1 Introduction

Significant effort is currently directed toward developing high efficiency, low emission engines, especially those that can be operated at pressures considerably higher than the current state of the art [1,2,3]. Unfortunately, currently available combustion models for practical fuels suffer from significant uncertainties at elevated pressures. Understanding both the physical and chemical nature of fuels at high pressures is necessary to build more accurate simulation models [4,5,6,7,8,9,10,11,12,13,14]. Shock tubes are ideal environments for studying high-pressure combustion phenomena and time-resolved laser-absorption spectroscopy (LAS) speciation measurements made within these facilities can be used to guide high-pressure engine development.

Compared with LAS diagnostics that operate well at lower pressure conditions, high-pressure LAS diagnostics are more challenging to develop. First, it becomes difficult to fully sweep across absorption features with typical lasers at high pressures, resulting in difficulty to infer a zero-absorption baseline for recovering the correct absorption spectrum [15]. Second, some non-absorption transmission losses, such as beam-steering, due to density gradients along the optical path, can play a dominant role in degrading the detection limit of optical sensors. In addition, imperfect optical alignment can further exacerbate non-absorption transmission losses, especially when using small-aperture windows designed for surviving high pressures.

Tunable diode laser-absorption spectroscopy (TDLAS) is especially well-established for in-situ, non-intrusive detection of gas composition, pressure, and temperature [16,17,18,19,20]. Among the variety of TDLAS techniques, direct-absorption spectroscopy (DA) and wavelength modulation spectroscopy (WMS) are the two most common sensing techniques. In contrast with DA, where the laser is typically operated at a fixed wavelength or rapidly scanned across an absorption feature, the WMS technique relies on modulating the laser wavelength at some frequency \(f_{\text {m}}\) and detecting absorption at the modulation harmonics (\(n\cdot f_{\text {m}}\)), resulting in the rejection of low-frequency noise [21,22,23,24]. In addition, since the harmonic signals of WMS are proportional to transmitted intensity, non-target harmonic signals can be used to normalize the target harmonic signal to account for variations of transmitted laser intensity, including non-absorption transmission losses such as scattering, beam-steering [25, 26], and optical misalignment. Among the normalization strategies, 1f-normalized WMS-2f detection is the most popular strategy for calibration-free WMS diagnostic systems.

As a key intermediate species in combustion, CO concentration and time history contain key information on fuel oxidation chemistry [27,28,29]. CO can be used in tracking the distribution of carbon atoms, and the amount of CO is an indicator of local fuel-to-oxidizer ratio in incomplete combustion. In addition, the reaction CO + OH = CO\(_2\) + H plays a central role in combustion chemistry. It consumes nearly all of the CO to produce CO\(_2\) and accounts for nearly one-third of the heat released when hydrocarbon fuels are oxidized. In addition, at appropriately chosen conditions, the CO concentration is sensitive to some of the key elementary reactions, making it a potential candidate for indirect measurement of reaction rates [30,31,32]. As a result, CO serves as one of the most popular targets in shock tube experiments. In addition, for engine design, a strong correlation exists between excess CO in the exhaust and poor engine efficiency. Hence, there are many reasons supporting the demand for a highly robust carbon monoxide diagnostic system.

In this work, we experimentally demonstrate the relative insensitivity of a WMS diagnostic system to laser intensity fluctuations in high-pressure environments by directly comparing WMS-based carbon monoxide (CO) concentration time histories within a shock tube against DA-based measurements at identical shock conditions and optical alignments. Measurements were conducted with shock-heated mixtures of CO diluted in \(N_2\) at temperatures between 1050 and 1350 K and pressures between 3 and 18 atm. The sensor architecture was based on the CO sensor developed by Spearrin et al. [33] for detonation detection, which employed a quantum cascade laser (QCL) targeting the P(20) fundamental band transition of CO near 4.87 \(\upmu\)m. For DA measurements, the laser was operated at a constant wavelength corresponding to the transition linecenter with sampling rate of 10 MS/s determined by the acquisition system. The DA results were processed by a 1 MHz low-pass filter, which is a common choice for the DA systems used in shock tube experiments [34, 35]. For WMS measurements, the laser was modulated at 90 kHz, resulting in a measurement bandwidth of 40 kHz, sufficient to resolve most combustion-relevant time scales in shock tubes.

