1. Introduction

Laser absorption spectroscopy (LAS) with tunable semiconductor lasers is a commonly used technique for spectroscopic measurements of trace gas concentrations. It offers great flexibility, relatively simple and robust setup, and the ability to achieve high measurement precisions [1–7]. However, a common drawback observed in field deployable sensors is the lack of long-term stability, which is the most critical parameter to achieve high accuracy guaranteed over extended periods of time (e.g., [8–10]). Although LAS sensors can often achieve remarkably high short-term sensitivity/precision, their accuracy is inevitably eroded by long-term drifts that arise mainly from environmental factors affecting opto-mechanical stability of the instrument or from drifts in the electronics. Such drifts are not purely random and cannot be easily removed through time averaging [11, 12].

In particular, mechanical instability and thermally-driven optical alignment changes can result in laser beam steering causing fluctuations of parasitic optical interference fringes that are almost unavoidable in systems based on highly coherent laser sources [11–13]. While LAS measurements can be performed using signal correction algorithms/hardware that account for photodetected power fluctuations (through direct absorption spectra fitting or power normalization in the case of wavelength modulation spectroscopy, WMS), these approaches are ineffective in suppression of optical fringes (especially those with a shape comparable to that of the target transition). Methods to mitigate fringe-induced drifts include: careful optical design, precise temperature control of the entire sensing instrument, or use of costly materials with low coefficients of thermal expansion (e.g., [5, 14–17]). Unfortunately, not only are these methods expensive or consume much power, but the improvement they provide is usually still not sufficient to obtain absolute long-term stability of a sensing system. Therefore, in order to ensure accuracy of the concentration measurement over long time, periodic calibration of the sensor with certified gas mixtures is usually performed [2, 12].

Conventional calibration schemes involve either using a separate optical branch with a reference gas cell probed by the same laser source and an additional detector, or cycling between the reference gas and the sample gas through a single gas cell probed by the same laser and detector at different times [3–7, 15, 18–22]. The approach with a separate optical branch containing the reference cell has two important drawbacks: 1) with two distinct optical paths the reference signal is subject to different parasitic fringes than the sample signal, and 2) this technique requires two photodetectors which are subject to their own sources of noise and drift. The second method that cycles two gases through the same gas cell seems to be free of such issues; however, since the measurements are not performed simultaneously and the parasitic fringes tend to drift, the fringe correction is never perfect. Moreover this single-gas cell approach brings challenges of gas handling, maintenance, reduced sampling time due to limited cell evacuation times, and lack of portability. All of these issues represent an impediment for autonomous systems.

A number of calibration techniques have been developed to account for these issues. Several involve using permanent inline reference cells to ensure minimal gas handling with only one optical path. One calibration approach reported in the literature uses an in-line reference cell which contains a gas species that is different from the target gas but with an absorption line that is near in frequency and can be measured together with the target gas line within a single laser scan [23, 24]. Another technique involves using an in-line reference cell of the same gas at different pressure and taking advantage of different WMS parameters to retrieve the reference and sample signals [25]. However, all these in-line reference cell approaches show some challenges in accounting for crosstalk between the sample and reference signals. Moreover, wavelength-dependent optical fringes can affect the sample and reference signals in slightly different ways, thus affecting system long-term performance.

Here we present a new in-line revolving reference cell approach for real-time calibration of laser spectroscopic measurements that do not require long optical paths. The system design ensures that sources of drift are minimized, while sample and reference signal crosstalk is eliminated. This results in significantly improved long-term system stability. Section 2 details the configuration of an experimental setup. In Section 3 the operating principle of this measurement technique is discussed and Section 4 presents experimental results demonstrating performance of the prototype system.

2. System configuration

A simple proof-of-concept setup has been developed to study the effectiveness of the revolving in-line gas cell calibration approach. This method is limited by the opto-mechanical design of its gas cell to relatively short optical paths. However by targeting the strongest fundamental rotational-vibrational transitions of various chemical species in the mid-infrared (mid-IR) [4, 26], high sensitivity trace-gas detection can be realized. In this work a compact mid-IR quantum cascade laser (QCL), which has a great potential of providing a miniaturized sensor system, has been used for proof-of-concept studies. The revolving in-line cell contains three sub-cells bored orthogonally to the plane of an aluminum disc and positioned in an axially symmetric pattern (Fig. 1(a)). All the sub-cells share two large optical-quality windows supported by the aluminum disc to form the gas cell assembly. For these experiments, the windows have been affixed to the aluminum disc with a low viscosity (300-450 cps) UV-curable epoxy (Norland Optical 61). After affixing the windows, the zero gas and reference gas sub-cells were filled and sealed through radially drilled holes. Once the UV-curable epoxy was fully cured, the gas compositions in the sealed cells have been observed to be virtually constant over the time of the experiment (< 1ppmv change over more than 6 months). To create an opening in the sample sub-cell, the aluminum disc is cut such that its outer wall is removed, providing access for the ambient air (Fig. 1(a)). The motion of the revolving cell additionally forces mixing of the ambient air into the sample sub-cell. In this configuration the three sub-cells (a zero-gas sub-cell, a reference (span) gas sub-cell, and a sample sub-cell) can be individually probed by the laser beam by rotating the assembly.

