The diagram of our CRDS system with an FMS-stabilized laser for CO₂ gas detection is depicted in Figure 1. We used two DFB-type diode lasers (NTT Electronics, NLK1L5GAAA), operated by two commercial laser controllers (Stanford Research System, LDC501). The output power and linewidth were 10 mW and 2 MHz, respectively. The primary laser (Laser-1) for CRDS was frequency stabilized and locked to a CO₂ transition based on an FMS technique, whereas a second laser (Laser-2) was used for measuring absorption-free background ring-down time. The system could be divided into two function modules: an FMS frequency-locking module and a CRDS gas mole fraction measurement module. The fiber-coupled Laser-1 output was split into two beam paths: 10% of the light went to the FMS frequency-locking module, while the remaining 90% went to the CRDS gas mole fraction measurement module. The output of Laser-2 was combined with the 90%-beam of Laser-1 via a fiber optical combiner. As the objective of this work was to measure CO₂ absorption, the absorption cell in the frequency-locking module was filled with CO₂ gases. The selection of an absorption line will be discussed in Section 2.2. This system is very adaptive. By changing the target gas in the absorption cell to different target gas species, the system could be tailored for sensing other gases.

In the frequency-locking module, the shape of the FMS signal should be optimized towards high amplitude, high signal-to-noise ratio and sharp slope to attain a best frequency locking effect. With this goal in mind, the following two efforts were made to the system. Firstly, a booster optical amplifier (BOA-1 in Figure 1, Thorlabs, BOA1080P) was used to amplify the 10%-beam of the Laser-1, as a high light intensity was beneficial for a high signal-to-noise ratio [41]. The phase modulation was achieved by an electro-optical modulator (EOM, Ixblue, MPZ-LN-20-00-P-P-FA-FA), which was driven by a radio frequency signal. Secondly, for a sharp slope, the CO₂ sample pressure in the gas cell was set at ∼200 mbar to keep the pressure broadening below 1 GHz. As the CO₂ absorption was weak, we used a Herriott multi-pass gas cell with a total path length of 10 m to increase the absorbance to ∼0.38. The transmitted light was collected by a fast photodetector (Thorlabs, DET08CFC/M) and converted into an electrical signal. The photodetector output was further amplifier by a radio-frequency amplifier (Mini-circuits, ZRL-700+) and then fed to two mixers for quadrature demodulation to obtain both the 0°-phase-shift absorption signal and 90°-phase-shift dispersion signal. Both low-pass filters after the mixers had a cutoff frequency of 1 kHz. As the FM modulation frequency of 430 MHz in this work was smaller than the spectral linewidth combining the ∼996 MHz pressure-broadening Lorentzian width (full width at half maximum, FWHM) and the ∼350 MHz FWHM Doppler width, both the signal profiles (see Section 3.1) were suitable to use for feedback controlling the laser frequency to the spectral line center. In this work, we utilized their difference signal as the error signal for laser frequency stabilization instead of only the dispersion signal. This would enable a possible cancellation of common offset drifts if happened in both channels of similar electronics. A proportional-integral-derivative controller (PID, New Focus, LB1005-S) was employed to finely regulate the operation current of Laser 1 and subsequently the laser frequency. A manual offset could be added to the error signal for fine frequency tuning.

The gas mole fraction measurement module in Figure 1 is based on the CRDS technique. The absorption coefficient α v at laser frequency v is given by Eq. 1 [42–44]: α v = 1 c 1 τ v − 1 τ 0 = P · X · S T · g v (1) where, τ v and τ 0 are the ring-down times with and without absorbers in the cavity, respectively. c is the speed of light, P is the total gas pressure and X is the mole fraction of the target gas. S T and g v are the intensity and profile of the gas absorption line as a function of temperature T and frequency v , respectively. Therefore, the mole fraction can be obtained based on τ 0 and τ v 0 , which is the ring-down time at the line center frequency v 0 . Generally, τ 0 of an absorption-free ring-down cavity is considered as a constant, as τ 0 is nominally only determined by the reflectivity R of the cavity mirrors and the cavity length L . However, in real-world measurement applications, τ 0 may drift as environmental conditions vary.

