Development of a Stable Oxygen Sensor Using a 761 nm DFB Laser and Multi-Pass Absorption Spectroscopy for Field Measurements

An optical sensor system based on wavelength modulation spectroscopy (WMS) was developed for atmospheric oxygen (O2) detection. A distributed feedback (DFB) laser with butterfly packaging was used to target the O2 absorption line at 760.89 nm. A compact multi-pass gas cell was employed to increase the effective absorption length to 3.3 m. To ensure the stability and anti-interference capability of the sensor in field measurements, the optical module was fabricated with isolation of ambient light and vibration design. A 1f normalized 2f WMS (WMS-2f/1f) technique was adopted to reduce the effect of laser power drift. In addition, a LabVIEW-based dual-channel lock-in amplifier was developed for harmonic detection, which significantly reduced the sensor volume and cost. The detailed detection principle was described, and a theoretical model was established to verify the effectiveness of the technique. Experiments were carried out to obtain the device’s sensing performances. An Allan deviation analysis yielded a minimum detection limit of 0.054% for 1 s integration time that can be further improved to 0.009% at ~60 s. Finally, the reliability and anti-interference capability of the sensor system were verified by the atmospheric O2 monitoring.


Introduction
Oxygen (O 2 ) is one of the most common gases and plays an indispensable role in people's daily lives, as well as in industrial production. For example, O 2 in indoor and outdoor environments is closely related to people's breathing. Low oxygen concentration in an environment can cause weakness, dizziness, and even loss of consciousness. Low oxygen levels can result from activity in certain workplace settings, such as mining or welding, where heavy machinery can deplete the oxygen supply. OSHA (the Occupational Safety and Health Administration) specifies that a hazardous atmosphere may include one where the O 2 concentration is below 19.5% or above 23.5%, so O 2 concentration monitoring is important for ensuring safety in confined spaces, such as coal mines and tunnels [1,2]. Thus, analyzing the oxygen levels in these settings is essential to ensuring the safety of individuals working in such environments. In metallurgy, energy, and other industrial fields, O 2 is used as an accelerant that directly affects the combustion process. Measuring the O 2 concentration can effectively improve the performance of the engine and reduce the emission of pollutants [3,4]. Furthermore, measuring O 2 concentration in natural environments, including forests and oceans, can help identify changes in ecosystems, which may indicate pollution or other underlying issues. O 2 concentration detection can be achieved through various methods, including the electrochemical method [5], gas chromatography [6], and optical methods. In recent years, optical-based measurement methods have garnered increased attention from researchers. Compared with traditional O 2 detection methods, such as electrochemical method, gas chromatography, optical methods including optical absorption spectroscopy, where I 0 and I indicate the incident and outgoing light intensity, respectively; C is the concentration of the gas; α(v) is the absorption coefficient of the corresponding gas: α(v) = NS(T)ϕ(v); S(T) (cm·mol −1 ) is the line strength; ϕ(v) (cm) is the line shape function; N = P/(k·T) is the molecular density of the gas, where P (atm) is the total pressure, k is the Boltzmann constant, and T (K) is the temperature. Considering that collisional broadening plays a major role in the full-width at half-maximum (FWHM) at normal temperature and pressure, Lorentz lineshape is selected as the line shape function in this paper.
As α(v)L 1, Equation (1) can be transformed into: In wavelength modulation spectroscopy (WMS) technology, a low-frequency triangular driver signal and a high-frequency sinusoidal driver signal were generated to scan across the selected absorption line and suppress the background noise. After modulation, the frequency and light intensity can be expressed as [18,26]: I 0 (t) = I 0 1 + i 1 cos(ωt + ψ 1 ) + ∞ ∑ m=2 i m cos(mωt + ψ m ) (4) where v 0 is the center frequency of the laser; a is the frequency modulation depth; ψ is the phase of frequency modulation; I 0 (t) represents the light intensity after modulation; I 0 is average laser intensity over modulation period; and i 1 and i m are the linear and nonlinear light intensity modulation coefficients. Generally, m is only 2, and the modulation coefficients of higher harmonics are small and can be ignored. The ψ 1 and ψ m represent the phase differences of the output light intensity before and after modulation; and ω = 2π f m , f m represents the modulation frequency of the high-frequency sinusoidal signal. After Fourier expansion of the transmissivity τ(v), the following can be obtained: Combined with Equation (5), the k-th harmonic coefficient can be obtained: When k = 0: It can be seen that the harmonic components are in direct proportion to the gas concentration. The X 2 f and Y 2 f components of the 2f signal can be obtained by an orthogonal lock-in amplifier (multiplying the absorbed signal with the cosine reference signal cos(2ωt) and the sine reference signal sin(2ωt), respectively, and then pass the low pass filter): Similarly, the X 1 f and Y 1 f can be expressed as follows: where G is the conversion coefficient of photodetector, and the 1f signal can be obtained: The expression of the WMS-2f /1f after deducting the background signal is as follows: Since the harmonic expansion of Lorentz lineshape has even harmonic characteristics, the amplitude of the odd harmonic component is 0 at the center frequency, and low concentration gases, H 0 , H 2 and H 4 , are both far less than 1. Therefore, at the center frequency, the Equation (12) can be simplified as: As can be concluded from Equation (13), the WMS-2f /1f method can effectively avoid the interference of laser intensity fluctuations, temperature drift, and pressure drift, thus improving the anti-interference of the system.