 

Fig. 1 (a) A schematic showing the gas cell construction and its placement on a Newport URB100CC rotary stage. The red dot marks the optical axis of the beam as it passes through the zero-gas sub-cell. (b) A schematic of the experimental layout demonstrating a basic arrangement of the optical setup with the laser beam transmitted through the revolving gas cell.

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Since the three sub-cells share the same optical interfaces, the differences between the parasitic interference fringes formed within the optical path for each cell are minimized. (The amplitude of the etalon filter effect can be further reduced by positioning the revolving in-line cell at an angle with respect to the incident laser beam.) Based on machining tolerances of the middle aluminum disc forming the cells (0.127 mm parallelism over 50.8 mm) and <1 arcminute parallelism for the two windows used (Edmund Optics 50 mm diameter uncoated CaF₂ windows), we estimated the maximum change in the fringe pattern associated with the worst case deviation of optical surface position. The rotation stage wobble of 50 µrad could be ignored due to much lower impact on the fringe stability. Based on the tolerances of system dimensions the maximum change in system transmission between the sub-cells was estimated at approximately ± 3 × 10⁻⁴ (this number was estimated using Fresnel reflectivity at the window surfaces at an incident angle of 50° used in this work; further reduction of this effect will be possible by miniaturizing the optomechanical construction and setting the incident angle at the Brewster angle of 54.7°, an effective suppression of reflection that takes advantage of the intrinsic purity of QCL polarization [27]). The short distances between the optical surfaces (8 mm for the cell length and 3 mm for the window thickness) generate fringes with free spectral range (FSR) of 0.625 cm⁻¹ for the cell and 1.18 cm⁻¹ for the windows, which is much larger than the 0.2 cm⁻¹ full width at half maximum (FWHM) of the target absorption line. Thus the residual fringe pattern, if present, will primarily act as a broadband baseline for each sub-cell spectral measurement. When the coefficients of thermal expansion of the materials involved are considered, this influence is expected to have negligible impact on the system performance.

The studies of the revolving cell calibration method have been performed using detection of carbon dioxide (CO₂) in the atmosphere as a test gas. CO₂ is a good test molecule because it is an important greenhouse gas that requires monitoring of atmospheric levels (~400ppmv) with high precision and high accuracy (approximately 1:1000 or better). The experimental setup shown in Fig. 1(b) consists of a thermoelectrically cooled (TEC) distributed feedback quantum cascade laser (DFB-QCL, provided by Corning Inc. for this study), the revolving reference cell with 8mm active optical path, and a TEC-cooled mercury-cadmium-telluride (MCT) photodetector (Teledyne-Judson, model J19TE3:5.5-66C-R01M, D* = 1.7 × 10¹⁰ cm Hz^1/2 W⁻¹). The 4.23 μm DFB-QCL targets the R6 line in the ν₃ ro-vibrational band of CO₂ at 2354.43 cm⁻¹ (S_ηη’ = 2.256 × 10⁻¹⁸ cm⁻¹/molecule cm⁻², γ_air = 0.0853 cm⁻¹/atm, γ_self = 0.1140 cm⁻¹/atm). The reference cell was mounted on a Newport URB100CC high speed rotational stage (see Fig. 1(a)) and its rotation was controlled via a Labview interface (future miniaturization would incorporate rotation stages capable of >10 rev./sec., enabling measurement of sub-second timescale environmental fluctuations). During experiments the rotational stage is driven at 360 deg./sec (1 rev./sec.). Given the dimensions of the revolving cell, each sub-cell was probed for approximately 0.2 seconds during one revolution. The acquisition bandwidth of the DAQ (NI USB6251) is 1.7 MHz. The photodetector bandwidth is 1.5 MHz. The zero gas sub-cell was filled with pure nitrogen and sealed, and the reference sub-cell was filled with ambient air and sealed (CO₂ concentration of 383.9 ppmv was estimated using direct absorption spectral fitting). The sample sub-cell remained open to the ambient laboratory environment and was flushed through revolution of the in-line reference cell. A function generator is used to provide sawtooth modulation to the laser driver (Wavelength Electronics, QCL500), which scans the QCL current at a rate of 100 Hz up to 2 kHz and provides an optical frequency scan across the target absorption line. The current scans start below laser threshold, which allows for measurement and correction of the detector offset (e.g. dark current, pre-amplifier offset, etc.). A Labview program in conjunction with Matlab routines performs signal processing and data storage.