To address the τ 0 drift, Laser-2 was introduced into the system. Laser-2 operated at an absorption-free wavelength close to the wavelength of Laser-1, for real-time baseline τ 0 measurements [45]. As illustrated in Figure 1, the output of Laser-2 and the majority (90%) of light output from the frequency-stabilized Laser-1 were combined via a fiber optic coupler and then passed through another booster optical amplifier (BOA-2 in Figure 1, Thorlabs, BOA1080P) to increase the beam optical power [46, 47]. An acousto-optic modulator (AOM, Smart Sci &Tech, SGTF200-1600-1P) operating at 80 MHz could be turned on or off with an extinction ratio of 60 dB, and acted as an optical switch to cut off the deflected beam to the cavity and to enable observation of the cavity ring-down process [7, 47, 48]. In this work, we preferred to operate the BOA at a constant operation condition, and use a separate AOM for making optical switching. The first-order deflected beam generated by the AOM experienced an 80 MHz frequency shift from the original laser frequency. This was much less that the spectral line width (with Lorentzian and Doppler components of ∼996 MHz and ∼350 MHz, respectively), but caused a ∼2.5% deviation from peak absorption. In this work, we calibrated measurement ring-down times against reference gas samples with various mole fractions. Therefore, this 80 MHz offset out of line peak did not impact correct mole fraction determination of late measurements under the same operation conditions. A slightly higher sensitivity on laser frequency jitter when operating out of line center did not make a noticeable impact. Alternatively, we could compensate for this frequency shift by adding an offset to the error signal in the frequency-locking module. An optical isolator (60 dB isolation, QINGHE Photonics, PMIS-1600-D-9-10-FA-F) was appointed to prevent the reflected light from the cavity mirror from affecting the laser operation and stability. Since the mirror reflectivity may vary slightly in different polarization states of the light [49, 50], a half-wave plate (λ/2) and a polarization beam splitter (PBS) were placed in front of the cavity to maximize and produce a linearly polarized light to the cavity. This established a well-defined linearly polarized light to the cavity for its stable operation. The subtraction of absorption-free ring-down time measured by Laser-2 minimizes impact of any possible birefringence effect. The 200-mm optical cavity was manufactured with quartz glass and comprised two mirrors. The ring-down time of the empty cavity was ∼98 µs, implying a mirror reflectivity of ∼99.993% and a cavity finesse of ∼44,880. The free spectral range (FSR) of the cavity was 750 MHz. We used quartz glass material for building a light-weight robust ring-down cavity. The long empty-cavity ring-down time of our system allowed the length of the cavity to be miniaturized (at a cost of proportionally reduced ring-down time) for future applications. An optical resonance between the ring-down cavity and the laser radiation was reached by scanning the cavity length [13, 51, 52], namely, by applying a sawtooth waveform to a piezoelectric transducer (PZT) to move one of the cavity mirrors for 1.1 FSR at 10 Hz. When the optical cavity was moved into optical resonance, the power of the cavity transmitted light at a μW level was received by a photodetector (GPD, GAP1000FC). Once the signal of the photodetector exceeded the preset trigger level of 0.6 V of a comparator circuit, it then generated a trigger signal, which triggered the AOM to cut off the incident light and triggered the data acquisition card (National Instruments, USB-6356, 16 bit analog-to-digital converter, 1.25 MS/s) to capture the resulting signal of ring-down decay process. Each ring-down profile was sampled for 400 μs or 500 data points. An example of photodetector ring-down signal profile will be presented late in Section 3.1. By numerically fitting the recorded ring-down signals to an exponential decay function based on a corrected successive integration (CSI) algorithm [53], the ring-down times were determined.

In the above system, the drivers of lasers and BOAs, the radio frequency signal source, the PID controller and the data acquisition card were individual commercial products. It would be possible in the future to integrate all these functions into a compact package and to miniaturize the system.

In this system, both FMS and CRDS techniques were used. FMS was for stabilizing and locking the frequency of Laser-1 to an absorption feature of target gas molecules filled in a gas cell—a CO₂ absorption gas cell in this instance, whereas, the primary purpose of the system is for CRDS sensing measurements. Therefore, the selection of the CO₂ absorption line and the corresponding frequency of Laser-1 used by the CRDS for sensing measurements of CO₂ gas needed to consider: 1) the absorption line possesses an appropriate intensity, so that a resulting absorbance not too much lower than the mirror losses (1-R = 70 ppm) was preferred; 2) it is an isolated absorption line so to reduce the influence of other nearby absorption lines which may have different pressure broadening and pressure frequency shifting; 3) it is free from interferences from other gases in the atmosphere, such as water vapor, methane, etc.

In this study using NIR diode lasers, we chose the CO₂ absorption line at the frequency 6251.761 cm⁻¹ (or the wavelength 1599.55 nm) with the following characteristic details: transition quantum number notation (30⁰1–00⁰0) R (36)e, line intensity 5.4 × 10⁻²⁴ cm/mol, air-broadening coefficient (value of half width at half maximum, HWHM) 0.0678 cm⁻¹/atm and self-broadening coefficient (value of HWHM) 0.083 cm⁻¹/atm (values extracted from the HITRAN database). Figure 2 shows the simulated absorption spectra of 400 ppm CO₂, 2% H₂O, 2 ppm CH₄, 10 ppb NO₂, 300 ppb NO, 300 ppb N₂O and 100 ppb CO for the frequency region from 6251.5 cm⁻¹ to 6252 cm⁻¹. The simulation spectra were at a temperature of 300 K, a total air pressure of 200 mbar and a path length of 1 cm, based on spectral parameters from the HITRAN database. These mole fraction values were typical for normal atmospheric air.

