1. INTRODUCTION

Shock-tube laser-absorption experiments can provide important species time-history data needed to test and validate models used to simulate the behavior of nonequilibrium gases near hypersonic vehicles. For many decades, shock tubes have served as an effective system to study chemical kinetics, providing a well-defined high-temperature test environment [1]. Given the highly transient conditions of hypersonic flow fields, species-specific laser absorption spectroscopy is well-suited to provide nonintrusive species detection with fast time resolution (order of microseconds) [2,3]. Here, a diluted mixture of 1% ${\mathrm{O}}_2$ in Ar was shock-heated to temperatures between 5400 and 8000 K behind reflected waves, and laser absorption was used to measure important thermodynamic properties of the gas following the dissociation of molecular oxygen. Rapid spectral scanning across electronic transitions of atomic oxygen provided lineshape data which were used to derive time-dependent populations in excited electronic states and kinetic temperature information of the shock-heated gas [4].

In laser-absorption studies of high-temperature gases, the Beer–Lambert relation is the governing spectroscopic law that describes the relationship between incident ($I_0$) and transmitted ($I_t$) monochromatic light intensities across a column of uniform gas,

For atoms, the preferred form of the frequency-integrated absorbance ($A_{\text{int}}$) is given by the product of the linestrength of the atomic transition $S_{lu}$, the number density in the lower state of the transition $n_l$, and the absorption path length $L$:

To improve the sensitivity of a laser absorption diagnostic at a given temperature and pressure, one must resort to choosing a line with larger linestrength, increasing the overall optical path length, or reducing the noise of the signal. The shock tube used in this study had an inner diameter of 15.24 cm and thus to improve the detection limit of the sensor, cavity-enhanced absorption spectroscopy (CEAS) was used to significantly increase the effective path length through the shock tube. High-finesse cavities (mirror reflectivity $>99.9\%$) can provide a large increase in path length [5–9]; however, the long residence time of light in the cavity may prevent the time resolution needed in extremely fast, high-temperature shock-tube experiments [10]. Recent studies using low-finesse cavities installed as windows on a shock tube demonstrated a significant increase in path length ($\sim 90\times$) for shock-heated measurements of ${\mathrm{C}}_2{\mathrm{H}}_2$ [10] and CO [11] while still making the transit time of the shock wave across the cavity the limiting time resolution of the experiments. In this study, a low-finesse cavity was employed where off-axis alignment and fast scanning of the laser wavelength were used to minimize noise resulting from spurious coupling of optical resonances within the cavity (this variation of light transmission with wavelength is discussed in detail in [12–14], and is referred to hereafter as “cavity noise”). Here, population time-histories of two excited states of atomic oxygen were monitored with improved detection sensitivity using CEAS compared to conventional single-pass techniques. Increased absorption sensitivity of excited oxygen atoms using CEAS is beneficial for a variety of reasons, since it:

The present work demonstrates the potential of utilizing cavity-enhanced laser-absorption spectroscopy to monitor multiple species and thermodynamic properties relevant to high-temperature electronic-excitation chemistry of atoms in hypersonic flow fields.

2. LASER ABSORPTION SPECTROSCOPY

Scanned-wavelength direct absorption spectroscopy is a well-established technique for nonintrusive gas sensing that has been extensively utilized to measure thermodynamic properties of high-temperature gases in a variety of reactive systems [2,3]. Here, we briefly discuss the spectroscopy of the selected electronic transitions of excited oxygen atoms and theoretical fundamentals used to infer the thermodynamic properties of interest.