3. Operating principle

The in-line revolving gas cell concept is best demonstrated in the context of direct LAS. In semiconductor laser based direct LAS implementations, frequency scanning is usually performed through variation of the injection current, which also results in variation of the laser intensity (i.e., the laser light-current curve, L-I). Therefore, in the frequency scanned LAS system the photodetected light intensity is affected by changes related to the sample transmission, intrinsic laser intensity changes due to the L-I curve, and any transmission fluctuations caused by parasitic optical fringes or broadband absorption/scattering present in the system. All of these characteristics are noticeable in the direct LAS data in Fig. 2(a) acquired by the system shown in Fig. 1 for two sub-cells of the revolving gas cell. The raw detector signal proportional to light intensity is acquired as a function of time (I(t)) with intervals t_n between consecutive points determined by the DAQ sampling rate.

 

Fig. 2 (a) Raw laser scan data collected for a sub-cell containing a zero-gas (background scan shown in black) and for a sub-cell containing a reference gas (reference scan shown in red). (b) The reference gas cell scan is background-corrected to isolate the actual reference gas spectrum. This background-corrected signal can be fitted by a spectral model (red) and the fit residuals are shown in the lower panel. (c) A reference scan from (a) in black fitted by the spectral fitting model (red) assuming polynomial baseline for the QCL L-I curve (the plotted spectrum is baseline-corrected). Optical fringes are evident in the residuals of (c) while they are strongly suppressed in (b).

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It is a common practice in direct LAS sensing to use spectral fitting algorithms to retrieve an accurate concentration of the target analyte [2, 5, 19]. Such algorithms require precise calibration of the optical frequency axis (I(t)→I(ν) for frequency or I(t)→I(λ) for wavelength) in order to perform a line-by-line spectral transmission simulation based on molecular transition parameters obtained from a spectral database. The broadband transmission and/or laser intensity drift are usually accounted for by the spectral transmission models through assumption of a polynomial baseline. However, the accuracy and precision of the fit can be compromised by optical fringes, which are difficult to model and cannot be removed through signal averaging.

In our spectral measurement technique the gas cell rotates at constant speed and for each sub-cell multiple spectra are collected and averaged. The number of spectra averaged for each cell depends on the experimental parameters chosen (data acquisition rate, scan frequency, etc.). As explained later in the text, the sample and the reference raw spectra are background-corrected in the data post-processing, which results in an efficient suppression of any unwanted baseline and fringes. The raw spectra shown in Fig. 2(a) clearly indicate that in addition to a signal originating from the gas within the sub-cells there is a significant absorption of the light within the beam path exposed to open air. In this particular case the total optical path outside the revolving cell is ~2 cm, which results in a background absorption of up to 35%. As shown in the Fig. 2(b) the background-correction effectively removes the large background absorption, the laser L-I dependence, and the fringes in the system. The latter is particularly important, because the uncontrolled drift of the parasitic fringes deteriorates long-term stability of the system. The fringe-suppression capability is noticeable in the residuals of the background-corrected spectrum in Fig. 2(b) as compared to the residuals of the conventional spectral fit in Fig. 2(c) indicating optical fringes of up to 3% level (peak-to-peak).

The key assumption in this technique is that the parasitic fringe pattern in the system, the atmospheric transmission (i.e., the background absorption outside the cell), and the optical alignment will not change within the time required for one full revolution of the cell during which all three sub-cells are sampled. The total optical path from the laser to the detector can be analyzed as two segments: the 8mm active optical path (L_a) within the cell, and the optical path outside the cell (L_b) contributing unwanted background gas absorption. The contribution of the background absorption can be minimized by purging the path with zero-gas or by minimizing the open path length L_b (e.g., by using optical fibers or any other solid waveguides). In any case the intensity received by the detector for all three sub-cells (I_Zero, I_ref, I_sample) can be described by the Beer-Lambert law of linear absorption:

4. Experimental measurements

The system performance analysis was performed in two operation modes: 1) a single spectral point measurement and 2) full spectrum mode. Both measurements were performed by scanning the laser frequency across the target transition. The single spectral point measurement was performed by analyzing data at the spectral point of interest (either at the spectral peak or away from it), while the entire scan was used in the full spectral mode. In a full spectral mode the concentration retrieval was performed either by conventional spectral fitting or by a specially optimized method utilizing spectral correlation between the sample and the reference spectra developed specifically for this system. The spectral fitting was performed using a nonlinear least squares curve fitting with the model absorption spectrum obtained by line-by-line simulation using the HITRAN database parameters and Voigt lineshape function along with a 3rd order polynomial for the transmission baseline [28]. Concentration, pressure, and absolute optical frequency were retrieved by the spectral fitting algorithm.

For convenient comparison with other absorption systems detection limits are usually quoted as acquisition bandwidth normalized data. If data averaging is performed over N consecutive data points dominated by random noise, the total measurement noise is reduced, which can be interpreted as effective reduction of the measurement bandwidth by $\sqrt{N}$. However, it should be noted that with the revolving gas cell technique, the data acquired during one cell revolution (1 s) correspond to a maximum of 0.2 seconds of averaged data for each sub-cell. This introduces a limitation in the duty-cycle of the actual measurement, and as such, for a well optimized system the noise observed within 1 second of the actual measurement time should be approximately$\sqrt{5}$ higher than the bandwidth normalized value estimated for a single spectral point. Some strategies to improve the measurement duty cycle are presented in this section. For clarity both the noise observed within the actual measurement time (presented as sensitivity achieved within 1 s measurement time) as well as the acquisition bandwidth normalized sensitivity for a single spectral point (presented as bandwidth normalized detection limit) will be quoted throughout the paper.

