compared with the one with no crosstalk.
4. Experimental
4.1. Setup
Figure 6 shows the schematic diagram of the experimental setup of the coherent-FMCW-based multi-point gas sensing system, following the basic design shown in Fig. 1(a). It comprises four parts: a tunable laser source (TLS), a measurement interferometer containing the distributed gas sensors, an auxiliary interferometer, and a data acquisition (DAQ) unit. The measurement interferometer adopts Mach–Zehnder configuration which takes 99% of the laser power from the TLS. The auxiliary Michelson interferometer generates clock pulses at equally spaced laser frequencies to trigger data acquisition, which is known as the frequency-sampling method widely used to cope with the laser tuning nonlinearity [24,25].
Fig. 6. Experimental setup of the coherent-FMCW-based multi-point gas sensing system. The inset shows the absorption line strength of acetylene gas in the vicinity of 1520 nm. TLS, tunable laser source; FRM, Faraday rotation mirror; CG, clock generator; PC, polarization controller; BPD, balanced photodetector; DAQ, data acquisition.
In the proof-of-concept experiments, acetylene is chosen as the sample gas which has abundant strong absorption lines around 1520 nm, as shown in the inset of Fig. 6. The employed TLS (Keysight, 81960A) has an output power of ∼5 mW and a linewidth of ∼100 kHz. It is repeatedly scanned with a span of 0.6 nm from 1519.78 nm to 1520.38 nm (6577.30 cm−1–6579.90 cm−1) at a tuning rate of 40 nm/s, crossing the strongest R(9) line in the ν1+ν2 band of acetylene. In the measurement interferometer, 99% of the laser power is allotted to the probe arm while the other 1% is assigned to the reference arm. The nominal refractive index of the optical fiber used is 1.468. Three gas sensors with intervals of ∼2 m in between are successively placed along the probe fiber, with each taking about 5% of the laser power from the probe arm. Each gas sensor contains a stainless-steel gas cell equipped with a pair of anti-reflection coated fiber collimators. The optical transmittance of each gas cell is ∼75%. The first and the third gas cells are filled with 1870-ppm and 9250-ppm acetylene gas, respectively, while the second gas cell is filled with nitrogen gas. A gold-coated fiber end with the reflectivity of about 90% is connected to the end of each gas cell to increase the reflecting light intensity for improving the signal-to-noise ratio (SNR). Using the FMCW technique, the lengths of free space between the collimators in the three gas cells are measured to be 29.41 cm, 28.96 cm and 29.25 cm, respectively. The absorption pathlengths in the sensors would be twice these values due to the reflection configuration. The optical beat signals are received by an AC-coupled balance detector (Fsphotonics, PDB1008) and acquired using a DAQ card (ART, PCI8514). The optical delay fiber in the auxiliary interferometer is 104.3 meters long, resulting a DAQ rate of 5.33 MHz.
4.2. Results and analysis
Figure 7(a) shows the raw beat signals output from the photodetector. The DFT results of the recorded beat signals are shown in Fig. 7(b), in which the reflection peaks corresponding to the three gas sensors are unambiguously identified and indicated. Except for the major reflections from the gas sensors, many minor reflection peaks coming from the Fresnel reflections by the fiber connectors can also be clearly seen. The spatial resolution determined by Eq. (1) is estimated to be 1.3 mm. Each labeled reflection peak is filtered by a rectangular window with a width of 20 cm. By applying inverse DFT to these selected data, transmission signals corresponding to the individual sensors are obtained, which are shown in Fig. 7(c).
Fig. 7. Data processing procedure of the retrieval of multi-point transmission signals. (a) Acquired raw signals. (b) DFT of the original beat signals with 20 results averaged (corresponding to an integration time of 0.3 s). (c) Retrieved transmission signals of the three gas sensors.
The amplitude oscillations at both ends of the transmission signals shown in Fig. 7 are due to the spectral leakage, which are suppressed by the SG filter. The transmission spectra of the three sensors are retrieved by simultaneously fitting a polynomial baseline and a Lorentz profile to the transmission signals, which are shown in Fig. 8. As analyzed in the simulation section, the SG filter also efficiently counters the crosstalk noise caused by spectral leakage. According to Eq. (4), the achieved spectral resolution is estimated to be 0.51 GHz or 0.017 cm−1, which is about one-tenth of the absorption linewidth of acetylene gas, and thus sufficient for performing high-specificity gas sensing. To further evaluate the efficacy of multi-point spectroscopic analysis, the retrieved transmission spectra are compared with the simulated results based on the HITRAN database. This direct comparison is also shown in Fig. 8, exhibiting a high agreement between the experimental and the simulated results. It illustrates the high accuracy of our proposed coherent-FMCW-based method to perform multi-point gas detection. According to the standard deviation of the residuals, the noise equivalent absorbance (NEA) of the three gas sensors is estimated to be 0.004. It yields a minimum detectable concentration (MDC) of 55 ppm for the measured acetylene gas, according to the Beer–Lambert law, which illustrates the high sensitivity of the system. As can also be seen in Fig. 8, the spectral residuals of the three sensors have similar structures, which indicates that the measurement sensitivity is mainly limited by optical interference noises.