A. Spectroscopic Parameters

Laser absorption spectroscopy was used to measure the populations in the lower state of the ${}^5{\mathrm{P}}_3\leftarrow {{}^5\mathrm{S}}_2^0$ and ${}^3{\mathrm{P}}_{0,1,2}\leftarrow {{}^3\mathrm{S}}_1^0$ electronic transitions of atomic oxygen. The lower states of the transitions near 777 and 844.6 nm are highly energetic at $\sim 9.15$ and $\sim 9.52\mathrm{eV}$ above the ground state, respectively, and require high temperatures to achieve detectable populations in these levels. The upper energy level of the 777 nm lines (${}^5{\mathrm{P}}_{1,2,3}$) is a degenerate level, but the spacing of the split upper levels is such that we probe only one of the triplet lines at 777.2 nm. The upper energy level of the 844.6 nm transitions (${}^3{\mathrm{P}}_{0,1,2}$) is also degenerate; however, due to the close energy spacing between the split levels the measured absorption lines are blended. The most critical spectroscopic parameters for the transitions of interest, such as linecenter wavelength (${\lambda }_o$), Einstein coefficient ($A_{ul}$), upper-state energy ($E_u$), upper-state degeneracy ($g_u$), lower-state energy ($E_l$), and lower-state degeneracy ($g_l$) are shown in Table 1 and were taken from NIST [16].

Table 1. Fundamental Spectroscopic Parameters for the Electronic Transitions Measured in this Study

View Table

B. Absorption Lineshape Analysis

Wavelength scanning across electronic transitions provides absorbance lineshape measurements that can be used to derive important thermodynamic properties of the shock-heated gases, such as state-specific electronic population and heavy-particle kinetic temperature. The lineshape function $\varphi (\nu )$ can be accurately modeled by the Voigt profile, which is a convolution of both Gaussian (Doppler broadening) and Lorentzian (collisional broadening) profiles. The Voigt “$a$” parameter is defined as

The lower-state population (number density, $n_l$) can be determined from the frequency-integrated absorbance, as shown in Eq. (2). This is particularly useful for blended transitions since the Voigt lineshape function for each blended line is defined to have an area of unity. Thus the area underneath the blended absorbance curve is equal to the sum of the areas of each individual transition, all with the same lower-state energy (see Fig. 1).

 

Fig. 1. Integrated absorbance from the isolated electronic transition near 777.2 nm (top panel) and from the three neighboring electronic transitions near 844.6 nm (bottom panel). Note that for the blended transitions near 844.6 nm, the total absorbance (dashed curve) is directly obtained from the superposition of all three lines.

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C. Cavity-Enhanced Absorption Signals

The use of an optical cavity enables a nonlinear gain in the measured absorption signals by increasing the effective optical path length through the absorbing gas. The measured cavity-enhanced absorbance, ${\alpha }_{\mathrm{CEAS}}$, can be related to the single-pass absorbance, ${\alpha }_{\mathrm{SP}}$, by the following expression [10,11],

 

Fig. 2. Wavelength-dependent reflectivity curve of the CEAS mirrors taken from manufacturer (Rocky Mountain Inc., USA).

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3. SHOCK-TUBE FACILITY

A schematic of the shock tube and laser-absorption experimental setup is shown in Fig. 3. The stainless steel shock tube has a 3.7 m driver section and a 10 m driven section. Initially, both sections are separated by a thin polycarbonate diaphragm. The driven section is filled with low-pressure test gas (1% ${\mathrm{O}}_2/\mathrm{Ar}$, $\sim 2–3\mathrm{Torr}$) and the driver section is filled with high-pressure helium. At a prescribed pressure, the diaphragm is ruptured and a shock wave travels along the tube thereby heating, compressing, and accelerating the test gas; upon reaching the end-wall, the shock wave reflects, further heating, compressing, and stagnating the gas.

 

Fig. 3. Schematic of the experimental setup used in this study. The optical cavity was located 2 cm from the shock tube end-wall.

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Laser absorption measurements were acquired behind reflected shock waves at 5400–8000 K and 0.5–0.8 atm. The initial gas temperature immediately behind the reflected shock was calculated using measured incident shock velocities and normal-shock jump relations [1]. The speed of the incident shock was measured using five piezoelectric pressure transducers mounted along the last 1.5 m of the tube. The pressure at the measurement location was measured by a Kistler 603B1 pressure gauge. Before filling the driven section with test gas, the shock tube was turbo-pumped to $\sim 5\times {10}^{-6}\mathrm{Torr}$ with a measured leak rate typically less than $1\times {10}^{-5}\mathrm{Torr}/\min$. Prior to running shock-tube experiments, the laser beam was redirected across a low-pressure microwave discharge cell ($\sim 2\mathrm{Torr}$, 4% ${\mathrm{O}}_2/\mathrm{Ar}$) to serve as wavelength reference for the transition probed.