Selection of O 2 Absorption Line
The main factors to be considered in the selection of an absorption line are the line strength, selectivity, and system cost [27]. O 2 has a relatively strong absorption band near 760 nm. A spectral simulation of 5% O 2 in this spectral range was conducted according to the HITRAN 2020 database [28] under a condition of 300 K, 1 atm, and 100 cm absorption length as depicted in Figure 1. Considering the sensor system should work normally in an atmospheric environment, the absorption of 0.038% carbon dioxide and 4.38% water vapor were also simulated. It can be seen that H 2 O and CO 2 in ambient air produce little interference to the O 2 detection in this wavelength, and the absorption line at 760.89 nm was selected as the optimal absorption line due to its strong line strength. Similarly, the and can be expressed as follows: where is the conversion coefficient of photodetector, and the 1f signal can be obtained:

= +
The expression of the WMS-2f/1f after deducting the background signal is as follows: Since the harmonic expansion of Lorentz lineshape has even harmonic characteristics, the amplitude of the odd harmonic component is 0 at the center frequency, and low concentration gases, , and , are both far less than 1. Therefore, at the center frequency, the Equation (12) can be simplified as: As can be concluded from Equation (13), the WMS-2f/1f method can effectively avoid the interference of laser intensity fluctuations, temperature drift, and pressure drift, thus improving the anti-interference of the system.

Selection of O2 Absorption Line
The main factors to be considered in the selection of an absorption line are the line strength, selectivity, and system cost [27]. O2 has a relatively strong absorption band near 760 nm. A spectral simulation of 5% O2 in this spectral range was conducted according to the HITRAN 2020 database [28] under a condition of 300 K, 1 atm, and 100 cm absorption length as depicted in Figure 1. Considering the sensor system should work normally in an atmospheric environment, the absorption of 0.038% carbon dioxide and 4.38% water vapor were also simulated. It can be seen that H2O and CO2 in ambient air produce little interference to the O2 detection in this wavelength, and the absorption line at 760.89 nm was selected as the optimal absorption line due to its strong line strength.  A DFB laser emitting at 761 nm was chosen as the laser light source. The tuning range of the laser was set to be 760.85 nm to 760.95 nm to scan across the optimal absorption line. According to the laser wavelength tuning experiment, the temperature and current tuning coefficient of the laser were 0.014 nm/mA and 0.06 nm/ • C, respectively. In the experiment, the laser operating temperature was set to 40 • C, and the driving current was swept from 27 mA to 40 mA.