The success of this WMS diagnostic system relies primarily on one key attribute, namely, the benefits of 1f-normalization to mitigate the influence of fluctuations in shock tube experiments. Of course, to maximize the benefits of using WMS, it is necessary to find an appropriate compromise in laser-tuning parameters to achieve an optimized combination of signal-to-noise ratio (SNR) and sensor bandwidth [36].

To the authors’ knowledge, this work represents the first direct comparison between WMS- and DA-based TDLAS sensors for high-pressure environments and quantifies the non-absorbing interference rejection.

2 Theory

2.1 Absorption spectroscopy

The spectral transmissivity, \(T_\nu\), of monochromatic light as it passes through a gas medium is described by the Beer–Lambert law:

$$\begin{aligned} T_\nu =\left( \frac{I_{\text {t}}}{I_0}\right) _\nu = \exp (-k_\nu L), \end{aligned}$$
(1)

where \(I_0\) is incident light intensity, \(I_{\text {t}}\) is transmitted light intensity, \(k_\nu\) is spectral absorption coefficient at frequency \(\nu\) (cm\(^{-1}\)), and L (cm) is optical path length. \(k_\nu\) is given by the following expression:

$$\begin{aligned} k_\nu = S \phi _\nu P_i, \end{aligned}$$
(2)

where S (cm\(^{-2}\)atm\(^{-1}\)) is transition linestrength, \(\phi _\nu\) (cm) is frequency-dependent lineshape function. \(P_i\) (atm) is the partial pressure of species of i, which for an ideal gas can be expressed as \(P \cdot X_i\), where P (atm) is total pressure of gas, \(X_i\) is mole fraction of the absorbing species i. Both Eqs. (1) and (2) assume uniform temperature, pressure, and gas composition along the laser path. At the thermodynamic conditions of interest, \(\phi _\nu\) is well-approximated by the Voigt function, which models the combined effects of collisional broadening and Doppler broadening, characterized by their respective full-width at half-maximum (FWHM), \(\varDelta \nu _{\text {C}}\) (cm\(^{-1}\)) and \(\varDelta \nu _{\text {D}}\) (cm\(^{-1}\)). The collisional FWHM for the target species (CO) is modeled as follows:

$$\begin{aligned} \varDelta \nu _{\text {C}} = P \sum _{\text {A}} X_{\text {A}} 2 \gamma _{\text {CO-A}}, \end{aligned}$$
(3)

where the subscript A represents all species within the gas mixture and \(\gamma _{\text {CO-A}}\) (cm\(^{-1}\) atm\(^{-1}\)) is the collisional broadening coefficient for CO collision with species A. Variation of the broadening coefficient \(2\gamma\) with temperature is well-approximated by a power law as follows:

$$\begin{aligned} 2\gamma (T) = 2\gamma (T_0)\left( \frac{T_0}{T}\right) ^N, \end{aligned}$$
(4)

where T (K) is the temperature, and \(T_0\) (K) is the reference temperature, often 296 K. N is the temperature coefficient for collision broadening. In this paper, collisional broadening coefficients between carbon monoxide and nitrogen \(2 \gamma _{{\text {CO-N}}_2}\) are documented in existing literature [31].

The Doppler half-width (FWHM) is given by

$$\begin{aligned} \varDelta \nu _{\text {D}} = \nu _0 \left( 7.1623 \times 10^{-7}\right) \left( \frac{T}{M}\right) ^{0.5}, \end{aligned}$$
(5)

where \(\nu _0\) is transition center frequency, and M is the molecular weight (g/mol).