4.1 System stability in different operation modes

Long-term direct LAS spectroscopic measurements were performed by scanning the DFB-QCL optical frequency across the target absorption line at a scan-rate of 100 Hz. 500 spectral points were acquired within each scan with an acquisition bandwidth of 1.5 MHz determined by the photodetector. For each sub-cell the acquired spectral profile was averaged 15 times (yielding an effective acquisition bandwidth of 100 kHz for each spectral point within the scan). The reference and sample spectra were corrected according to Eqs. (4) and (5). To assess signal stability a single spectral point positioned at the peak of the target absorption line was analyzed over time. This signal was converted to CO₂ concentration by using a calibration factor determined before this measurement. The time plots of the raw and corrected signal values are shown in Figs. 3(a) and 3(c), respectively.

 

Fig. 3 (a) Time series measurements of the raw signals acquired for the sample, zero-gas, and reference sub-cells are shown in the top panel. The background-corrected reference gas concentration data are shown in the bottom panel. (b) Allan deviation calculated using the raw (black) and background-corrected (red) reference signal from (a). The grey line in (b) represents Allan deviation plot generated for white noise for comparison. CO₂ concentration in the laboratory air calculated using the background-corrected sample signal absorption peak value is shown in (c).

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Allan deviation analysis of the signal representing optical absorption is used to assess the long-term stability of the system. The Allan deviation plot calculated for the raw reference signal measured at the absorption peak and normalized by the first point in the time plot (shown in black in Fig. 3(b)) differs significantly from the curve calculated for the background-corrected (Eq. (4)) measurements shown in red in Fig. 3(b). While the uncorrected measurements become limited by the system drift after only ~45 seconds of averaging time, the background-corrected measurements continue to be random noise limited until ~1000 (with slight increase around 50 s due to some periodicity in the data originating most likely from incomplete fringe suppression and/or slow laser frequency oscillations [11]) seconds. In this experiment the 1σ sensitivity achieved within 1 s measurement time for the corrected reference signal is 2.8 × 10⁻³ (which corresponds to 14 ppmv of CO₂) and the ultimate minimum detection limit achieved after 1,000 s of actual measurement time is 1.9 × 10⁻⁴ (which corresponds to 0.95 ppmv of CO₂). If the measurement bandwidth and number of averages are both taken into account, the bandwidth-normalized value of the short-term detection limit becomes 8.85 × 10⁻⁶ Hz^-1/2. This number reflects ultimate sensitivity achievable with the system if the actual duty cycle (the time spent on measurement of the absorption peak divided by the total measurement time) approaches 100%. Of course system drift correction requires additional measurements (e.g., for determination of the baseline drift), which results in reduction of the effective duty cycle. Thus an optimization of the system parameters is required to assure best sensitivity with minimal long-term drifts.

As shown in the example scans from Fig. 2, it is expected that the background-correction applied via Eq’s (4) and (5) increases measurement noise by a factor of $\sqrt{2}$ due to the division of two signals with uncorrelated noise; however the Allan plots in Fig. 3(b) clearly show a different trend. This is attributed to uncontrolled variations in the absorption originating from the optical path outside the gas cell, which effectively increases noise in the raw signal. However these variations occur as common-mode signal fluctuations in all three traces shown in Fig. 3(a) and are effectively suppressed by the background-correction procedure, resulting in significant improvement of the short- and long-term performance. To assess the effectiveness of the background-correction method without the influence of ambient CO₂ fluctuations, long-term measurements of the reference cell transmission (shown in Fig. 4) were performed at an optical frequency away from the absorption line.

 

Fig. 4 (a) A raw transmission measurement (top) and a background-corrected transmission measurement (bottom) performed for a reference gas sub-cell at an optical frequency away from the CO₂ absorption line are showed as time series. (b) Allan plots produced from the time series in (a) . The grey line in (b) represents white noise trend for comparison.