Simulation
In order to verify the feasibility of WMS-2f /1f technology and optimize the parameters of the system, a simulation model of the O 2 sensor system was established by the MATLAB Simulink platform based on the WMS-2f /1f theory and the parameters of the selected absorption line. Next, the influence of concentration and modulation coefficients on the sensor output signals were simulated by the model.
In WMS, the modulation coefficient is defined as m = a ∆v c /2 , where a is the frequency modulation depth, and ∆v c /2 is the half-width at half-maximum (HWHM) of the gas sample absorption line. At the central frequency, the amplitude of the second harmonic coefficient is: From Equation (14), it can be seen that the modulation coefficients (m) directly affect the amplitude of the second harmonic (H 2 (0, m)). Using dH 2 (0,m) dm = 0, it can be calculated that the largest second harmonic amplitude is at m ≈ 2.2. In the simulation, the concentration was set to 1%, and m was changed from 0.5 to 4. The waveform and amplitude of 2f signals under different modulation coefficients were simulated as depicted in Figure 2a,b. The largest 2f amplitude was obtained at m ≈ 2.2, which is consistent with the theoretical value.
line. According to the laser wavelength tuning experiment, the temperatur tuning coefficient of the laser were 0.014 nm/mA and 0.06 nm/°C, respectiv periment, the laser operating temperature was set to 40 °C, and the drivin swept from 27 mA to 40 mA.

Simulation
In order to verify the feasibility of WMS-2f/1f technology and optimiz ters of the system, a simulation model of the O2 sensor system was estab MATLAB Simulink platform based on the WMS-2f/1f theory and the para selected absorption line. Next, the influence of concentration and modulatio on the sensor output signals were simulated by the model.
In WMS, the modulation coefficient is defined as = ∆ / , where quency modulation depth, and ∆ /2 is the half-width at half-maximum (H gas sample absorption line. At the central frequency, the amplitude of th monic coefficient is: From Equation (14), it can be seen that the modulation coefficients ( ) the amplitude of the second harmonic ( (0, )). Using ( , ) = 0, it can that the largest second harmonic amplitude is at ≈ 2.2. In the simulatio tration was set to 1%, and was changed from 0.5 to 4. The waveform and 2f signals under different modulation coefficients were simulated as depi 2a,b. The largest 2f amplitude was obtained at ≈ 2.2, which is consistent oretical value.  The relationship between the 1f normalized 2f (WMS-2f/1f) signal and t tration was simulated under the condition of optimal modulation coefficien 2f/1f signals with a concentration of 1~20% were obtained by the simulatio the relationship was fitted as shown in Figure 3. The correlation coeffic which indicates this method has good linearity. The relationship between the 1f normalized 2f (WMS-2f /1f ) signal and the O 2 concentration was simulated under the condition of optimal modulation coefficients. The WMS-2f /1f signals with a concentration of 1~20% were obtained by the simulation model, then the relationship was fitted as shown in Figure 3. The correlation coefficient is >0.999, which indicates this method has good linearity.

System Structure
The architecture of the O2 sensor system, depicted in Figure 4, is mainly composed of three modules: light source module, optical path transmission module, and signal processing module. In the light source module, the temperature of the DFB laser (Nanoplus, nominal power is ~5 mW) was stabilized by a temperature controller (Thorlabs, TED200C, NJ, USA). A low-frequency triangular signal (2 Hz) and a high-frequency sinusoidal signal (2 kHz) were generated and superimposed to a current driver (Thorlabs, LDC210C) to modulate the laser current. The DFB laser was connected to an optical isolator (Thorlabs, IO-F-780APC) to avoid the interference of the reflected light to the light source. Then the emitting light was collimated by a collimator (Thorlabs, F230APC-780). A flip mirror and two reflective mirrors (M1 and M2) were used to induce the laser and the reference light into a compact multi-pass gas cell (URAY-Herriott Cell). With 16 times reflection in the gas cell, an effective optical path of 3.3 m was obtained. The optical signal with O2 concentration information emitted from the multi-pass gas cell was focused to a photoelectric detector (Thorlabs, PDA100A2) and then processed in a computer with a DAQ card (National Instrument, USB-6211, Austin, TX, USA) and LabVIEW software platform. The dimensions of the optical path transmission module are 47 × 32 × 24 (length × width × height), the light source module has dimensions of 31 × 26 × 11 (length × width × height), and the signal processing module has dimensions of 33 × 23 × 3 (length × width × height). By selecting lasers and detectors of different wavelengths, it is possible to detect various other gases.
To achieve reliable and accurate ambient O2 detection in field environments, the sensor design incorporates the following measures. To reduce the effect of vibration in the environment, a switchable gain Silicon amplified detector with a large active area of 75.4 mm 2 was selected. To reduce the interference of ambient O2 and the environmental light, the optical module was sealed and covered with black shade papers. Before measurement, the optical module was purged with pure nitrogen through Inlet 1, while air was discharged through Outlet 1. A vacuum pump (Kamoer, HLVP15, Shenzhen, China) was connected to Outlet 2 to pump gas into the gas cell, and a drying tube was connected to Inlet 2 to remove moisture from the gas sample.