2.2 Fixed-wavelength WMS-2f/1f

The fixed-wavelength WMS and simulation strategy used in this paper are documented in Sun et al. [37]. This section provides a brief overview of the important details. In fixed-WMS, the laser is sinusoidally modulated at frequency \(f_{\text {m}}\), giving rising to simultaneous modulation of frequency and intensity. The instantaneous optical frequency modulation (FM) can be written as follows:

$$\begin{aligned} \nu (t) = \bar{\nu } + a_{\text {m}} \cdot \cos (2\pi f_{\text {m}} t), \end{aligned}$$
(6)

where \(\bar{\nu }\) (cm\(^{-1}\)) is the mean frequency of the laser and \(a_{\text {m}}\) (cm\(^{-1}\)) is the modulation depth. The instantaneous intensity modulation (IM) can be written as

$$\begin{aligned} I_0(t) = \bar{I_0} \cdot \left[ 1+\sum _{k=1}^{\infty } i_k \cos \left( 2\pi kf_{\text {m}}t+\varphi _k\right) \right] , \end{aligned}$$
(7)

where \(\bar{I_0}\) is the average laser intensity, and \(i_k\) are the normalized linear and nonlinear IM amplitudes, with \(i_1\) representing the linear IM amplitude and higher orders of \(i_k\) representing the nonlinear IM amplitudes. \(\varphi _k\) are the temporal phases between the FM and IM waveforms. The relationship between drive current and \(a_{\text {m}}\), \(\bar{I_0}\), \(i_k\) and \(\varphi _k\) are characteristics of the laser source and are characterized in the lab. For maximum accuracy, \(\bar{I_0}\), for this diagnostic system was directly measured using a photoelectric detector (PD).

The nth harmonic signal (nf) of the transmitted intensity is directly related to \(I_0\) and absorption spectra, which can be used to infer gas property information. A lock-in amplifier (LIA) combined with a low-pass filter (LP) is utilized to extract the nf signal. In the 1f-normalized WMS-2f technique, the 2f signal is used for measurement, while the 1f signal is used for normalization to account for non-absorption transmission losses such as scattering or beam-steering. With thermodynamic properties (T, P), laser properties (\(f_{\text {m}}, \bar{\nu }, a_{\text {m}}, I_0(t)\)), gas properties (\(S, \phi _{\nu }\)), and optical length (L) known, the target species concentration can be inferred from the transmitted intensity by matching simulated WMS signals to the measured WMS signals.

3 Sensor design

3.1 Line selection

The selection of an appropriate target absorption transition is crucial to the performance of all TDLAS diagnostic systems. Appropriate absorbance and minimal spectral interference from other species within the target range of thermodynamic conditions are the two primary criteria for transition line selection and are discussed in Spearrin et al. [33]. These authors chose the P(20) transition of the CO fundamental rovibration band with (\(\nu ^{\prime }=1, \nu ^{\prime \prime }=0\)) centered at 2059.9 cm\(^{-1}\) for high-temperature and high-pressure CO detection due to its superior absorption linestrength and spectral interference characteristics. In addition to these criteria, for shock tube, experiments and other kinds of measurements, where temperature nonuniformity or uncertainty influence the accuracy of the TDLAS measurements, it is important to consider the sensitivity of the probed absorption transition to uncertainties in temperature.

Within each rovibrational band, linestrengths of transitions with smaller rotational quantum number (J) peak at lower temperatures and decrease rapidly at elevated temperatures, resulting in strong temperature sensitivity. Although transitions with larger J do not absorb strongly at lower temperatures, their sensitivity to temperature is in general lower than lower J transitions. To illustrate this principle, the linestrength temperature dependence of the P(20) and R(13) transitions of the CO fundamental rovibrational band is shown in Fig. 1. At room temperature, the R(13) is more than 6 times stronger than the P(20) transition; therefore, it is one of the most common choices for ambient CO detection [30, 38, 39]. At higher temperatures, however, the linestrengths become comparable at higher temperature. In addition, the sensitivity of the P(20) transition to temperature uncertainties, modeled as \(\mid ({\text {d}}S/S)/({\text {d}}T/T)\mid\) and also shown in Fig. 1, is in general lower than the R(13) transition. As can be seen, at temperatures above 410 K, the temperature sensitivity of the P(20) transition becomes less than that of the R(13) transition, demonstrating that the P(20) transition is less impacted by temperature fluctuations and is better-suited for species detection at high temperatures.