Atomic oxygen was generated by shock heating a diluted gas mixture of 1% ${\mathrm{O}}_2$ in Ar. For the temperature range of interest, the ${\mathrm{O}}_2$ fully dissociates within $\sim 100\mathrm{\mu s}$ after passage of the reflected shock. The majority of the atomic oxygen formed is in the ground state, and only a small fraction can be found in excited states. The total constant-pressure test time ($\sim 1\mathrm{ms}$) was limited by the arrival of compression waves reflected from the contact surface, yet there was sufficient time for the populations in each measured electronic state to achieve a quasi-steady state for the conditions studied here.

4. CEAS FOR In Situ MEASUREMENTS OF EXCITED OXYGEN ATOMS

A. Optical Cavity Design

The shock tube’s optical cavity consists of two small (25 mm diameter) coated dielectric mirrors with a radius of curvature of $-1\mathrm{m}$. The mirrors (Rocky Mountain Inc, USA) were backside-polished and antireflection-coated, mounted on pressure-sealing plugs flush to the inner wall of the shock tube and used as the windows for laser absorption experiments conducted 2 cm from the tube end-wall (as illustrated in Fig. 3). Laser light from two distributed feedback (DFB) diode lasers (Nanoplus GmbH) were used to generate monochromatic light ($\sim 10\mathrm{mW}$) near 777.2 and 844.6 nm. In the study reported here, the experiments with each laser were conducted separately. A small lens (12 mm diameter, 8 mm focal length) was used to collimate the laser light, and the collimated beam was directed through the shock-tube test section with $\sim 1\%$ of the laser power coupled into the cavity. The transmitted light was collected on a lens (antireflection-coated) and focused on the sensing element of a photodiode detector (Thorlabs PDA 20CS, chip $\text{diameter}=2\mathrm{mm}$, 1.9 MHz bandwidth at 20 dB gain). Also, a narrow bandpass optical filter ($\pm 10\mathrm{nm}$) was used to reduce postreflected-shock emission signals.

A slightly off-axis alignment was used to minimize cavity noise [12–14]. This off-axis alignment setup formed an elliptical beam pattern inside the cavity (see Fig. 1 of [10]) where the small axis of the ellipse was aligned with the shock-tube axis and the width of the ellipse was optimized to a reduced length of $\sim 5\mathrm{mm}$ (measured with a knife edge scanned across the beam pattern). For the experiments shown here, the incident shock traveled at $\sim 2000\mathrm{m}/\mathrm{s}$, thus limiting the time resolution of the experiments to $\sim 2.5\mathrm{\mu s}$ due to the transit time of the shock wave across the laser light in the cavity. Fast laser wavelength scanning (50 kHz triangular waveform, frequency scan range of $\pm 1.25{\mathrm{cm}}^{-1}$) further suppressed cavity noise and allowed for measurements at both up-scan and down-scan for a 10 μs resolution, critical for the extremely fast excitation processes encountered in these experiments ($\sim 200–500\mathrm{\mu s}$). A solid fused-silica etalon ($\mathrm{FSR}=0.067{\mathrm{cm}}^{-1}$) was used to characterize the wavelength scanning, and detector signals were digitally sampled with a fast acquisition system at 100 MS/s (14-bit, NI PXIe-5122 digitizer).

