A model of the compact MPC was designed based on MATLAB, and the reflection of light in the cell was simulated using a similar method with Ref. [31]. The radius of curvature of the used spherical mirror is 150 mm with a diameter of 50.8 mm and a mirror reflectivity of >95%. The obtained spot distribution on the two mirrors is shown in Figures 1A,B, where the first 20 reflection points are labeled. On mirror A, the injection hole (IH) shown as a blue circle is labeled as 0, the second reflection point is labeled 2, the third is labeled 4, the fourth is labeled 6, and so on. The connection of the first ten reflection points (numbered as 0, 2, … , 18) will form the first ellipse. The next ten reflection points (numbered as 20, 22, … 38) will be offset clockwise, and also the connection between them forms the second ellipse. It can be seen that the second ellipse can be treated as the clockwise rotation of the first ellipse. A similar distribution can be found on mirror B. All the reflection points and the formed rings on mirror A and mirror B are found to rotate clockwise to form the spot distribution. When the light is reflected for the 809th on mirror B, it escapes through the injection hole on mirror A. There are 810 reflections between the mirrors, 40 and a half ellipses and five rings are formed on each mirror. Eq. 1 is used to calculate the total optical path length L = ∑ i = 1 N [ ( x i − x i - 1 ) 2 + ( y i − y i - 1 ) 2 + ( z i − z i - 1 ) 2 ] (1) where (x _i, y _i, z _i) is the coordinates of the ith reflection point, and N = 810 is the total reflection number. Due to the limitation in laser power and the mirror reflection loss, the signal derived by output from the detector cannot be large with too many reflections. Therefore, the laser beam was designed to exit in advance with 76 reflections. As shown in the model in Figures 1C,D, when the light is reflected for the 76th time, it escapes through the designed ejection hole (EH) on mirror B, reaches the detector for optoelectrical conversion, and the derived electrical signal enters a data acquisition (DAQ) card for data processing. The total optical path length with 76 reflections was calculated to be 9.36 m through simulation.

According to the designed model and optimized parameters, a compact MPC with 76 reflections was fabricated, whose photo is shown in Figure 2A. The spot distribution of the mirror shown in the inset was obtained using a He-Ne laser as a trace laser, which basically coincides with the simulated spot distribution in Figure 1D. The external dimension size of the fabricated gas cell is 18.5 × 8 × 9 cm³ with an internal volume of 683.9 mL. Two optical windows (i.e. CaF₂ lens) were placed at both sides with the same aperture as the reflection mirror, and the groove where the window is placed was designed to tilt 15° to prevent the infrared light from directly reflecting into the laser collimator resulting in laser damage. An air inlet and outlet were equipped on the gas cell, separately for gas injection and ejection, and the whole gas chamber was sealed for a good gas tightness. Glass glue was used to fix the optical window at both ends of the MPC, and the upper opening was sealed with a sealing ring to ensure air tightness. With a sealing detection, the air leakage rate was measured to be 2.4 × 10^–3 TorrL/s.

To determine the actual effective optical path length, a saw-tooth scan signal with a frequency of 50 Hz was used to change the current of the DFB laser and a CH₄ sample with a concentration level of 20 ppmv was injected into the compact MPC. The output signal from the detector with CH₄ absorption, defined as v _abs(t), is shown in Figure 2B. The red line is the background fitting signal, expressed as v _base(t). A differential signal can be obtained by subtracting v _abs from v _base, which represents gas absorption. The maximum absorption (i.e. v _base–v _abs) occurred at t = 0.1986 s and the corresponding voltage (V ₂ = v _abs (t = 0.1986 s)) is 1.443 V. The non-absorption voltage (V ₁ = v _base (t = 0.1986 s)) is 1.453 V. Then the absorbance (α) can be calculated from Eq. 2, as α = − ln ( V 2 / V 1 ) (2)

According to Eq. 2, the absorbance is 0.0069, and the actual total optical path is determined to be 9.39 m by referring to the high-transmission (HITRAN) molecular absorption database, which are highly consistent with the simulation result of 9.36 m.