Fig. 1
figure 1

Linestrength and temperature sensitivities of the P(20) and R(13) absorption transitions in the (1, 0) CO fundamental rovibrational band

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With a thorough analysis, we can conclude that for temperature between 1000 and 1500 K, transitions with J between 19 and 28 of the CO fundamental band are well-suited for sensitive CO detection. As shown in the literature [33], the CO\(_2\) fundamental band exhibits a dense spectrum that interferes with the R branch of CO fundamental band. Including additional consideration for H\(_2\)O spectral interference, the P(20) and P(21) transitions were determined to be ideal targets for high-temperature applications. In this work, the P(20) transition was probed because of its slightly stronger absorption at most combustion-relevant temperatures.

3.2 Modulation frequency and modulation depth strategy

While both DA- and WMS-based sensors are dependent on the linestrength and lineshape of the targeted absorption transitions, WMS is additionally dependent on the optical and intensity tuning parameters of the laser as defined in Eqs. 6 and 7. It is, therefore, important to characterize and optimize these tuning parameters for the desired application. The laser we used for CO measurements is a single-mode distributed-feedback quantum cascade laser (DFB-QCL, Alpes Lasers SA, Switzerland) with wavelength centered near 2059.9 cm\(^{-1}\) and laser power output of approximately 100 mW. Laser modulation depth \(a_{\text {m}}\) and IM amplitude are primarily functions of injection current amplitude and modulation frequency (\(f_{\text {m}}\)) and can vary widely between lasers. However, these tuning parameters are generally fixed and stable for each laser, so only a one-time characterization measurement experiment is sufficient. The characterization method utilized was identical to the method presented in Sun et al. [37].

For WMS diagnostic systems for shock tube applications, both high signal-to-noise ratio (SNR) and high sensor bandwidth are desirable. The optimal modulation index, m, defined as \(2a_{\text {m}}/(\varDelta \nu _{\text {C}}+\varDelta \nu _{\text {D}})\), for WMS-2f detection is 2.2 [25]. However, it is difficult to achieve this optimal value for typical solid-state lasers at high pressures due to strong collisional lineshape broadening; therefore, the laser was modulated at the maximum possible injection current amplitude to maximize the pressure at which the sensor can operate. The behaviors of \(a_{\text {m}}\) and \(i_1\) as a function of modulation frequency for the QCL at the maximum safe injection current amplitude of 20 mA are shown in Fig. 2.

Fig. 2
figure 2

Variation of the QCL modulation depth \(a_{\text {m}}\) and linear intensity tuning amplitude \(i_1\), as a function of modulation frequency at the maximum injection current amplitude of 20 mA

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For most shock tube experiments at combustion-relevant conditions, most chemical processes have time scales on the order of 500 \(\upmu\) s and above. To resolve detailed time histories of these processes, sensor bandwidths in general should be at least 20 kHz. In the present work, the modulation frequency and lock-in detection frequency were set at 90 kHz. A low-pass filter with 40 kHz bandwidth was applied to isolate the target harmonic signals, resulting in a measurement bandwidth of 40 kHz. For most chemical reactions studied in shock tubes, a 40 kHz measurement bandwidth is sufficient to resolve reaction transients. At this modulation frequency, the modulation depth was 0.25 cm\(^{-1}\). Figure 3a shows the simulated absorbance profiles of CO P(20) transition at a temperature of 1300 K, optical path of 5 cm and CO mole fraction of 0.29 \(\%\) at different pressures. Figure 3b shows the variation of the WMS-2f signal modulated at the transition linecenter (approximately proportional to the SNR) and modulation index as a function of pressure calculated according to the laser-tuning parameters and the simulated absorbance profiles from the HITEMP database [40] at a temperature of 1300 K. Though the QCL was modulated at the maximum injection current amplitude, the sensor is unable to reach optimum modulation index of \(m=2.2\) at pressures above 6 atm. Nevertheless, the WMS-2f signal amplitude is satisfactory for sensitive detection, as it is only \(44\%\) smaller than the optimum value at 15 atm.