System Structure
The architecture of the O 2 sensor system, depicted in Figure 4, is mainly composed of three modules: light source module, optical path transmission module, and signal processing module. In the light source module, the temperature of the DFB laser (Nanoplus, nominal power is~5 mW) was stabilized by a temperature controller (Thorlabs, TED200C, Perth Amboy, NJ, USA). A low-frequency triangular signal (2 Hz) and a high-frequency sinusoidal signal (2 kHz) were generated and superimposed to a current driver (Thorlabs, LDC210C) to modulate the laser current. The DFB laser was connected to an optical isolator (Thorlabs, IO-F-780APC) to avoid the interference of the reflected light to the light source. Then the emitting light was collimated by a collimator (Thorlabs, F230APC-780). A flip mirror and two reflective mirrors (M1 and M2) were used to induce the laser and the reference light into a compact multi-pass gas cell (URAY-Herriott Cell). With 16 times reflection in the gas cell, an effective optical path of 3.3 m was obtained. The optical signal with O 2 concentration information emitted from the multi-pass gas cell was focused to a photoelectric detector (Thorlabs, PDA100A2) and then processed in a computer with a DAQ card (National Instrument, USB-6211, Austin, TX, USA) and LabVIEW software platform. The dimensions of the optical path transmission module are 47 × 32 × 24 (length × width × height), the light source module has dimensions of 31 × 26 × 11 (length × width × height), and the signal processing module has dimensions of 33 × 23 × 3 (length × width × height). By selecting lasers and detectors of different wavelengths, it is possible to detect various other gases.

LabVIEW-Based Data Processing and Signal Generation Platform
A LabVIEW-based platform was developed for data processing and laser driver signal generation. The function diagram of the platform was shown in Figure 5. The analog electronic signal generated by the detector was sent to the laptop through the analog-todigital converter (ADC) module of the DAQ card. Then the collected digital signal was processed in the LabVIEW platform including harmonic extraction, filtering, and background signal fitting. The third order polynomial baseline fitting was conducted to reduce the influence of light intensity variation and waveform distortion. A dual-channel digital lock-in amplifier was developed for the extraction of 1f signal and 2f signal. Peak-to-peak optical module was sealed and covered with black shade papers. Before measurement, the optical module was purged with pure nitrogen through Inlet 1, while air was discharged through Outlet 1. A vacuum pump (Kamoer, HLVP15, Shenzhen, China) was connected to Outlet 2 to pump gas into the gas cell, and a drying tube was connected to Inlet 2 to remove moisture from the gas sample.

LabVIEW-Based Data Processing and Signal Generation Platform
A LabVIEW-based platform was developed for data processing and laser driver signal generation. The function diagram of the platform was shown in Figure 5. The analog electronic signal generated by the detector was sent to the laptop through the analogto-digital converter (ADC) module of the DAQ card. Then the collected digital signal was processed in the LabVIEW platform including harmonic extraction, filtering, and background signal fitting. The third order polynomial baseline fitting was conducted to reduce the influence of light intensity variation and waveform distortion. A dual-channel digital lock-in amplifier was developed for the extraction of 1f signal and 2f signal. Peakto-peak amplitude of 2f signal was chosen and normalized by 1f signal to calculate the concentration. The signal generator module in LabVIEW was designed to generate a driver signal for laser current modulation. Simultaneously, the module produced a reference signal with the same frequency and phase as the driver signal, which serves for the harmonic extraction of the lock-in amplifier.