Fig. 8. Comparison of the measured and simulated transmission spectra of three acetylene gas sensors. The lower panel shows the residuals for all spectra to present the excellent agreement between the experimental and the simulated results.
Finally, we experimentally examine the cross response between the neighboring sensing channels, which is one of the most concerned factor for multi-point gas sensing. In the experiments, the sensors S1 and S2 are filled with nitrogen gas, while the sensor S3 is filled with 10% acetylene gas, which is a relatively high concentration resulting saturation absorption. Figure 9 shows the retrieved transmission signals of the three sensors. It clearly shows that the absorption of sensor S3 reaches saturation. However, at such a high absorption level, the cross response of the neighboring sensors S1 and S2 is below the noise level and not detectable. Since the noise level corresponds to an acetylene concentration less than 100 ppm, the cross response is below -30 dB. It illustrates the advantage of low cross response provided by the demonstrated multi-point gas sensing system.
Fig. 9. Transmission signals of three neighboring gas sensors with the third sensor filled with acetylene gas while the other two with nitrogen gas.
5. Discussion
The focus of this work is to propose a new multi-point gas sensing method based on coherent FMCW, and demonstrate its capability of distributed high-resolution spectroscopic analysis with high sensitivity. In practical applications, the achieved sensitivity of a multi-point sensing system is highly related to the sensing range and the number of sensors multiplexed. For coherent FMCW, the maximum sensing range is mainly limited by the coherence length of the laser source. In the current work, the laser linewidth is about 100 kHz which limit the sensing range up to 2 km. By compressing the laser linewidth [26], a larger sensing range could be expected. In the proof-of-concept demonstration experiments, the sensing range is 52.15 m, which is restricted by the length of the delay fiber used in the auxiliary interferometer according to the Nyquist law. Another important factor influencing the sensing range is the tuning nonlinearity of the laser frequency, which would cause spreading of the reflection energy and thus worsen both the spatial resolution and measurement sensitivity. Although in the experiments the equivalent-frequency-sampling method is used to compensate the frequency nonlinearity, the remaining high-order frequency nonlinearity can still worsen the sensing performance at large distances [27].
In a multi-point gas sensing system, the maximum number of sensors can be multiplexed is in principle determined by the sensing range and the sensing spatial resolution. However, in practical conditions, the number of sensors can be multiplexed would be mostly limited by the optical power budget. Increasing the sensing distance and the number of sensing nodes would lead to significant optical power loss. In the current work, each sensor takes 5% of the light power from the backbone fiber. Because of the sufficient light power, the achieved NEA (0.004) is mainly limited by optical interference noises. Figure 7(b) shows that the ratio of the sensor signal to the base noise is ∼30 dB, according to which we estimate that around 100 sensors with each taking ∼1% of the light power from the probe arm can be multiplexed while maintaining the same level of measurement sensitivity. The compromise among measurement sensitivity, sensing range and the number of multiplexed sensors merits further detail investigations.
Although this work is dedicated to multi-point spectroscopic gas sensing, we note there have also been a few investigations focusing on distributed spectroscopic gas analysis. In 2017, Garcia-Ruiz et al. preliminarily demonstrated distributed, qualitative detection of acetylene gas based on photothermal (PT) effect in a 10-m solid-core photonic crystal fiber (PCF) [28], in which the sensing localization is realized by a phase-sensitive optical time-domain reflectometry (OTDR). In [29], Lin et al. demonstrated a distributed spectroscopic gas sensing system based on PT interferometry [30,31] and phase-sensitive OTDR, achieving a sensing range over 200 m with a spatial resolution of 30 m and a sensitivity of 5 ppm for acetylene gas. The PT-based gas sensing systems show an advantage of high sensitivity over the LAS-based ones, but they require complex pump-probe configurations and their currently achieved spatial resolutions are relatively low. By integrating with the PT interferometry presented in [29], the measurement sensitivity of the current FMCW system may be greatly improved while maintaining the high spatial resolution.
6. Conclusions
In summary, we have developed a novel spectroscopic method based on coherent FMCW interferometry, which can realize multi-point, highly sensitive gas detection with low cross response. Multi-point acetylene gas sensing experiments demonstrate a ppm-level sensitivity, a cm-level sensing spatial resolution and a sub-GHz spectral resolution. This new method offers intrinsic gas sensing selectivity by digging out the spectral information encoded in the FMCW signals. Furthermore, it takes full advantages of simplicity and low cost of the FMCW technique: the system needs only one laser source, one photo receiver and one fiber backbone. We therefore believe that it could inspire a new class of multi-point or quasi-distributed gas sensing system for challenging applications such as gas leakage detection and gas emission monitoring, where quantitative detection and precise localization of chemicals over an extended distance or area are required.
Funding
National Natural Science Foundation of China (61775049, 61575052).
Disclosures
The authors declare no conflicts of interest.
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