Fig. 3
figure 3

a Simulated absorbance profiles at pressures of 4 atm and 15 atm, respectively. Simulation was conducted at temperature of 1300 K, optical length of 5 cm, and CO mole fraction of 0.29%. b WMS-2f signal amplitude at transition linecenter and modulation index as a function of pressure. Target gas temperature and laser modulation frequency were set at 1300 K and 90 kHz, respectively, corresponding to a modulation depth of 0.25 cm\(^{-1}\)

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4 Demonstration experiments

4.1 Experimental setup

Validation experiments were performed in the flexible applications shock tube (FAST) and the high-pressure shock tube (HPST) facilities at the Stanford High-Temperature Gasdynamics Laboratory. The FAST facility has a circular cross section with an inner diameter of 13.97 cm with wedged sapphire optical access ports located 1 cm from the end wall. The HPST facility has a circular cross section with an inner diameter of 5.0 cm and wedged sapphire optical access ports located 1.1 cm from the end wall. A thorough discussion of the HPST facility can be found in the previous studies [41, 42].

The optical setups for the two shock tube facilities are nearly identical and are shown in Fig. 4. The QCL was packaged in a sealed laser housing with a collimation optic (Alpes HHL package) and thermoelectrically stabilized at 12 \(^\circ\)C with a controller (Alpes TC-3). In addition, a water-cooled heat sink was connected to the laser housing to achieve a more stable laser operation. The laser wavelength was tuned by varying the injection current that was controlled by a commercial laser driver (ILX Lightwave LDX-3232). The laser beam was focused at the center of the shock tube with a 15 cm focal length lens to achieve high temporal resolution. With a beam waist of 1 mm in diameter and shock speeds typically on the order of 1000 m/s, the effective time resolution of these measurements was 1 \(\upmu\)s. Emission interference was suppressed via a spectral filter (Spectrogon) and the resulting intensity was measured by a photodetector (PVI-4TE-5 IR Photovoltaic Detector, VIGO System S.A.) with a 10 MHz detection bandwidth.

Fig. 4
figure 4

Schematic of the experimental setup used in this study

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Within the shock tube, the driven section was filled with low-pressure test gas (CO/N\(_2\)) and the driver section was filled with high-pressure helium to burst the diaphragm. Gas temperatures and pressures behind the reflected shock waves were calculated using standard normal-shock relations and the measured incident shock speed. Incident shock speeds were measured using five piezoelectric pressure transducers mounted along the tube. The pressure at the measurement location was measured by Kistler 603B1 pressure gauges. It is worth noting that a small amount of hydrogen was added to the test gas mixture to accelerate vibrational relaxation of the CO/N\(_2\) mixtures [43].

4.2 FAST facility experiments

Fig. 5
figure 5

a Detected laser signal and pressure trace during a FAST facility shock experiment using WMS at 3.5 atm. The figure inset magnifies the raw photodetector signal near the moment the reflected shock arrives; b measured absorbance using the DA and WMS methods; c measured mole fraction using the DA and WMS methods (solid lines) compared against the known CO mole fraction (dotted line)

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This WMS diagnostic system was first evaluated in the Stanford FAST facility for non-reacting CO/N\(_2\) mole fraction detection at intermediate pressure (3.5 atm), where non-absorbing interference noise is not dominant. Figure 5a shows a representative WMS measurement in a 0.28% CO, 2.6% H\(_2\), and N\(_2\) balance test gas mixture at reflected shock conditions of 1056 K and 3.47 atm with the raw photodetector voltage shown in blue and the test section pressure in red. A figure inset is also included to highlight the laser-absorption behavior near the arrival of the reflected shock. The bulk change in the measured laser intensity near \(t = 0\) (defined as the moment the reflected shock passes the test section) is caused by a combination of beam-steering and lineshape broadening of the targeted absorption feature (marked with green arrows) due to the shock-induced pressure jump. A lock-in amplifier combined with a low-pass filter was utilized to extract the harmonic signals (nf) of the photodetector output that relates directly to the absorption spectrum. Figure 5b compares the transition linecenter absorbance of the DA experiment against the equivalent linecenter absorbance for the WMS-2f/1f experiment. It should be noted that for each comparison between WMS and DA measurements, two independent experiments (one using the DA and the other using WMS) with nearly identical post-reflected shock conditions were performed. Despite the similarity in conditions, fluctuations in the results due to shock-to-shock variability are expected to be uncorrelated and are responsible for the difference in behavior between each WMS and DA data trace. Figure 5c shows the converted mole fraction results for both measurement methods. Assuming a constant temperature, which is valid given the flat pressure trace, as shown in Fig. 5a, and no chemical reaction during the shock tube test time, the standard deviations of the WMS and DA results were calculated to be \(0.5\%\) and \(1.6\%\), respectively. Electronic and beam-steering noise were the largest contributors to the fluctuations for both measurement methods. The precision of the DA and WMS sensors based on the standard deviation in measured mole fractions is 43 and 14 ppm, respectively.