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Similarly to Fig. 3(a), data in Fig. 4(a) also indicate that the background-corrected signal shows significantly better long-term stability. Here the 1σ sensitivity achieved within 1 s measurement time is 6.9 × 10⁻⁴ (corresponding to bandwidth-normalized σ = 2.0 × 10⁻⁶ Hz^-1/2 for β = 1.5 MHz and N = 12) for the uncorrected absorption measurement and 9.7 × 10⁻⁴ (bandwidth-normalized σ = 2.7 × 10⁻⁶ Hz^-1/2) for the background-corrected measurement. The difference in noise between the uncorrected and background-corrected measurements is approximately $\sqrt{2}$, which is consistent with the error propagation expected from Eq. (4). A factor of 3 difference between the bandwidth-normalized sensitivities for off-line (2.7 × 10⁻⁶ Hz^-1/2) and on-line (8.85 × 10⁻⁶/Hz^1/2) measurement indicates that the noise observed in the on-line measurements in Fig. 3 was additionally affected by fluctuations associated with the CO₂ signal (most likely due to incomplete removal of fluctuations associated with the absorption outside the gas cell or due to laser frequency instabilities that are faster than the full cell rotation of 1s). Based on this off-line stability test the 1σ CO₂ concentration detection sensitivity for 1 s measurement time is 3.5 ppmv for the uncorrected signal measurement and 4.85 ppmv for the background-corrected measurement. Without background-correction the system drift deteriorates long-term performance for measurement times beyond 10-20 s. Despite the $\sqrt{2}$higher short-term noise, after measurement time of 3,500 seconds the background correction provides the ultimate detection sensitivity of 0.15 ppmv (corresponding to ~3.0 × 10⁻⁵ noise equivalent absorption), which is an order of magnitude better than ultimate sensitivity without background-correction. Except for the slight increase around 50 s caused by periodic changes in the signal (most likely due to the same process as in Fig. 3), the Allan plot for the background-corrected measurements closely follows an ideal $1/\sqrt{t}$ trend (where t is the averaging time).

Data presented in this section clearly show that a large discrepancy (factor of ~360) exists between the sensitivity achieved within one second of actual measurement (9.7 × 10⁻⁴) and a one second sensitivity (2.7 × 10⁻⁶) estimated from the bandwidth-normalized measurements. This discrepancy is significantly larger than expected from the duty-cycle associated with the rotation of the gas cell. However this is expected because full spectral scanning is performed instead of single spectral point acquisition, which reduces the effective duty cycle by factor of 500 (the bandwidth-normalized sensitivities are quoted for a single spectral point within the 500-point scan). Moreover parameters of the data acquisition process have not been optimized to match the acquisition bandwidth of the system, which results in significant under-sampling of the signal.

After sampling rate optimization, a more efficient data averaging can be performed enabling single-ppmv CO₂ sensitivity within 1 s measurement time. The experiments with an increased sampling-rate were performed with a pre-amplified photodetector with 5 MHz bandwidth (Vigo Systems SA, photodetector model PVI-4TE-8, with estimated D* = 1.0 × 10¹⁰ cm Hz^1/2/W at 4.3 μm; Vigo Systems SA, pre-amplifier model VPDC-5S). In this case the acquisition bandwidth is effectively determined by the DAQ bandwidth of f_BW = 1.7MHz. With an assumption of a maximum acquisition rate of f_BW/3 = ~567KHz that would assure no correlation between the consecutive spectral points, the acquisition hardware (NI-DAQ) was set to its maximum sampling rate of 500kHz. The test is also performed in a scan mode that allows evaluating both a single spectral point measurement and a full spectrum mode. With 250 points per spectrum the spectral scan rate is set to 2 kHz. With these settings 414 scans can be acquired and averaged within each sub-cell, then the signals are background-corrected according to Eq’s (4) and (5). Using the single spectral point measurement approach, signal stability both at the peak of the absorption line and off-line were analyzed. In the spectral fitting operation mode the retrieved CO₂ concentration was converted to equivalent transmission changes measured at the peak of the absorption line and a long-term time trace of this value was used in Allan analysis. The resulting Allan plots are presented in Fig. 5 (for easier comparison the Allan plots from Figs. 3 and 4 are also included in this plot).

 

Fig. 5 Allan deviation calculations comparing the effect of increased sampling rate. Measurements with higher sampling rate marked as “many avgs” are performed using a single spectral point both on the absorption line peak (marked as “peak”) and away from the target transition (marked as “wing”). The same data were analyzed using a spectral fitting and the corresponding peak absorption fluctuations of the scanned absorption line profile are shown as “Fit, many avgs”. Allan plots for background-corrected measurements from Figs. 3(b) and 4(b) are shown for comparison (labeled as “few avgs”).

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As expected, at higher data acquisition rate both the on-line and off-line single spectral point measurements show reduction of noise within 1 s measurement time down to 3.5 × 10⁻⁴ which corresponds to CO₂ sensitivity of ~1.75 ppmv. The bandwidth-normalized sensitivity calculated for β = 1.7 MHz and N = 414 is 5.46 × 10⁻⁶ Hz^-1/2. An increase in the bandwidth normalized sensitivity with respect to Fig. 4 indicates 2 × higher detector noise (D* of the Vigo detector is 1.6 × lower than D* of the Teledyne Judson detector). The absolute sensitivity observed within 1 second measurement time improved by a factor of ~2.8 (with respect to Fig. 4(b)), which is consistent with a factor of ~2 increase in detector noise and a factor of 34.5 increase in the number of averages $\left(\frac{\sqrt{34.5}}{2}=~2.9\right)$. After ~10 seconds of averaging, both the on-line and off-line measurements reach sub-ppmv precision. However, after 100 seconds the drift starts dominating the on-line measurement data. It is clear that despite a significant difference in number of averages the timescale of this drift (and thus its origin) is the same as in data from Fig. 3. At the same time the off-line measurements show significantly better long-term performance reaching precision of approximately 5 × 10⁻⁵ or 0.25 ppmv after about ~100s (maintained up to >1000s).