The absorbance of CO₂ at the line center was 2.28 × 10⁻⁷, while the maximum absorbance among the interfering gases was 6.21 × 10⁻¹⁰ by H₂O. The absorbance of the other interfering gases was at the level of 10⁻¹² or less, and was below the detection limit of our CRDS system. To minimize the impact of residual H₂O vapor in the input gas sample, we let the inlet gas sample pass through a 20-cm-long silica gel desiccant. It reduced the H₂O vapor from 2% to (0.4–0.6)%, corresponding to a residual absorbance of (1.3–1.9) × 10⁻¹⁰. The ring-down time of the system at this CO₂ absorption was about 59 μs and could be measured by data acquisition electronics reliably.

As for the frequency of Laser-2, it was managed and finely tuned so that it was away from any gas absorption lines and more importantly, it did not resonate with the optical cavity at the same time as Laser-1. This ensured that the ring-down decays of each laser were observed separately without being disturbed. The laser beam geometry was mode matched to the cavity longitudinal modes by using lenses, so that cavity transverse modes did not get excited. The frequency difference of Laser-2 should meet the requirement in Eq. 2. v l a s e r 2 − v l a s e r 1 ≠ m   ∗   F S R (2) where v l a s e r 2 and v l a s e r 1 are the frequencies of Laser-2 and Laser-1, respectively. m is an integer number. When not in optical resonance, the highly reflective cavity mirrors effectively blocked the input laser radiation from passing the cavity [13, 14]. The time interval between the ring-down events of Laser-1 and Laser-2 during the PZT cavity length sweep was manually set for more than 1 ms by finely tuning the frequency of Laser-2. In this work, the frequency of Laser-2 was set at 6257.762 cm⁻¹. After passing through the silica gel desiccant, the maximum absorbance among the above gases at the frequency of Laser-2 under the same simulation conditions was 1.66 × 10⁻¹⁰, which was of a similar magnitude as the residual H₂O vapor absorbance at Laser-1 frequency.

Based on the selected CO₂ absorption line discussed in Section 2.2, two DFB lasers (NTT Electronics, NLK1L5GAAA) centered around wavelength 1,599 nm were used as light sources. Laser-1 was operated at 35°C and 69 mA. Wavelength tuning was achieved via the laser operation temperature and current. By applying a sawtooth waveform (50 Hz, 2 Vpp, as shown in Figure 3A) to the current modulation port of Laser-1 controller, the frequency of Laser-1 could be scanned over the CO₂ absorption line at 6251.761 cm^-1. The EOM was modulated at 430 MHz with a modulation index of 0.2. Figure 3B presents the dispersion and absorption signal waveforms of the FMS obtained by the two mixers for quadrature demodulations. The error signal used for frequency locking was obtained by their difference.

To stabilize and lock the laser frequency, the frequency of Laser-1 was turned to the CO₂ absorption line center by shifting the laser operation current from 69 mA to 85.4 mA. The error signal was fed to the PID controller and its output was connected to the modulation port of Laser-1’s controller instead of the sawtooth sweep signal. Comparisons in the error signal and ring-down time, with and without laser frequency locking, are plotted in Figure 4. For these measurements, the cavity was filled with ambient air with higher CO₂ mole fraction to a 200-mbar pressure. Before locking, the average value of error signal in Figure 4A was 16.3 mV at a manual laser frequency setting. After activating the PID controller, the mean value got to 0 mV. Furthermore, the standard deviation was greatly reduced from 4.23 mV to 0.133 mV, denoting a ∼32 times improvement in the laser frequency stability. For the ring-down time measurements with CO₂ absorption in Figure 4B, its fluctuation was reduced by improved laser stability. Correspondingly, the mean value of the 1000 ring-down times varied slightly from 19.175 μs to 19.074 μs while the standard deviation fell significantly from 0.228 μs to 0.053 µs The higher frequency stability made a 5-fold reduction in fluctuation of ring-down time measurements as demonstrated in Figure 4B. The exhaled CO₂ of indoor air was responsible for this shorter ring-down time. To get the ring-down time quickly and efficiently, the number of acquisition points for these ring-down profiles was reduced to 125, with a corresponding acquisition time of 100 μs which was about five times the ring-down time. Figure 5A depicts the acquired ring-down profile and the modelling of exponential decay via a CSI algorithm. The maximum residual between the data and the fitting curve is about 0.002 V for the ring-down signal profile with a magnitude of 0.6 V, as shown in Figure 5B.