Modulation Amplitude Optimization
The experiments were conducted at pressure of 1 atm and temperature of 23 °C. The frequency of the triangular signal was 2 Hz. In order to scan across the selected absorption line at 760.89 nm, the amplitude of the triangular signal was set to 0.15 V. In order to determine the optimum modulation amplitude of the sensor system, experiments on different modulation amplitudes were conducted. Measured amplitude of the 2f signal versus the modulation amplitude were shown in Figure 6. It can be seen that the variation trend of 2f signal amplitude with modulation amplitude is consistent with the theoretical, and the maximum amplitude is ∼0.02 V. Thus, 0.02 V was selected as modulation amplitude.

Modulation Amplitude Optimization
The experiments were conducted at pressure of 1 atm and temperature of 23 • C. The frequency of the triangular signal was 2 Hz. In order to scan across the selected absorption line at 760.89 nm, the amplitude of the triangular signal was set to 0.15 V. In order to determine the optimum modulation amplitude of the sensor system, experiments on different modulation amplitudes were conducted. Measured amplitude of the 2f signal versus the modulation amplitude were shown in Figure 6. It can be seen that the variation trend of 2f signal amplitude with modulation amplitude is consistent with the theoretical, and the maximum amplitude is ∼0.02 V. Thus, 0.02 V was selected as modulation amplitude.

Calibration and Fitting
O2 samples with different concentrations from 3.5% to 20.9% were prepared by mixing pure N2 with pure O2. The prepared gas samples were pumped into the multi-pass gas cell, and the extracted 1f and 2f signals were shown in Figure 7. As for the 3.5% O2

Calibration and Fitting
O 2 samples with different concentrations from 3.5% to 20.9% were prepared by mixing pure N 2 with pure O 2 . The prepared gas samples were pumped into the multi-pass gas cell, and the extracted 1f and 2f signals were shown in Figure 7. As for the 3.5% O 2 sample, the amplitude and noise level of 2f signals were roughly 1.206 mV and 2.02 µV. The SNR was calculated to be 27.06 dB. It can be seen that the maximum value of the 2f signal increases with the concentration levels, while the mean value of the 1f signal remains constant. Hence, the mean value of the 1f signal was used to normalize the 2f signal in the experiment to reduce the effect of laser power variations.   When the concentration in the gas cell reaches a stable level, the ratio of maximum (2f)/mean (1f) was recorded for 50 s at a sampling frequency of 1 Hz, as shown in Figure  8a. Figure 8b shows the relationship between the ratio of maximum (2f)/mean (1f) and the concentration. After averaging the sampling data at each concentration, linear fitting was carried out, and the relationship was calculated as follows: The square of the correlation coefficient of the fitting curve is = 0.9995. When the concentration in the gas cell reaches a stable level, the ratio of maximum (2f )/mean (1f ) was recorded for 50 s at a sampling frequency of 1 Hz, as shown in Figure 8a. Figure 8b shows the relationship between the ratio of maximum (2f )/mean (1f ) and the concentration. After averaging the sampling data at each concentration, linear fitting was carried out, and the relationship was calculated as follows:

Response Time and Stability
The response time mainly depends on the gas cell volume and the gas flow rate. In order to determine the response time of the designed sensor system, a pump was connected to the outlet of the 50 mL gas cell, and the pumping rate was set to 400 mL/min. The experiment was divided into two phases: in phase I, the O2 concentration was changed from 20.9% to 13.3% starting from point A; and in phase II, the O2 concentration was changed from 13.3% to 20.9% starting from point B. The variation trend of the measured concentration was shown in the Figure 9a. At the same time, a commercial electrochemical O2 detector (SAFEGAS, SKY6000, Shanghai, China) was connected in series with The square of the correlation coefficient of the fitting curve is R 2 = 0.9995.