In addition to the experiment shown in Fig. 5 with relatively high absorbance (2800 ppm CO with linecenter absorbance of about 0.63), experiments at lower CO concentrations were conducted. Mole fractions of 610 ppm, 305 ppm, and 150 ppm CO with absorbance of about 0.13, 0.06, and 0.03 were measured at the same temperature and pressure as the experiment, as shown in Fig. 5. These results are summarized in Fig. 6. The SNRs of the DA sensor were calculated to be 37.5, 18.4, and 11.5, respectively, whereas for the WMS sensor, SNRs were 44, 3,3 and 17.5. SNRs were calculated by dividing the average signal amplitude within the post-reflected shock region by the measurement standard deviation within the same period. As is well known, the post-reflected shock region in a shock tube is both quiescent and homogenous, and therefore, any fluctuations in the signal amplitude within this period should be entirely attributable to measurement noise.

Fig. 6
figure 6

Comparison between WMS and DA CO mole fraction time histories for shock tube experiments with CO mole fractions of 610 ppm, 305 ppm, and 150 ppm

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These results demonstrate that the WMS strategy indeed suppresses interference sources better than the DA strategy. However, as will be discussed in the next section, significant improvements in measurement SNR can be gained when using the WMS strategy at higher pressures.

4.3 HPST facility experiments

The HPST facility was used to validate the WMS diagnostic system at higher pressures between 8 and 18 atm. As noted previously, density gradients within the optical path introduce beam-steering effects that reduce the detection collection efficiency. These effects are more pronounced for higher pressure shocks, which, when combined with the smaller window sizes in HPST experiments, magnifies the influence of non-absorption transmission losses on TDLAS measurements. As a result, typical HPST TDLAS experiments suffer from greater intensity-fluctuation noise than experiments with lower pressure shock tubes or research facilities. The WMS-2f/1f strategy was applied to deal with these challenges, which helps improve the quality of results and productivity of experiments using these shock tubes.

Fig. 7
figure 7

a Detected laser signal and pressure trace during an HPST facility shock experiment using WMS at 8.5 atm. The figure inset magnifies the raw photodetector signal near the moment the reflected shock arrives; b measured absorbance using the DA and WMS methods; c measured mole fraction using the DA and WMS methods (solid lines) compared against the known CO mole fraction (dotted line); d CO time histories of both the WMS and DA methods at known CO concentrations of 617 ppm and 308 ppm

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Fig. 8
figure 8

a Measured absorbance with DA and WMS method, respectively; b calculated mole fraction with DA and WMS method, respectively

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Target gases filled in the shock tube driven section were 0.29% CO, 2% H\(_2\) and N\(_2\) as bath gas with a total pressure of 201 torr in the driven section. Figure 7a shows a representative pressure trace (in red) and laser-absorption measurement (in blue) using the WMS strategy for a shock-heated mixture at 1232 K and 8.5 atm. Like in Fig. 7a, a figure inset magnifying the region near \(t = 0\) is included to highlight the step change in behavior of the collected laser intensity due to shock-induced beam-steering and lineshape broadening. An identical set of lock-in and low-pass filter settings as the set used in Sect. 4.2 were employed to demodulate the WMS signal, which was then converted to an effective absorbance and compared against DA results in Fig. 7b. Measured mole fractions using the two systems are shown in Fig. 7c. Again, assuming a constant temperature and no reaction during shock tube test time, relative standard deviations of the WMS and DA measurements were calculated to be \(1.6\%\) and \(3.3\%\), respectively. Additional measurements were conducted at various CO loadings of 617 ppm and 308 ppm for the same post-shock pressure. For these conditions, the SNRs of the WMS measurements were determined to be 18.8 and 7.5, respectively, whereas the SNRs of the DA measurements were calculated to be 4.6 and 3.7, respectively.

