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Pulsed cavity ringdown spectroscopy (CRDS) is used to develop a novel, ultra-fast, high-sensitivity diagnostic for measuring species concentrations in shock tube experiments. The diagnostic is demonstrated by monitoring trace concentrations of ethylene in the mid-IR region near 949.47 cm−1. Each ringdown measurement is completed in less than 1 µs and the time period between successive pulses is 10 µs. The high sensitivity diagnostic has a noise-equivalent detection limit of 1.08 x 10−5 cm−1 which enables detection of 15 ppm ethylene at fuel pyrolysis conditions (1845 K and 2 bar) and 294 ppb ethylene under ambient conditions (297 K and 1 bar). To our knowledge, this is the first successful application of the cavity ringdown method to the measurement of species time-histories in a shock tube.
© 2015 Optical Society of America
1. Introduction
Fast-time response diagnostics capable of performing sensitive measurements are invaluable in the study of transient combustion systems such as shock tubes, internal combustion engines, and gas turbines. High-sensitivity diagnostics can be employed to detect trace species, such as HO2 and H2O2, important for low-temperature chemistry [1–4]. These species and other combustion radicals have been difficult to measure using currently available measurement techniques [4–6]. Ability to measure very small concentrations at very fast rates can be quite useful in the measurement of reaction rate coefficients. In this work, we have developed a highly sensitive ultra-fast diagnostic based on pulsed cavity ringdown spectroscopy (CRDS) and deployed it for making in situ species time-history measurements in shock tube chemical kinetic experiments.
A shock tube is a transient homogeneous reactor which almost instantaneously creates a test environment of high-temperature and high-pressure gases. Due to these unique characteristics, it has been widely used in chemical kinetic studies for the past few decades. Since the test environment in a shock tube exists only for a few milliseconds, it is imperative to use diagnostic tools with fast time-response. Therefore, continuous-wave (cw) laser absorption spectroscopy based diagnostics with microsecond time resolution [7] have extensively been used for measuring species concentrations in shock tube experiments. Since absorption-based diagnostics are most commonly used for measuring species concentrations in shock tube experiments, a closer look at Beer-Lambert law provides us the possible routes to increase the sensitivity of these diagnostics:
Here, I0 is the incident intensity and I is the transmitted intensity. Absorbance is a function of the total pressure of the gas, P, the mole fraction of the absorbing species,, the linestrength, S, the lineshape and the path-length L. For a specific experimental condition (fixed T, P and), linestrength and path-length play decisive role in deciding the measurement sensitivity for a given molecule. Linestrength depends on the molecular transition being probed and stronger vibrational bands can be chosen to increase the diagnostic sensitivity within the limits of laser availability and interference from other species. The only other parameter that can be varied is the absorption path-length. However, shock tubes and other transient combustion systems usually have small physical dimensions that result in single-pass absorption path-lengths of the order of 1 – 20 cm. Therefore, the only possible solution to increase path-length and consequently the measurement sensitivity is to employ cavity-based techniques which make the laser light undergo multiple passes through the absorbing medium.Many flavors of cavity-based absorption techniques have been developed over the years, such as multi-pass cells, cavity ringdown spectroscopy (CRDS), cavity enhanced absorption spectroscopy (CEAS), off-axis integrated cavity output spectroscopy (OA-ICOS), intracavity laser absorption spectroscopy (ICLAS), optical feedback (OF) cavity techniques, and noise-immune cavity-enhanced optical heterodyne molecular spectroscopy (NICE-OHMS). Measurements performed using CRDS can achieve better spatial resolution compared to multi-pass cells and other cavity-based techniques. Moreover, CRDS measurements are immune to laser intensity fluctuations. Pulsed CRDS, when implemented with high-repetition-rate lasers, offers significantly better temporal resolution compared to cw-CRDS. These features make pulsed-CRDS well-suited for studying homogeneous transient systems. Since CRDS is an absorption based diagnostic, data interpretation becomes challenging when density/concentration gradients exist along the line-of-sight. Previously, multi-pass cells were used to increase the path-length and, therefore, sensitivity of shock tube measurements [8,9]. However, the twelvefold increase in path length obtained in those studies resulted in only a fivefold increase in sensitivity because the laser intensity loss was dominated by the losses caused by shock tube windows present inside the cavity. Recently, Sun et al. [7,10] utilized OA-ICOS technique to develop sensitive diagnostics for shock tube kinetic studies. They were able to achieve high sensitivity by replacing shock tube windows with cavity mirrors. However, as compared to CRDS which is an on-axis technique, the off-axis alignment required for OA-ICOS technique limited the spatial resolution of their measurements to 5 mm.