An overall sensor system structure is shown in Figure 3, which is divided into three parts, including an optical part, an electrical part and a gas sampling part. In the optical part, two near-infrared DFB lasers were used as the excitation source for the detection of CH₄ and C₂H₆. In order to facilitate the optical path establishment, the two lasers followed the same light propagation path. For CH₄ detection, the laser operating temperature was set to 20°C, and the center current was set to 84 mA for targeting the absorption line at 6046.95 cm⁻¹. For C₂H₆ detection, the laser was operated at 26°C with a center current of 90 mA for targeting the absorption line at 5951.73 cm⁻¹. The emitted infrared laser beams were combined and the collimated laser beam enters the MPC through an optical fiber collimator. A fiber adapter as well as an optical switch can be used to automatically exchange the 1,654 nm and 1,680 nm laser for different gas detection. Because of the loss resulting from light reflection, the light power will be reduced after multiple reflections. An off-axis parabolic lens was therefore added at the exit to focus the light intensity, and then the signal amplitude output from a Ge transimpedance photodetector was increased. The electrical part included a laptop (HP model BH872PHB), a DAQ card (Model USB-6211, National Instrument, United States ), two current and temperature integrated drive modules (LDTC0520, Wavelength, United States ). Laser direct absorption spectroscopy (LDAS) technique was used for CH₄ and C₂H₆ dual-gas detection, which is easy to realize and suitable for portable applications, compared to wavelength modulation spectroscopy (WMS). A scan signal was generated by the DAQ card controlled by the LabVIEW platform to drive the DFB laser. The output signal from the detector was sampled by the DAQ card, and synchronous sampling was realized triggered by the signal generation module. With respect to the gas sampling module, the MPC was equipped with an inlet and an outlet, allowing gas flow during measurements. CH₄/C₂H₆:N₂ mixtures were diluted from a standard 50 ppmv CH₄ sample and a 100 ppmv C₂H₆ sample in N₂ using a commercial gas mixing system (Series 4,000, Environics).

The selected absorption line of CH₄ is shown in Figure 4A. According to the simulation results of HITRAN, under the conditions of temperature of 300 K, pressure of 760 Torr and optical path length of 1 m, the absorbance of CH₄ at a concentration level of two ppmv and H₂O at a concentration level of 2% were obtained. It can be seen that when the H₂O concentration is high, it will have a certain influence on the detection of CH₄. Therefore, a dehumidification treatment was performed in the gas inlet to reduce the interference of H₂O. CH₄ has a strong absorption line located at 6046.95 cm⁻¹. Accordingly, we chose the laser emission wavelength range of 6046–6048 cm⁻¹ for CH₄ detection. Figure 4C shows the current variation within the selected wavenumber range when the temperature of the DFB laser is 19°C, 20 and 21°C. In Figure 4E, the emission spectrum under a laser driving current of 10–120 mA was measured at 20°C. In order to cover the CH₄ absorption line, the laser temperature was set at 20°C and the central current at 84 mA.

The selected C₂H₆ absorption line is shown in Figure 4B. According to the simulation results of HITRAN, under the condition of temperature of 300 K, pressure of 760 Torr and optical path length of 1m, the C₂H₆ absorption line with one ppmv concentration was obtained. C₂H₆ has a strong absorption line at 5,951.73 cm⁻¹, and the selected wavenumber range is 5,951–5,953 cm⁻¹ for C₂H₆ detection. Figure 4D shows the current variation in the selected wavenumber range at a laser temperature of 24°C, 25 and 26°C. The laser drive temperature was set at 26°C, and the central current was 90 mA for C₂H₆ detection. In Figure 4F, the emission spectrum of the laser under a current of 10–120 mA was measured at a temperature of 26°C.

The measured amplitude of the differential signal of CH₄ (i.e. v _d = v _base–v _abs) at different concentration levels of 0, 5, 10, 15 and 20 ppmv is shown in Figure 5A. In order to speeding the response of the sensor, a high sampling frequency was adopted, and one data point was acquired per 0.8 s. The amplitude (defined as Amp(v _d), in V) at each concentration was recorded for 40 s, leading to 50 points. The average value of these 50 data was used to obtain the linear relationship between CH₄ concentration and the amplitude, as shown in Figure 5B. The linear relationship is expressed by Eq. 3 with a good linear fitting degree of 99.97%, as C C H 4 = 2037.42458 × Amp ( v d ) − 0.05898 (3) where C _CH4 (in ppmv) is the concentration of CH₄. Then, the CH₄ sample with a concentration of 0 ppmv was injected into the MPC to observe the stability of the whole system, and the overall observation time was ∼16 min. The sampled signal amplitude was substituted in Eq. 3 to calculate the corresponding CH₄ concentration levels. Curve of CH₄ concentration level changing with measurement time is shown in Figure 5C, which is relatively stable overall and verifies the reliability of the whole sensor system. The measured concentration was then used for Allan variance analysis to obtain the detection limit of the CH₄ sensor, as shown in Figure 5D. The first data point is the minimum concentration that can be detectable, which indicates that the 1σ detection limit of CH₄ is 71 ppbv at an averaging time of 0.8 s. As integration time increases, system noise occurs leading to the decrease of sensor stability. This type of noise is the sensor system drift, mainly originating from the drift of the near-infrared detector, the laser power and wavelength as well as the electrical circuits for signal processing.