Response Time and Stability
The response time mainly depends on the gas cell volume and the gas flow rate. In order to determine the response time of the designed sensor system, a pump was connected to the outlet of the 50 mL gas cell, and the pumping rate was set to 400 mL/min. The  Figure 9b. The concentration curve indicated that the designed sensor response time is ∼50 s for phase I and phase II, which is shorter than the commercial electrochemical O 2 detector. The trends of the two sensors were consistent, a finding which also verifies the effectiveness of the designed sensor system.  In order to test the stability of the system, measurements of an O2 sample with a concentration of 20.9% over time periods of ~2.2 h were performed. An amount of 8000 measured points was obtained as shown in Figure 10a. Allan variance analysis was performed to evaluate the MDL of the system. As shown in Figure 10b, the MDL is 0.054% under 1 s integration time. When the integration time reaches ~60 s, the optimal MDL is 0.009%. In order to test the stability of the system, measurements of an O 2 sample with a concentration of 20.9% over time periods of~2.2 h were performed. An amount of 8000 measured points was obtained as shown in Figure 10a. Allan variance analysis was performed to evaluate the MDL of the system. As shown in Figure 10b, the MDL is 0.054% under 1 s integration time. When the integration time reaches~60 s, the optimal MDL is 0.009%.

Atmospheric O2 Detection
The designed sensor system was also evaluated for the detection of atmospheri at the Beijing Jiaotong University. The optical module was sealed in a black box, w

Atmospheric O 2 Detection
The designed sensor system was also evaluated for the detection of atmospheric O 2 at the Beijing Jiaotong University. The optical module was sealed in a black box, which can effectively avoid the influence of ambient light. Indoor measurements were conducted in the Optoelectronic Science and Technology Laboratory. The measurements were conducted on 8 April, lasting for a total of seven hours, from 11 a.m. to 6 p.m. The summarized results of the measurements can be found in Figure 11a. The O 2 concentration in an indoor environment exhibited relatively minor variations of 20.85~21.2% during the measurement. In outdoor measurement, the sensor system was mounted on a cart and placed outside the Optoelectronic Science and Technology Laboratory. The outdoor detection experiments were conducted on 9 and 10 April, each lasting for a period of seven hours, from 11 a.m. to 6 p.m. The results of these experiments can be found in Figure 11b,

Conclusions
In this paper, an O2 sensor system using multi-pass absorption spectroscopy and WMS-2f/1f technology was developed. A DFB laser with butterfly packaging was used to target the O2 absorption line located at 760.89 nm. A compact Herriott cell was used which can provide an effective optical path of 3.3 m. The optimum modulation amplitude was obtained, and sensor performance was evaluated by experiments. Based on Allan variance analysis, the MDL is 0.054% under 1 s integration time, which can be improved to 0.009% when the integration time reaches ~60 s. Table 1 listed the performance and parameters of O2 detection systems based on TDLAS technology in recent years. Upon comparison, it is evident that the system exhibits high sensitivity. Additionally, the dual-channel orthogonal lock-in amplifier, which was designed using LabVIEW, has effectively reduced the sensor system's size and weight. This has made the system smaller, enabling easy measurement of O2 concentration in outdoor environments. Atmospheric O2 monitoring in indoor and outdoor environment on the Beijing Jiaotong University campus was conducted, and the results show that the designed system has good stability, anti-interference ability, and the ability to meet the requirements of long-term on-line monitoring of O2 in the environment.

Reference
Light Source Absorption Line Optical Path MDL cubic diffuse integrating cav-

Conclusions
In this paper, an O 2 sensor system using multi-pass absorption spectroscopy and WMS-2f /1f technology was developed. A DFB laser with butterfly packaging was used to target the O 2 absorption line located at 760.89 nm. A compact Herriott cell was used which can provide an effective optical path of 3.3 m. The optimum modulation amplitude was obtained, and sensor performance was evaluated by experiments. Based on Allan variance analysis, the MDL is 0.054% under 1 s integration time, which can be improved to 0.009% when the integration time reaches~60 s. Table 1 listed the performance and parameters of O 2 detection systems based on TDLAS technology in recent years. Upon comparison, it is evident that the system exhibits high sensitivity. Additionally, the dual-channel orthogonal lock-in amplifier, which was designed using LabVIEW, has effectively reduced the sensor system's size and weight. This has made the system smaller, enabling easy measurement of O 2 concentration in outdoor environments. Atmospheric O 2 monitoring in indoor and outdoor environment on the Beijing Jiaotong University campus was conducted, and the results show that the designed system has good stability, anti-interference ability, and the ability to meet the requirements of long-term on-line monitoring of O 2 in the environment.  Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.

Data Availability Statement:
The data presented in this study are available on request from the corresponding author.