In this work, we have used a high-repetition-rate (100 kHz) external cavity quantum cascade laser (EC-QCL) and relatively low reflectivity (99.8%) mirrors to develop an ultra-fast high-sensitivity diagnostic based on pulsed-CRDS. Numerous previous pulsed-CRDS studies [11–15] utilized optical cavities with high reflectivity mirrors (̴ 99.99%) to obtain substantial increases in sensitivity. However, the time resolution of such cavities is much lower than that required to carry out measurements in homogeneous transient chemical reactors like shock tubes. Here, we harness the low reflectivity (99.8%) of the optical cavity mirrors to obtain measurement times of less than 1 µs. In what follows, we present a detailed description of the design and optimization of our sensitive and fast time-response diagnostic. We then demonstrate its capability to make fast time-response and sensitive species concentration measurements by recording ethylene concentration time-histories in shock tube pyrolysis experiments. To our knowledge, this is the first successful application of the CRDS technique to shock tube kinetic experiments.
2. Experimental details
Cavity ringdown spectroscopy (CRDS) with pulsed or continuous lasers is a highly sensitive absorption technique that has been used previously in the development of calibration-free trace gas diagnostics. The theory of CRDS has been detailed previously [16], and we present it briefly to clarify the notation used in this study. In CRDS, light from a laser source enters a stable optical cavity and undergoes multiple passes. In the case of pulsed lasers, when the laser pulse ends, the light inside the cavity decays exponentially. The decay rate depends on the length of the cavity, the reflectivity of the mirrors forming the cavity and absorption losses inside the cavity. The decay time constant, also called the ringdown time, is the time taken for the light intensity to fall to 1/e of its initial value. It is given as:
In the absence of any absorbing molecules inside the cavity, the ringdown time is given as:
In the above equations, L is the total length of the cavity, c is the speed of light, R is the reflectivity of the mirrors forming the cavity,is the absorption coefficient in cm−1 and d is the absorption path-length. By measuring the decay time constants in the presence and absence of absorbing species, the absorption coefficient can be calculated from Eq. (2) and Eq. (3) as:The absorption coefficient,, is related to absorbance through path-length, L, as:Equation (5) in conjunction with Eq. (1) enables the determination of the mole fraction of the absorbing species if spectroscopic parameters (S and ) are known.The experimental setup used in this work is shown in Fig. 1. We employed a pulsed external cavity quantum cascade laser (Daylight Solutions), tunable over 9.53-12.95 µm (775-1020 cm−1), with maximum average power of 15 mW. The laser pulse duration can be varied over 40 – 500 ns and the repetition frequencies range from 0.1 to 100 kHz. Single-mode emission at the wavelength of interest was ensured with the help of a spectrum analyzer (Bristol 721). A 10 mW He-Ne laser was made collinear with the infrared QCL beam to facilitate the cavity alignment process. The infrared beam emerging from the QCL head was directed into the optical cavity formed by two plano-concave mirrors (II-VI Infrared). A ZnSe plano-convex lens (500 mm focal length) was used to facilitate mode-matching between the laser beam and the TEM00 mode of the optical cavity. The infrared laser beam leaking out of the optical cavity was focused on to a thermoelectrically-cooled, optically-immersed photovoltaic detector (Vigo PVI 4TE-10.6-1x1-TO8-BaF2). The photo-detector was custom-designed to have a high bandwidth of 500 MHz to adequately resolve relatively short ringdown times (~40 - 180 ns). The detector signal was recorded with a digital oscilloscope (Tektronix DPO 3014) having a sampling rate of 2.5 GS/s.
Fig. 1 Experimental setup used for pulsed CRDS employed for a carrying out species measurements in shock tube. BS: Beam splitter, MMO: Mode matching optics, BPF: Band pass filter.
