As the main green energy, methane (CH₄) has become increasingly important in human production and life. Meanwhile, as explosive and flammable harmful gas, it also causes significant problems such as production safety accidents and environmental pollution, it is particularly important to detect CH₄ concentration in real time and online. Additionally, carbon isotopes in CH₄ are also significant for environmental analysis of sources and sinks. Traditional isotope ratio measurement methods, such as mass spectrometry and gas chromatography, often require sample preprocessing and are difficult to achieve real-time online detection. At the same time, traditional absorption spectroscopy techniques often need large absorption cells and other devices to measure the gas isotopes, which results in difficult temperature and pressure control. We report a methane isotope measurement method based on off-axis integrated cavity output spectroscopy (OA-ICOS) technology, which eliminates residual mode noise in the measurement results by adding an RF white noise source and further expands the optical power of the incident laser using booster optical amplifier (BOA) to increase the effective optical path length of the measurement results. We hope our method can further reduce the minimum detection limit and provide solid theoretical and technical support for future measurement of isotope ratio changes in CH₄ under atmospheric background concentration.

We establish a system for carbon isotope detection in CH₄ based on OA-ICOS technology (Fig. 3), and the laser output laser changes the angle and position of the incident into the integration cavity through the fiber collimator fixed on the five-dimensional adjustment frame. Meanwhile, the outgoing light after multiple reflections is formed in the cavity by the lens to converge on the photosensitive surface of the detector, and the detector converts the collected integrated light signal for photoelectric conversion. The detected electrical signal is converted analog-to-digital via the data acquisition card and uploaded to the computer software by the USB serial port to realize gas concentration measurement. The opening ratio of the needle valve and the pumping speed of the vacuum pump are changed in the experiment to control the flow rate of the outlet end and thus ensure the measured pressure stability. Additionally, the mass flow controller is adopted to adjust the flow rate of the inlet in real time to realize the pressure control in the cavity. Radio frequency (RF) white noise is loaded on the current drive of the laser in the experiment and the laser linewidth is further widened, with eliminated remaining mode noise and improved signal-to-noise ratio (SNR) of the measurement results, which aims to minimize the mode noise interference in the cavity and improve the SNR of the measurement results. Additionally, to further improve the effective optical path length of the system and the signal-to-noise ratio of the measurement, we amplify the output power by adding a BOA after laser, after which the absorbance measured is greatly improved.

When the RF white noise power is greater than -30 dBm, the residual mode noise in the cavity is eliminated. When the RF white noise power is greater than -20 dBm, the absorption peak shows a significant decrease with the broadening linewidth (Fig. 5). Thus, the RF white noise with -30 dBm is adopted in the experiment. Meanwhile, the rising current of BOA leads to a significantly increasing absorption peak (Fig. 6) and effective optical path length. When the drive current is greater than 400 mA, the effective optical path length of the system at this time is approximately 6000 m, which increases by approximately 1.22 times. The SNR increase of ¹²CH₄ is 1.16 times and of ¹³CH₄ is 1.18 times, which is consistent with the rise in effective optical path length (Fig. 6). By employing the carbon isotope standard value given by NBS-20 [R_standard (¹³C/¹²C)=0.0112253] as the standard value for calculating the isotope ratio changes, δ(¹³C) in the CH₄ standard gas with a volume fraction of 494.14×10^-6 and a volume fraction of 5.55×10^-6 at a volume fraction of ¹³CH₄ is continuously measured for 1 h, and the measurement results are shown in Fig. 8(a). To further analyze the stability and detection limit of the measurement system, we perform the Allan variance analysis of the measured δ(¹³C), with the results shown in Fig. 8(b). The analysis results indicate that the limit of detection (LoD) is 4.57‰ when the average time is 1 s, and its LoD decreases to 0.567‰ when the average measurement time increases to 663 s, at which time the detection accuracy of the system can be further improved by increasing the average time.

To realize the real-time measurement of the change of stable carbon isotope ratio in CH₄, we establish a high-precision δ(¹³C) measurement system based on OA-ICOS technology. Meanwhile, for further improving the measured effective optical path length and reducing the measurement limit, we add the BOA behind the laser output to enhance the output laser power, increase the effective optical path length of the system from about 2700 m to about 6000 m, an increase of about 1.22 times, and increase the SNR of ¹²CH₄ and ¹³CH₄ by 1.16 times and 1.18 times respectively. By leveraging the gas distribution instrument, the system is calibrated by high-purity N₂ and CH₄ with a volume fraction of 5008×10^-6 to configure different volume fractions of sample gases, and the calibration curve is obtained by fitting the relationship between the gas volume fraction and the absorption spectrum peak, with the volume fraction inverted by the calibration curve. After performing the stability test of CH₄ with a volume fraction of 500×10^-6 for 1 hour, Allan variance analysis shows that the minimum variance of the system stability for δ(¹³C) measurement in CH₄ is 0.567‰. The utilization of this system can improve the SNR and reduce the minimum LoD to achieve long-term stable measurement of δ(¹³C) in CH₄. Additionally, by further improving the stability of the optomechanical structure, reducing system noise, and increasing the effective optical path length, the minimum detection limit can be further reduced. Finally, solid theoretical and technical support can be provided for future measurement of methane-stabilized carbon isotope characteristic values at atmospheric background concentrations.