The response time of the sensor system for CH₄ detection was determined by the measured time that was needed for the CH₄ concentration exchange between 0 ppmv and 10 ppmv. The sampling time for each data point was 0.8 s, as shown in Figure 6. Several repeated experiments were done to change the concentration level either from 0 ppmv to 10 ppmv or from 10 ppmv to 0 ppmv for multiple times. At each time the concentration became stable, 40 points were recorded. The response time was measured to be 4 s.

As shown in Figure 7A, the measured amplitude (Amp(v _d)) of C₂H₆ at six different concentration levels of 0, 2, 4, 6, 8, and 10 ppmv were obtained. A data point was derived per 0.8 s, and the total time for recording the amplitude at each concentration was 40 s. The linear relationship between C₂H₆ concentration C _C2H6 (in ppmv) and Amp(v _d) (in V) was obtained as shown in Figure 7B, expressed as C C 2 H 6 = 10929.09126 × Amp ( v d ) + 0.29314 (4)

Then the C₂H₆ concentration was set to 0 ppmv to observe the stability of the whole system, and the overall observation time was 18 min. The real-time C₂H₆ amplitude was substituted into Eq. 4 to calculate the corresponding concentration. The variation of C₂H₆ concentration with time is shown in Figure 7C, which proved the overall stability and verified the reliability of the whole sensor system. The obtained concentration was used for Allan variance analysis, and the C₂H₆ detection limit of the sensor system was achieved, as shown in Figure 7D. The first point is the minimum concentration detected, and the subsequent data is the deviation value, which indicates that the limit of detection of C₂H₆ is 189 ppbv at an averaging time of 0.8 s.

Then, the response characteristics of the dual-gas sensor system for C₂H₆ detection was determined by measuring the response time by switching the C₂H₆ concentration level between 0 ppmv and 100 ppmv. The sampling time for each data point was 0.8 s. The response time from 0 ppm to 100 ppmv for the first concentration exchange was about 16 s. Then several repeated experiments were done, that is, either from 0 ppmv to 100 ppmv or from 100 ppmv to 0 ppmv. 40 data points were recorded each time when the measured concentration was stabilized. As shown in Figure 8, The measured response time was maintained at 16–20 s.

The sensor system was evaluated by measuring the indoor CH₄ concentration levels in a laboratory environment on 4 January 2021 between 2:00 p.m. and 3:20 p.m. The laboratory is located at Tang Aoqing building (GPS position, 125.291,448^◦ E, 43.831,747^◦ N) of Jilin University, Changchun, Jilin Province, China. The total measurement duration was 1.2 h with a sampling interval of 0.8 s (i.e. no averaging on the sampling data). As shown in Figure 9, fluctuations in CH₄ concentration levels were observed during the measurement from 1.5 ppmv to 2.2 ppmv, and the concentration of CH₄ showed an average of ∼1.86 ± 0.17 ppmv (1σ). Since the air circulation in the laboratory was relatively slow, the change of CH₄ concentration was not obvious. It thus can be observed that the CH₄ concentration level in the laboratory was relatively stable during this period.

The sensor system was re-evaluated by measuring the outdoor CH₄ concentration levels in the atmosphere. The outside air was pumped into the gas cell via a Poly Tetra Fluoroethylene (PTFE) for outdoor atmospheric CH₄ testing. Pre-treatment was carried out before the atmosphere enters the gas cell to remove ambient impurities, aerosols and water vapor. The outside air was pumped into the gas cell via a PTFE filtered tube to detect the outdoor CH₄ concentration levels for 1 day. The measurement was conducted in zone D, Tang Aoqing building, Jilin University, Changchun, and the measurement time was from 4:40 p.m. on 4 January 2021 to 4:40 p.m. on 5 January 2021. The sampling data was averaged per 40 s (i.e. 50 data points were averaged as one data point). As shown in Figure 10, it can be concluded from the variation trend that the CH₄ concentration decreased at night and was eventually down to 2.2 ppmv–2.3 ppmv. The CH₄ concentration level suddenly increased at 10:00 a.m. with a peak up to 2.7 ppmv and was eventually around 2.6 ppmv at 4:00 p.m. in the next day. Over the 1 day, the measured CH₄ concentration ranged between 2.2 and 2.8 ppmv, with an average value of 2.42 ± 0.19 ppmv.