Long-term laser frequency and broadband baseline drifts can be eliminated by performing a full spectral fitting of the background-corrected data. Since all spectral points within the target absorption line are utilized, further reduction of the random noise is also expected. Indeed as shown in Fig. 5 the sensitivity observed within 1s measurement time was reduced down to 2 × 10⁻⁴ (CO₂ detection limit of 1 ppmv). The ultimate minimum detectible absorption of 5.5 × 10⁻⁵ is achieved after 60 s of averaging. Beyond the 60s mark the fitting results become affected by the same source of drift that is present in the on-line measurements. This suggests that the background-correction is not able to fully suppress the CO₂ absorption outside the gas cell (e.g., we suspect that the strong absorption signal outside the cell is not fully suppressed due to small photodetector nonlinearity). Since the background signal magnitude is approximately 4-5 times greater than the reference or sample signal magnitude, its suppression below 10⁻⁵ level becomes challenging. Therefore the best strategy to minimize the system drift is by eliminating or strongly suppressing the background signal. This will be attempted in the next version of the instrument by introducing solid optical waveguides and minimizing open path distances of the laser light in the atmosphere containing the target analyte.

4.2 System self-calibration

Concentration retrieval methods based on single spectral point measurements as presented above do not account for potential changes in the broadband transmission of individual sub-cells (parameters T_Zero, T_ref, T_sample in Eqs. (1)-(5)), which can influence the accuracy of concentration data. On the other hand, concentration retrieval through spectral fitting can account for those changes by simultaneously fitting the baseline parameters, but this process requires precise, wavelength calibration (I(t)→I(ν)) to allow utilization of spectral databases.

Since the revolving gas cell allows both the sample and the reference spectra to be measured nearly simultaneously, the background-corrected spectrum of the sample gas can be conveniently calibrated against the background-corrected spectrum of the reference gas. This can be performed directly using a point-by-point spectral correlation of the data acquired in the time domain (e.g., a scatter plot of T_sample,c(T_ref,c)), which does not require the critical and time consuming frequency calibration procedure required to perform full spectral fitting.

As shown above, sources of baseline and laser frequency drift occurring at a time scale longer than the cell rotation are observed as common-mode for all sub-cells, and thus can be efficiently suppressed. Example drift effects can be clearly seen in Fig. 6(a) that shows transmission spectra for the sample and reference gas acquired at two different times. While laser wavelength drift can be effectively corrected by taking the ratio of the sample to reference spectrum, uncorrelated drifts in broadband transmission (clearly visible in Fig. 6(a)) are not corrected.

 

Fig. 6 (a) Spectral scans of background-corrected reference and sample spectra acquired at the beginning and the end of a long-term measurement. (b) A scatter plot of a T_sample,c(T_ref,c) for one set of spectral scans collected during one revolution of the cell is shown in black. The same plot after applying transmission-correction to both the reference and the sample spectrum showing effectively m_sample/ref × T_sample,c(T_R) (in blue). The grey line, which indicates perfect 1:1 correlation with a reference spectrum of 383.9 ppmv CO₂ in air is shown for comparison.

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In an ideal case a background-corrected spectral scan acquired for the reference and sample sub-cells, when plotted as T_sample,c(T_ref,c), should yield a line which intersects the (1,1) coordinate (100% transmission) and has slope proportional to the ratio of analyte concentrations in the reference and the sample gas respectively ([CO₂]_ref/[CO₂]_sample). Such a correlation plot of background-corrected experimental data (through Eqs. (4) and (5)) is shown in Fig. 6(b). Due to differences in broadband transmission parameters (T_zero, T_ref, T_sample) the linear fit to the scatter plot does not intersect the (1,1) coordinate, which introduces error into the concentration retrieval when simply analyzing the slope of the linear correlation fit.

To enable direct sample spectrum calibration, we have developed an algorithm for correction of drifts in the broadband transmission (T_ref/T_Zero in Eq. (4) for the reference spectrum and T_sample/T_Zero in Eq. (5) for the sample spectrum). It should be noted that because the CO₂ absorption cross-section in this spectral region is large, there is no spectral point within the acquired spectral scan that represents 100% transmission. We have selected the spectral region away from the CO₂ line center corresponding to the frequency range between 2354.915 cm⁻¹ and 2354.989 cm⁻¹ (shown as “baseline window” in Fig. 6(a)) to perform correction for the broadband transmission. Data within this spectral region were averaged to estimate the mean measured transmission (B_meas). Subsequently, a transmission (B_sim) expected from the reference gas concentration of 383.9 ppmv CO₂ in air was simulated within the same spectral range using HITRAN [28] database parameters. The transmission-corrected reference spectrum T_R was calculated by multiplying the spectrum obtained from Eq. (4) by a transmission correction factor B_sim/B_meas that yields:

