2.2. Principle of Operation and Analysis Method

The ammonia sensor is based on WMS detection via the strongest absorption line of ammonia in mid-infrared (MIR) spectral region (the Q branch of v₂ bending band) [31,32]. At ambient pressure and temperature there is a very isolated (free from other species) absorption feature at 10.337 µm (967.35 cm⁻¹) due to the rotational transition J=3, K=3→J=3, K=3. The WMS technique has been described in detail previously [24,28,33,34,35], and here, we focus on elements specific to our implementation. WMS is fundamentally a laser absorption technique, where species concentrations are inferred through the Beer-Lambert Law, similar to direct absorption spectroscopy (DAS). One of the drawbacks of DAS is that its sensitivity is limited by low frequency noise in the signal, which originates mainly from the laser and detector noise. Also, in open-path configurations at atmospheric pressure, the absorption features are often not fully isolated such that determining the background (absorption-free baseline) signal can be challenging. These issues are addressed in WMS by modulating the laser wavelength (typically through laser current) at a relatively high frequency (typically ~10 kHz). This fast modulation is superimposed on the slower wavelength scan ramp (typically ~1–100 Hz) that serves to wavelength scan over the transitions absorption feature (as in regular DAS). The fast modulation, when combined with phase-sensitive (lock-in) detection, moves the measurement into a higher frequency regime where laser and detector noise (usually described by 1/f noise, or flicker noise) are greatly reduced thereby yielding higher signal-to-noise.

Another important feature of WMS is that it is a “derivative” technique, meaning that the 1f and 2f signals (i.e., the first and second harmonic signals found from the lock-in) closely resemble the first and second derivatives of the absorption spectrum. Measurements are therefore sensitive to spectral absorption shape or curvature rather than absolute absorption levels. This feature is particularly helpful for measurements in atmospheric pressure (or above) with non-isolated absorption features. For a robust measurement approach that is immune to laser power fluctuations (and atmospheric induced fluctuations, e.g., dust which can weaken the beam), appropriate signal normalization schemes can be used. Past research has shown that normalizing the 2f signal by the 1f signal is effective in this regard [28,33,34,36], and we follow such an approach.

We use a best-fit simulation approach, based on the 2f:1f spectrum, to infer ammonia concentration from measured signals [37]. A convenient feature (in addition to its strength) of the specific transition we employ is that it is very isolated, and though we include nearby absorption lines of other species (water and carbon dioxide), we find their effect to be completely negligible for our specific 2f:1f measurement of ammonia (for concentrations at ppb level and above). We can therefore simulate the 2f:1f spectrum for a fixed ammonia concentration and then seek the scaling factor that gives the best agreement between a measured spectrum and this reference spectrum to infer the measured concentration (equal to the scaling factor multiplied by the reference ammonia concentration). To account for atmospheric variation, which influences the signals partly and primarily due to line-broadening but also more weakly through the line intensity, reference spectra (at one NH₃ concentration) are generated for 100 different combinations of ambient pressure and temperature (where we take 5 values of pressure spanning 0.81, 0.82 … 0.85 atm paired with 20 values of temperature spanning from 1, 2, …, 20 °C) based on typical conditions in our region. (We find from numeric simulation that the coarseness in our temperature and pressure discretization introduces at most 0.1 ppb of error in NH₃). The simulated signal used is the ratio of the 2f amplitude to the 1f amplitude, denoted as R_2f/R_1f, where each amplitude is found from the in-phase (X) and (out-of-phase) quadrature (Y) components, i.e., Rnf=Xnf2+Ynf2 (where n = 1,2). The fast current modulation (10 kHz) also serves as the reference frequency input of the lock-in amplifier. The time-dependent QCL injection current is taken as the sum of a DC component (350 mA) plus a linear term (modulated at 100 Hz) for the main scan ramp plus the fast 10 kHz modulation:

The modulation of injection current leads to simultaneous variation of laser wavelength and intensity. These functions were determined in separate experiments using an ammonia reference cell and etalon for establishing the frequency axis [37]. In particular, we find a phase difference of 1.08π between the laser frequency and the current modulation, which is similar to that obtained from other QCL characterizations. The injection current, measurement path length and spectroscopic parameters from HITRAN [32] allow calculation of the absorption and signal amplitude on the detector. The software lock-in (both for measurement and signal simulation) finds the in-phase and quadrature components by multiplying the (averaged) signal by sine and cosine waveforms at the reference frequency and phase (to create the X and Y components, respectively) and then passing the resulting waveforms through identical low-pass filters (1 kHz bandwidth) [36]. A given experimental measurement is based on averaging four cycles (40 ms) of detector signal. The time needed for a single measurement is found as 40 ms (4 cycles of the 100 Hz wavelength ramp) added to 160 ms of computation time (digital lock-in analysis and spectrum fitting) giving 200 ms (data rate of 5 Hz). Figure 4 shows an example of a simulated (unnormalized) in-phase 2f and 1f signal, i.e., X_2f and X_1f, respectively, as function of laser wavelength in the vicinity of the ammonia absorption for the following conditions: P = 0.83 atm, T = 300 K, [NH₃] = 100 ppb, [H₂O] = 0.013 (50% relative humidity), and [CO₂] = 390 ppm.

Simulated lock-in signals for 2f and 1f frequency amplitudes. See text for detail.