When a laser is in free-running operation mode without frequency stabilization and locking, not only frequency jitter but also a frequency drift occurs. Therefore, tests on the long-term stability of the frequency locking effect were performed. A high-stability wavelength meter (Bristol Instruments, model 721 spectrum analyzer) was used to measure the frequency of Laser-1. Figure 6 reports the comparison of wavelength measurement data with and without locking the laser frequency to the CO₂ absorption line for 7 h. Obviously, without locking there was a drift during the first 3.5 h. However, with the help of frequency locking, the laser frequency was precisely stabilized to the absolute frequency of the CO₂ absorption line, and remained constant throughout the latter 3.5 h of measurements. In summary, the frequency locking based on FMS improved the laser frequency stability and effectively facilitated the subsequent high-precision CRDS measurements.

The detection limit of the CDRS system is usually given by the ability to determine the minimum change Δ τ in ring-down times from an absorption-free ring-down time τ 0 . Applying this to Eq. 1 leads to Eq. 3: α min = Δ τ c τ 0 2 (3)

In one experiment, the gas in the 200-mm-long ring-down cavity was slowly pumped empty by a vacuum pump to become free of absorption. A total of 15,000 ring-down times of the empty cavity were acquired within a total time of 1650 s (or at a data rate of 9.1 Hz). These measurements are displayed in Figure 7A, together with an Allan deviation analysis [54] on the measurements for evaluating long-term system stability, detection limits and optimum averaging time as presented in Figure 7B. The optimum averaging time happened at around 5.0 s, and the corresponding minimum detection limit of absorption coefficient came to 4.4 × 10⁻¹¹ cm⁻¹. When applying this to the CO₂ absorption measurement conditions (Figure 2), it amounted to a minimum detectable mole fraction of 78 ppb of CO₂. The time-normalized noise equivalent absorption coefficient at 1 s was 7.3 × 10⁻¹¹ cm⁻¹/Hz^1/2. It was noted that the Allan deviation started to increase after 5 s. This was possibly due to a mediocre hermeticity of the ring-down cavity and surface adsorption/desorption and minor laser frequency fluctuations under such high measurement sensitivity. The plot shows the ultimate stability of the system’s “absorption-free” background. Therefore, drifts of an empty-cavity ring-down time should be checked within a <5 s time interval before it starts to increase. For measurements with gas samples in the cavity, a change in ring-down time relative to such absorption-free ring-down time measured by laser-2 reduces impact of background drifts.

We made comparison measurements on the same ring-down cavity with and without laser frequency locking. The Allan deviation plot for the measurements with-out laser frequency locking is presented also in Figure 7B. For averaging time of less than 10 s, the improvement in Allan deviations with laser frequency stabilization is about x5.

CO₂ standard gas samples at mole fractions of 400 ppm, 600 ppm, 800 ppm, and 1000 ppm (with an uncertainty of 2%, from a commercial supplier) were used to calibrate the CRDS system. With the gas flow rate fixed at 60 mL/min, the measurement time at each and every mole fraction lasted for more than 10 min and the cavity was purged by N₂ gas when changing gas samples to avoid any interference. Figure 8 depicts the results of the calibration measurements. Apparently, the system exhibits a good linear response over a wide range of CO₂ mole fractions with an outstanding linear correlation coefficient of 0.99999. The fitting parameters a and b of the straight-line modelling will be used for calculating CO₂ mole fraction of CRDS measurements of unknown atmospheric samples.

Measurements of ambient CO₂ were performed by our CRDS system and spanned approximately 7 h. Both the temperature and pressure values were recorded simultaneously in real-time to avoid errors in the mole fraction introduced by their fluctuations during the long-time measurement. Each mole fraction value was obtained based on averaging 14 pairs of acquired ring-down times τ and τ 0 , within a measurement time of 1.5 s. In addition, a top-quality commercial CRDS instrument (Picarro, G2401) was applied for comparison of the mole fraction data to verify the reliability of our developed system. Figure 8 shows the results of the comparison. At the start of the measurement run, the sampled ambient air in the lab contained a significant exceeding amount of exhaled CO₂. After the laboratory became unoccupied, the CO₂ mole fraction gradually approached its typical atmospheric value. Moreover, it is clearly shown in Figure 9 that the mole fraction trends between the two devices were in high agreement. The relative deviation between their measurements was within ∼0.5%, demonstrating the reliability of our CRDS system.