Unfortunately the same approach cannot be used to correct the sample spectrum transmission because the transmission baseline is concentration-dependent, and the sample concentration is not known a priori. Instead, the knowledge of the fundamental property that the correlation plot should intersect the (1,1) coordinate can be utilized to perform transmission-correction of the sample spectrum. This is performed by finding a transmission correction factor β for the sample spectrum (where T_S(t_n) = β T_sample,c(t_n)), such that the correlation plot T_S(T_R) intersects (1,1). As a result the calibrated sample concentration ([CO₂]_sample) is calculated as a product of the T_S(T_R) slope m and the known reference concentration ([CO₂]_ref = 383.9 ppmv in this work):

This calibration method takes advantage of all spectral points within the scan, which results in measurement precision similar to that attained employing a full spectral fit (alternatively m can be found as a slope for a line intercepting the coordinates (T_R0,0) and (1,1), where T_R0 is an x-axis intercept of the linear fit for the T_sample,c(T_R) scattered plot). To evaluate the effectiveness of the calibration method described above we have performed a comparison of CO₂ concentration time series retrieved in three different calibration modes: 1) single spectral point calibration, 2) spectral fitting of the T_sample,c(ν) spectrum with the HITRAN database, and 3) spectral correlation based calibration based on Eqs. (6) and (7) above.

In calibration mode #1 a single spectral point corresponding to the peak CO₂ absorption is analyzed (at t_n-peak), and the CO₂ concentration is retrieved by direct comparison of the background-corrected sample transmission to the background-corrected reference-gas transmission measured at this spectral point:

In calibration mode #2 the spectral fitting of the T_sample,c(ν) spectrum is performed after prior calibration of the wavelength axis (an additional elaborate and very critical step required with this method). CO₂ concentration and absolute optical frequency were used as fit variables.

The top panel of Fig. 7(a) shows a time series of the background-corrected reference cell transmission and sample cell transmission measured at a spectral point (t_n-peak) coinciding with the CO₂ line center. It is evident that there is a long-term drift that affects both transmission signals. We attribute this effect to be primarily related to the laser wavelength and baseline drift clearly noticeable in Fig. 6(a).

 

Fig. 7 (a) Long-term corrected reference and sample peak transmission time-series measurements are shown in the top panel. Lower panel shows concentration time series after calibration using three different calibration methods. (b) Allan deviation plots calculated for sample concentration data series shown in (a). (At higher integration times, the elevated Allan deviation values after drift reduction are related to measurement of actual variations in the laboratory CO₂ level.)

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As shown in the lower panel of Fig. 7(a) the calibration mode #1 based on single spectral point comparison clearly suppresses the long-term drift in the calibrated sample CO₂ concentration data (the short-term fluctuations are the actual measurements of ambient CO₂ concentration changes; in this case experimental constrains of the table-top prototype system precluded use of a controlled environment). Long-term drift suppression is also evident in the corresponding Allan plot in Fig. 7(b), which shows reduction of the system drift at long averaging times. The short-term (1 s) sensitivity of ~2.3ppmv achieved in this calibration mode is consistent with data presented in Fig. 5 (the operation in Eq. (8) increases the 1 s detection limit of 1.75ppmv observed for a single spectral point by a factor of $\sqrt{2}$).

In the calibration mode #2, the CO₂ concentration retrieved using a full spectral fitting (Fig. 7(a)) shows levels in the 310-320 ppmv range. This is significantly lower than results obtained with other calibration modes. It is also lower than the ambient background CO₂ concentration expected at ~390 ppmv level. A spectral fit performed for the reference gas data yielded a value of 314.5 ppmv, which is also significantly lower than the calibrated concentration of 383.9 ppmv. These discrepancies have been attributed to a detector/pre-amplifier nonlinearity that was observed after a change in photodetected optical power from ~16.9 μW to ~23.5 μW (67% to 93.5% of maximum pre-amplifier output) caused by system re-alignment. To account for this effect we have made the first order approximation and used a scaling factor derived as a ratio between the actual and measured reference gas concentration and applied it to the sample data. The properly scaled sample concentration data resulting from the spectral fit show significantly more consistent values with other methods as shown in Fig. 7(a) (labeled as “scaled fit”).

The most significant discrepancy noticeable after applying all three different calibration approaches is the offset of the data retrieved using the single point calibration method with respect to the other two methods. This offset is equal to ~6% of the actual concentration value. However it is clear that Eq. (8) does not take into account differences in transmissions of the sample and the reference gas spectrum. As shown in Fig. 6(a) the transmission differences of ~3 × 10⁻³ are clearly noticeable. With the peak absorption of ~5 × 10⁻² observed at the center of the CO₂ line these transmission differences correspond to ~6% of this value, which is consistent with the observed offset in the retrieved concentration. This clearly demonstrates an effect of differences in broadband transmission on calibration accuracy and disqualifies the single spectral point calibration from being suitable for accurate concentration measurements.