Experiments at 17.9 atm were conducted to further verify intensity-fluctuation suppression. The results for absorbance and mole fraction are shown in Fig. 8a, b, respectively. Standard deviations of WMS absorbance is calculated to be \(1.7\%\), while the value for DA is \(4.7\%\) at pressure of 17.9 atm.

It is worth noting that it took the authors 5 h to establish the optical alignment that yielded the results presented above in the HPST. As shown in the previous experiments within the HPST, it is possible to achieve better optical alignment and beam-steering noise suppression with additional effort. However, achieving the optimal alignment often requires significant time, patience, and expenditure of driver gas resources due to the repeated test shocks needed to validate the alignment. With another 36 h of alignment work, an improved optical alignment was achieved for the DA arrangement, and the results for the WMS and improved DA measurements are shown in Fig. 9. The relative standard deviation of WMS absorbance was calculated to be \(1.4\%\), while the value for DA was \(2.7\%\) at pressure of 17.9 atm.

Fig. 9
figure 9

Measured CO absorbance time histories using the DA and WMS methods at 17.9 atm. An additional 36 h of alignment work was done between the results, as shown in Figs. 7, 8 and this figure to achieve the improved optical alignment

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Compared with a DA detection system, the extra effort to operate a WMS system is minimal, involving only the need to modulate the laser before experiments and demodulate during data processing. For the experiments mentioned above, it took only 2 more seconds to process each set of WMS experimental data as compared to each DA data set, but a large amount of time and resources were saved owing to the reduced time needed to align the WMS system for the same experiment quality as a comparable DA system.

As can be seen, the measurement quality of DA experiments depended strongly on the quality of optical alignment, whereas the performance of the WMS was stable regardless of the alignment quality. Overall, at pressures ranging from 8.5 to 17.9 atm, the WMS sensor performs better than the DA sensor regardless of the absorption and optical alignment quality, thus demonstrating that the WMS strategy is an effective tool for suppressing non-absorbing transmission losses and improving detection limits for high-pressure shock tube experiments. However, the SNR of the WMS-based sensor deteriorated at very high pressures because of enhanced collisional lineshape broadening, as evidenced in Fig. 3b. For our system, the WMS system SNR became comparable with that of the DA system at 25 atm and further deteriorated with pressure increasing.

5 Conclusion

This work served to quantify the benefits of the WMS-2f/1f strategy for suppressing non-absorbing intensity fluctuations in high-pressure shock tube TDLAS speciation experiments. Carbon monoxide was chosen as the validation species and a QCL was used to target the P(20) transition of the CO fundamental vibrational band to achieve strong absorbance, to minimize interfering spectra from common combustion species, and to reduce temperature sensitivity. A modulation frequency of 90 kHz was chosen to balance the competing needs of high SNR and temporal resolution.

Evaluation experiments were conducted with the Stanford FAST facility and HPST facility. The performance of the WMS sensor was slightly better than DA measurements at a pressure of 3.5 atm. However, when experiments were conducted at pressures above 8 atm, beam-steering noise seriously degrades the SNR of the DA measurements even with well-optimized optical alignment. Throughout these comparative tests, the WMS results showed superior performance relative to the DA measurements and far less sensitivity to optical alignment. These results demonstrate that the WMS strategy is an effective tool for suppressing non-absorbing intensity fluctuations in high-pressure shock tube TDLAS experiments. With this strategy, not only can experimental results in high-pressure shock tubes be improved relative to DA measurements, significantly less time and resources are needed to yield high-quality measurements, thus improving the productivity of high-pressure shock tube facilities.