The cavity on the shock tube was formed by two plano-concave mirrors with 20 cm radius of curvature, 12.5 mm diameter and reflectivity of 99.8% at 10.6 µm. Small diameter mirrors had to be used because of the limited optical access available on the shock tube. Mirrors were glued to custom designed plugs which were then mounted on the shock tube shock tube ports located at a distance of 2 cm from the shock tube end-wall. The mirrors were flush to the inside wall of the shock tube. Alignment of the ringdown cavity was achieved by using three fine adjustment screws (Thorlabs FAS100) which allowed three-axis rotation of the custom designed plugs.
The cavity used for CRDS experiments is similar to the cavity used by Sun et al. [7,10] for OA-ICOS experiments in terms of the optical components; however, the alignment procedure is different. OA-ICOS is an off-axis technique in which the laser beam is transmitted at a small angle with respect to the cavity axis such that the beam undergoes multiple passes while traversing different paths along an oval. On the other hand, CRDS is an on-axis technique wherein the laser beam undergoes multiple passes by going back and forth on the same path. Due to this fundamental difference in the way the laser beam undergoes multiple passes within the cavity, the spatial resolution of CRDS is better than OA-ICOS. In shock tube transient experiments, high spatial resolution is desired along the axial (shock-propagation) direction to achieve adequate time resolution.
In order to make the best use of the energy available from the pulsed laser, the pulse width was varied to identify its optimum value. Frequency down-chirp of the laser was determined by passing the laser beam through a Fabry-Perot Germanium etalon (free spectral range of 0.016 cm−1) and detecting the transmitted beam with a high bandwidth (500 MHz) photovoltaic detector. Transmitted laser signals, with and without the etalon, are shown in Fig. 2 for a 100 ns pulse width. The wavenumber tuning (ω-tuning) or the frequency chirp of the laser increased from 0.032 cm−1 at 80 ns pulse width to 0.08 cm−1 at 120 ns pulse width. This increase in the frequency chirp is an undesired effect because it leads to artificial broadening of the spectral absorption transitions. However, an increase in pulse width also increases the amount of energy entering the optical cavity, thereby increasing the signal-to-noise ratio (SNR) of the transmitted laser signal. Laser pulse width of 100 ns was, therefore, used as a compromise to achieve relatively low frequency chirp and high SNR.
All measurements reported here were performed in a 14.2 cm diameter stainless steel shock tube. The shock tube facility consisted of a 9-meter long driven section and a variable length driver section with a maximum length of 9 meters. The incident shock velocity was measured using five PCB 113B26 piezoelectric pressure transducers (PZTs) that were located axially along the last 1.3 m of the driven section. The incident shock speed at the end-wall was determined by linear extrapolation of the velocity profile. One-dimensional shock-jump equations were used to calculate the conditions (temperature, pressure) behind the reflected shock wave. Ethylene mixtures were prepared manometrically in a stainless steel mixing tank equipped with a magnetic stirrer.
The diagnostic is applied to measure ethylene time-histories behind reflected shock waves in ethylene pyrolysis experiments. The pulsed CRDS measurements were carried out near the peak of the ethylene Q-branch at a fixed frequency of 949.472 cm−1. The laser frequency was carefully selected after carrying out spectral simulations using HITRAN database [17] to consider potential interference from species produced during ethylene pyrolysis. Earlier, Pilla et al. [18] had selected a nearby frequency of 949.487 cm−1 for measuring ethylene concentrations in ethylene pyrolysis experiments. Their detailed analysis showed that absorption interference is negligible at their probe frequency. For all measurements reported here, laser pulse width of 100 ns was used which resulted in a frequency chirp of 0.064 cm−1.
3. Results and discussion
A stable optical cavity is necessary for pulsed CRDS to function properly and the cavity locking can potentially be disturbed by the arrival of the shock wave and other related disturbances at the measurement location. Shock waves are accompanied by mechanical vibrations as well as significant changes in temperature, pressure and refractive indices of the shock-heated gases. Mechanical vibrations perturb the mirror alignment while changes in the density and refractive index of shock-heated gas cause beam steering. These combined effects can potentially disturb cavity locking and make the application of CRDS technique to shock tubes quite complicated. Therefore, these effects were considered very carefully during the development of the diagnostic reported here. The cavity locking was then investigated by measuring the ringdown times before and after the arrival of the incident and reflected shock waves for non-reactive (argon) experiments. The pressure trace and the ringdown times for a representative non-reactive shock are presented in Fig. 3. The arrival of both the incident and the reflected shock waves, identified by the sudden jumps in the pressure trace, did not cause any significant reduction in the value of the ringdown time, indicating that the cavity locking was maintained throughout the experiment. The mean value of the ringdown time reduced from 178 ns in pre-shock conditions to 167 ns behind the reflected shock due to the absorbance by trace impurities present in argon gas.