B. Absorption Measurements of Excited O-Atoms

Figure 4 shows examples of raw scanned-wavelength transmission data. The figure in panel (a) shows the absorption transition near 777.2 nm and the figure in panel (b) shows the blended absorption lines near 844.6 nm. The cavity noise is highlighted in the figures near 10 μs, which occurs when $d\nu /dt\approx 0$ (i.e., when the triangular laser wavelength scan changes direction). Note how the cavity noise is suppressed by fast wavelength scanning in the nearly linear portion of the scan where the absorption features are located. The small asymmetry between up-scan and down-scan is indicative of the phase delay between laser intensity and laser wavelength due to rapid tuning of the injection current. Since only a small fraction of the laser power was coupled into the cavity, the detector gain had to be adjusted to 20 dB (1.9 MHz bandwidth) to measure sufficient levels of signal, while allowing fast laser scan rates for better cavity noise suppression without distorting the absorption lineshapes. The CEAS cavity proved robust against beam-steering effects; at the measurement location, Schlieren spikes due to the passage of incident and reflected shocks were less than 2.5 μs. The transmitted signal level fully recovered after each experiment and realignment was not necessary throughout the measurement campaign (more than 30 shock events).

 

Fig. 4. Measured transmitted laser intensity for a single scan cycle. Panel (a) shows the transition near 777.2 nm ($T_{\text{tr}}=6460\mathrm{K}$, $P=0.64\mathrm{atm}$, $X_O=1.980\%$) and panel (b) shows the transitions near 844.6 nm ($T_{\text{tr}}=7186\mathrm{K}$, $P=0.62\mathrm{atm}$, $X_O=1.975\%$).

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Figure 5 shows the measured CEAS absorbances, ${\alpha }_{\mathrm{CEAS}}(\nu )$, in the frequency domain for a single scan. Data analysis for up-scan and down-scan measurements were performed separately. Thermal emission from the hot gases behind the reflected shock was measured from the nonabsorbing region of each laser scan assuming no nonabsorbing losses and subtracted off prior to baseline-fitting transmitted signals. Time-averaged preshock scans were used as a baseline ($I_0$) for fitting the measured postshock signals ($I_t$). Minor corrections (scaling and/or tilting) to $I_0$ were sometimes necessary to account for the small variations ($<3\%$) of the transmitted signal in the postreflected-shock region due to emission; this particular baseline-fitting technique improved scan-to-scan measurement quality with less scatter compared to the conventional polynomial-fit method. The CEAS absorbance was converted to single-pass absorbance, ${\alpha }_{\mathrm{SP}}(\nu )$, using Eq. (6) and the resulting lineshape was then least-squares fit to a Voigt profile. The fitting procedure was done by varying the Voigt “$a$” parameter and the Doppler width until the residual between measurement and fit was minimized. This two-parameter fitting technique enabled direct measurement of both the Doppler and collisional broadening components of the Voigt profile, where translational temperature and collisional broadening information were obtained using Eqs. (4) and (5), respectively (more details are presented in Section 5). To simplify the fitting routine of the blended lines, we constrained the relative linecenter positions according to the values from NIST (see Table 1) for a more robust measurement of the integrated area.

 

Fig. 5. Measured CEAS absorbance profiles (top) converted to single-pass absorbances (bottom) for transitions near (a) 777.2 nm ($T_{\text{tr}}=6460\mathrm{K}$, $P=0.64\mathrm{atm}$, $X_O=1.980\%$) and (b) 844.6 nm ($T_{\text{tr}}=7186\mathrm{K}$, $P=0.62\mathrm{atm}$, $X_O=1.975\%$). Residuals from Voigt-fitting the measured data are also shown.

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Upon converting the measured CEAS absorbance to single-pass absorbance and least-squares fitting a Voigt profile to it, the electronic population of excited states was directly determined for each individual scan by frequency-integrating the fitted absorbance across the transition and using Eq. (2).