Allan deviation analysis in Fig. 7(b) also reveals the capabilities of all three calibration methods. Both mode #2 and mode #3 utilize all data points within the measured spectrum, which results in 1.7 × improvement in short-term (1s) sensitivity over the single point measurement from 2.35 ppmv to 1.33 ppmv (Fig. 7(b)). This is consistent with the trend observed for the reference signal measurements in Fig. 5. Interestingly, at long averaging times the spectral fitting does not suppress the drift present in the system and the Allan deviation plot shows similar long–term drift as in data without calibration. This drift is clearly reduced with the single spectral point calibration mode #1 and spectral correlation mode #3. These results suggest that the background-correction performed with Eqs. (4) and (5) is not able to fully suppress the CO₂ absorption outside the gas cell, which contributes drift in the spectral fitting mode (other calibration modes perform correlation of the sample and the reference spectra, which suppresses this drift).

This incomplete suppression of the background absorption can be included in the model by modifying Eq. (5):

where γ represents the background suppression coefficient (γ is expected to be 0< γ << 1). Since the unsuppressed absorption spectrum γα_b(ν) is spectrally indistinguishable from the sample absorption spectrum α_sample(ν), the concentration retrieved through the spectral fitting will be offset by a small error Δ (where Δ ∝ γα_b(ν)):

In the case of the spectral correlation method #3, the unsuppressed background absorption should be considered for both the reference and the sample spectra, thus the slope measured for the T_S(T_R) scattered plot will be affected by Δ and proportional to:

Assuming Δ<<[CO₂]_ref, the first order approximation using Taylor series at Δ≈0 yields:

If the m_meas is used to retrieve the sample concentration using Eq. (7), the concentration value measured with the spectral correlation method will be proportional to:

This clearly shows that with careful selection of the concentration in the reference gas such that [CO₂]_ref≅[ CO₂]_sample the effects of the unsuppressed background absorption can be significantly reduced. For the experiment presented in Fig. 7 with [CO₂]_ref = 383.9 ppmv and [CO₂]_sample≅390 ppmv the influence of Δ is reduced by >50 times as compared to the spectral fit method (in Eq. (10)). This is consistent with experimental data shown in Fig. 7.

The calibration mode #3 based on spectral correlation clearly outperforms the other two calibration modes tested. The transmission correction performed with Eq.’s (6) and (7) eliminates the accuracy issues (offset) observed with the simple single spectral point calibration (Fig. 7(a)). Moreover, unlike the spectral fit method the spectral correlation method seems immune to detector related nonlinearities, provides the same short term precision through effective utilization of the entire absorption profile without the need for wavelength calibration, and improves the long-term performance of the system even with incomplete suppression of the background absorption through Eqs. (4) and (5).

Ideally the system should be tested under a controlled environment to separate the influence of the environmental CO₂ concentration fluctuations and the system drift. Unfortunately, due to the experimental constraints of this optical table-top prototype system, it was not possible to enclose the entire instrument in an atmosphere with a controlled concentration of a calibrated gas. Consequently, the drift observed at integration times larger than 20s in all Allan plots shown in Fig. 7(b) is related to natural variations in the CO₂ level measured in the laboratory. Therefore a complete accuracy assessment beyond this simple comparison between calibrated and non-calibrated data was not feasible in this work. As a part of the future work we plan to miniaturize the instrument and increase its portability, which will enable experiments in a controlled environmental chamber for fully controlled accuracy assessment. Nevertheless the presented data are consistent and show increased performance of the spectral correlation method with respect to other calibration techniques.

5. Conclusions

We have demonstrated a real-time calibration technique using a spectral correlation based on a revolving in-line gas cell for laser absorption spectrometers. The construction of the revolving in-line cell assures that the same optical interfaces are shared by the sample, reference, and zero-gas sub-cell, which allows for effective suppression of parasitic interference fringes. Despite significant interference fringes in the prototype system studied here (fringes with 3 × 10⁻² peak-to-peak transmission variations are visible in Fig. 2), this technique results in excellent long-term stability of trace-gas measurements.

For the experiments presented in this paper, CO₂ was used as the trace-gas of interest. The system shows consistent bandwidth-normalized absorption detection limits at ~5 × 10⁻⁶ Hz^-1/2. Depending on the specific operation mode this absorption sensitivity translated to CO₂ concentration detection limits in a 1-3 ppmv range (for 1 s measurement time). Most importantly the background-correction technique used in this work allowed for significant suppression of system long-term drifts extending white noise limited operation up to >1000s of averaging time (in comparison to 10-100 s without background-correction/calibration). We have also demonstrated a reliable real-time calibration method based on spectral correlation, which exhibits the advantages of a full spectral fit (utilization of all available spectral points) without the need for wavelength calibration. This method further improves long-term accuracy by suppressing influence of the unwanted ambient absorption within the optical path outside the sample cell, and eliminating problems with photodetector system nonlinearities that are often observed in TEC-cooled mid-IR detectors. This approach uses simplified data processing that does not require sophisticated spectroscopic fitting algorithms, which shows great potential for field deployable sensor systems and applications that require high energy efficiency and minimal computing resources such as wireless sensor networks [29–31].