Fig. 3 Measured pressure (blue trace) and ringdown times (black dots) for a non-reactive (pure argon) shock. Reflected shock conditions are 1976 K (T5) and 1.99 bar (P5).
The standard deviation in the measured ringdown times for the non-reactive shock, shown in Fig. 3, is 8.6 ns. The minimum detectable absorption coefficient can then be calculated as:
where is the standard deviation in the ringdown time, c is the speed of light and is the measured ringdown time. The minimum detectable absorption coefficient comes out to be 1.08 x 10−5 cm−1 which is a significant increase as compared to 2.95 x 10−4 cm−1 [19] achieved using single-pass direct absorption based diagnostic for the Q-branch of ethylene.The increased sensitivity of pulsed-CRDS technique enables detection of trace concentrations of the species of interest and the use of dilute mixtures. When using highly dilute reactive mixtures in shock tube kinetic experiments, the temperature and pressure remain almost constant throughout the reactive experiment. Since the knowledge of temperature and pressure is required to convert the measured absorption coefficient to concentration time-histories, having a constant temperature and pressure reduces the uncertainty in measured species concentration time-histories. Additionally, the use of dilute mixtures enables the operation of the shock tube close to ideal conditions of constant volume and energy (constant UV). Finally, when measuring reaction rate coefficients, dilute mixtures provide sensitivity to the target reaction and minimize the interference from secondary reactions.
With the knowledge that the cavity locking was not being disturbed due to the arrival of shock waves as well as the perturbations that accompany it, the diagnostic was applied to reactive experiments of ethylene pyrolysis. The diagnostic was first used to measure ethylene concentration time-history at reflected shock temperatures where ethylene is not expected to decompose. Figure 4 shows the measured ethylene concentration time-history for 316 ppm C2H4/Ar mixture at reflected shock conditions of 1306 K and 2.43 bar. As expected, ethylene concentration remained constant throughout the experiment. We can also observe excellent agreement between CRDS measurement and prediction of Marinov et al. [20] chemical kinetic model. The constant ethylene concentration measured over 1.5 ms was further proof that the cavity locking was not disturbed by arrival of the shock waves and the accompanying mechanical vibrations. The measured ethylene concentration has a standard deviation of 34 ppm for the conditions of Fig. 4.
Fig. 4 Ethylene time-history profile for initial mixture of 316 ppm C2H4/Ar. Reflected shock conditions are 1306 K (T5) and 2.43 bar (P5).
The CRDS diagnostic was then utilized to measure ethylene pyrolysis at higher reflected shock temperatures. Figure 5 shows the ethylene concentration time-history measured at reflected shock conditions of 1845 K and 1.96 bar. Time zero has been set to coincide with the start of the test time, i.e., when the reflected shock wave arrives at the measurement location. Sensitivity analysis was carried out for the aforementioned reflected shock conditions to identify the reactions which significantly affect ethylene time-history. The most dominant reaction at high temperatures is the decomposition of ethylene to form acetylene and hydrogen:
The rate coefficient (k1) for ethylene decomposition reaction was extracted from the experimentally measured ethylene concentration profile at 1845 K and is listed in Table 1. The measured rate constant compares well with the measurement of Ren et al. [19] and the prediction of Marinov et al. [20].Fig. 5 Ethylene time-history profile for 316 ppm C2H4/Ar. Reflected shock conditions are 1845 K (T5) and 1.96 bar (P5).