5. FORMATION OF EXCITED OXYGEN ATOMS BEHIND REFLECTIVE SHOCK WAVES

A. Chemical Kinetics

Figure 6 shows an example shock-tube experiment where CEAS was used to monitor the lower-state population of the 777.2 nm transition. Here, a gas mixture of 1% ${\mathrm{O}}_2/\mathrm{Ar}$ at an initial pressure of 2.35 Torr in room temperature was shock-heated to 6742 K (at 0.62 atm) immediately behind the reflected shock (assuming chemically and vibrationally frozen gas). The measured incident-shock speed of $1752\mathrm{m}/\mathrm{s}$ corresponds to the value extrapolated to the end-wall of the shock tube. Shock-speed attenuation due to nonideal viscous effects in the shock tube was approximately 1.58%/m.

 

Fig. 6. Off-axis CEAS measurements of ${\mathrm{O}}^{*}$ (777.2 nm) versus time for initial test gas mixture of 1% ${\mathrm{O}}_2/\mathrm{Ar}$. The solid curve shows the measured pressure by the Kistler probe; note the two sharp pressure rises due to passage of incident and reflected shocks. The dashed curve corresponds to simulated ground-state atomic oxygen concentration using the ${\mathrm{O}}_2$ decomposition rate from Owen et al. [15] and the circles represent the measured excited-state population using CEAS. Here, concentration time-histories of O and ${\mathrm{O}}^{*}$ were normalized by the average steady-state concentration of each species following dissociation and excitation chemistry.

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Vibrational relaxation of ${\mathrm{O}}_2$ occurs mainly due to collisions with argon atoms and was modeled using previously measured rates [17], where the gas was assumed to be in vibrational equilibrium once the vibrational temperature approached within 3% of the translational temperature ($\sim 2.7\mathrm{\mu s}$ after passage of the reflected shock for the experiment shown in Fig. 6). Given that highly diluted mixtures were used in this study, energy transfer during vibrational relaxation only reduced the translational temperature of the gas by less than 0.5%.

The dissociation process of ${\mathrm{O}}_2$ due to collisions with argon atoms is the primary mechanism for O-atom formation. For the entire temperature range investigated in this paper, more than 99.9% of ${\mathrm{O}}_2$ dissociates into atomic oxygen after passage of the reflected shock (within the total test time of $\sim 1\mathrm{ms}$). In the example discussed here, the endothermic dissociation process further reduced the gas translational temperature to $\sim 6460\mathrm{K}$. Driver inserts were used to reduce the pressure rise behind the reflected shock to $dP/dt<1\%/\mathrm{ms}$ [18].

Since detectable amounts of excited O-atoms were not measured immediately behind the reflected shock, it was assumed that O-atoms formed from dissociation were in the ground state (dashed curve in Fig. 6). Excited-state population increased due to inelastic collisions of ground-state atomic oxygen with other gas particles (black circles in Fig. 6), and at long test times ($t\sim 300\mathrm{\mu s}$) the population reached a quasi-steady state.

B. Electronic-State Population Measurements

The quasi-steady-state populations of excited O-atoms were measured for a variety of shock conditions (see Fig. 7). In addition to measurements using CEAS, single-pass experiments using the same DFB diode lasers (at reduced power of $<30\mathrm{\mu W}$ and beam diameter of $\sim 2\mathrm{mm}$ to avoid lineshape saturation) were also conducted using ${\mathrm{CaF}}_2$ windows instead of CEAS mirrors for optical access. Single-pass measurements were restricted to higher-temperature experiments due to lower sensor detectivity at $T\lesssim 7000\mathrm{K}$. The results shown in Fig. 7 demonstrate the significant improvement of detection sensitivity using the CEAS scheme over conventional single-pass experiments, and the potential of using CEAS to extend the range of experimental conditions to lower temperatures, which offers a variety of benefits as previously discussed in Section 1 of this paper. In addition to measured populations using both CEAS and single-pass techniques, excited-state populations assuming a Boltzmann distribution between the ground state and lower excited state at the calculated translational temperature of the heavy gas were determined for comparison. The Boltzmann population fraction is given by the following Eq. [19],

 

Fig. 7. Steady-state population fractions of the lower energy state for transitions at (a) 777.2 nm and (b) 844.6 nm. CEAS improved sensitivity over single-pass experiments and enabled measurements at lower temperatures where the effects of ionization and radiation cooling are small.