Table 1. Measured rate constant for ethylene decomposition at 1845 K and 1.96 bar
For relatively slow transient situations, noise in species concentration can be further reduced by averaging the decay time over two successive pulses, as shown in Fig. 6. Due to dilute ethylene mixture used here, Marinov et al. model [20] predicts a temperature drop of less than 5 K and a pressure drop of less than 5 mbar during the measurement time of 1.5 ms. Previous experimental studies which reported ethylene concentration time-histories in ethylene pyrolysis experiments [18,19] relied on chemical kinetic models to provide temperature during the reaction and the model temperature was then used to convert absorbance profiles to ethylene mole fractions. In the current work, the use of dilute ethylene mixture led to negligible temperature change (~5 K) during pyrolysis which removed the dependence on kinetic model for the calculation of ethylene mole fractions. Additionally, as mentioned earlier, the use of dilute mixture increases the sensitivity of the measurement to the unimolecular decomposition rate of ethylene. We believe the results of this study can be used to obtain improved value of the rate coefficient of ethylene unimolecular decomposition.
Fig. 6 Ethylene time-history profile for 316 ppm C2H4/Ar. In this case, two successive laser pulses are averaged to increase SNR. Reflected shock conditions are 1845 K (T5) and 1.96 bar (P5).
Figure 7 shows the sensitivity gain that can be achieved by using higher reflectivity mirrors. Ethylene detection limit is plotted at two conditions, i.e., room temperature and pressure (black line) and at a temperature and pressure representative of typical fuel pyrolysis conditions (red line). The detection limit for ethylene was calculated by assuming that the value of σ/τ0 obtained for current work remains same for other mirror reflectivities. The increase in absorption sensitivity possible by using high reflectivity mirrors comes at the cost of measurement time resolution (defined as 5τ0) which increases to tens of microseconds for high reflectivity mirrors. Moreover, the use of high reflectivity mirrors necessitates using high power lasers. Despite these challenges, the tremendous gain in sensitivity offered by pulsed cavity ringdown spectroscopy makes it a very promising tool for studying species time-histories in shock tubes and other homogeneous systems. Future ethylene diagnostics which target a specific detection limit or time resolution can potentially be designed using Fig. 7. As an example, for a target time resolution of 5 µs, Fig. 7 shows that the ethylene detection limit will be 52 ppb at room temperature and pressure (297 K and 1 bar) and 2.45 ppm at 1800 K and 2 bar. It is to be noted that the value of σ/τ0 depends on the specific experimental setup and, among other factors, varies with mirror reflectivity. Figure 7 attempts to give the reader a general idea about the benefits and challenges of using higher reflectivity mirrors.
Fig. 7 Estimated ethylene detection limit and time resolution as a function of mirror reflectivity for pulsed CRDS.
Compared to the widely used single-pass direct absorption based diagnostics, the pulsed CRDS diagnostic developed in this study is able to achieve significant increase in sensitivity, as illustrated by the trace ethylene concentrations measured in shock tube experiments. The minimum detectable absorption coefficient was calculated after almost every reactive experiment by measuring ringdown times in a non-reactive argon shock and it remained constant throughout the experimental campaign spanning several days. Due to the maximum pulse repetition rate of 100 kHz, the time gap between successive data points was 10 µs. However, each ringdown event lasted for less than 1 µs for all experiments. Lasers with higher repetition rates can be utilized to further improve the sensitivity or time-resolution of the current diagnostic. To our knowledge, this work presents the first successful demonstration of the implementation of the cavity ringdown technique with high-repetition-rate lasers to measure species time-histories in a shock tube.
4. Summary
A novel highly-sensitive ultra-fast diagnostic based on pulsed cavity ringdown spectroscopy has been successfully developed and used for performing sensitive absorption measurements of ethylene in a shock tube experiment. The fast time-response diagnostic achieved a noise-equivalent detection limit of 1.08 x 10−5 cm−1 at 100 kHz which is a tremendous gain over the sensitivity of commonly used single-pass direct absorption techniques. High sensitivity of this diagnostic tool enables measurement of ethylene concentrations as low as 15 ppm at shock conditions of 1845 K and 1.96 bar. At room temperature and pressure (296 K and 1.01 bar), comparatively large absorption cross-sections of ethylene near 949.472 cm−1 bring the ethylene detection limit down to 294 ppb. The high sensitivity and fast time response diagnostic can be utilized for measuring other neutral molecules and radicals which cannot be detected using single-pass direct absorption techniques. We believe this is the first time that pulsed CRDS technique was successfully used to measure species time-histories in a shock tube. Further shock tube experiments are planned to implement this diagnostic to measure rate coefficients and species concentrations in fuel oxidation experiments.
Acknowledgments
Research reported in this paper was funded by King Abdullah University of Science and Technology (KAUST).
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