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C. In situ Measurements of Kinetic Temperature and Collisional Broadening Coefficient

In addition to measuring steady-state electronic populations, data analysis of the fitted Voigt profiles enabled comparison of the measured translational temperatures with calculated values using measured shock speed, normal-shock jump relations, and kinetic modeling of the dissociation/ionization/excitation processes. The fitting procedure is thoroughly explained in Section 4.B of this paper and the lineshape analysis described here applies only for measurements of the 777.2 nm transition (simple one-line fit versus complex multiple-line fit for the 844.6 nm transitions). Figure 8 shows a comparison plot between measured and calculated temperature values for both single-pass and CEAS experiments and the results show good agreement within experimental uncertainty. Note that the error in measured translational temperature for the CEAS method ($\pm 250\mathrm{K}$) are slightly larger than for the single-pass method ($\pm 200\mathrm{K}$), mainly due to a higher noise level of the CEAS signals associated with non-negligible fluctuations in transmitted intensity from spurious coupling of stable modes in the cavity. Moreover, using the optimized Voigt “$a$” parameter and best-fit translational temperature, information about the collisional broadening was extracted using Eq. (5). Assuming O-atoms are mainly broadened by collisions with argon, and neglecting the effects of Stark broadening due to low ionization of the gas, the broadening coefficient $2{\gamma }_{\mathrm{O}\text{-}\mathrm{Ar}}$ was measured from $\mathrm{\Delta }{\nu }_C\sim P(2{\gamma }_{\mathrm{O}\text{-}\mathrm{Ar}})$, where $P$ is the total gas pressure measured by the Kistler pressure gauge (see Fig. 9). Pressures obtained behind reflected shock waves ranged from 0.5–0.8 atm and although, theoretically, $2{\gamma }_{\mathrm{O}\text{-}\mathrm{Ar}}$ can be slightly pressure-dependent [24], this parameter was treated as temperature-dependent only given the small pressure variation seen here.

 

Fig. 8. Measured translational temperature (from Gaussian component of the Voigt lineshape for the 777.2 nm transition) and calculated values at long times, after dissociation chemistry is complete.

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Fig. 9. Measured collisional-broadening coefficient (from Lorentzian component of the Voigt lineshape for the 777.2 nm transition). For the best-fit, $n=0.6985$, $T_{\text{ref}}=298\mathrm{K}$, and $2{\gamma }_{\mathrm{O}\text{-}\mathrm{Ar}}(T_{\text{ref}})=0.4615{\mathrm{cm}}^{-1}/\mathrm{atm}$.

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6. UNCERTAINTY ANALYSIS

In this study, several sources of measurement uncertainty were carefully examined and are presented here. The measured incident-shock attenuation was typically less than 1.5%/m, and the scatter of the measured incident-shock speed at the end-wall was usually less than 0.3%. This accounted for an uncertainty in calculated postreflected-shock gas temperatures of $\pm 1\%$. The gas pressure measured by the Kistler gauge had an uncertainty less than $\pm 3\%$, and the measured pressure immediately behind the reflected shock consistently agreed with calculated values. The largest uncertainty in the measured translational temperature (Doppler component of the Voigt fit) came from the baseline-fitting procedure resulting in an uncertainty in $T_{\text{tr}}$ of less than $\pm 3\%$ for single-pass measurements and less than $\pm 4\%$ for measurements using CEAS. Uncertainties of measured excited-state populations were less than $\pm 10\%$, mainly attributed to errors in integrated absorbance measurements due to baseline-fitting (less than $\pm 7\%$) and uncertainties in cavity gain (less than $\pm 1.5\%$).

7. CONCLUSIONS

We have demonstrated the potential of using fast CEAS for sensitive, time-resolved, in situ measurements of the populations of electronically excited oxygen atoms in a shock tube. The sensor was demonstrated to quantitatively detect the populations of the ${{}^5\mathrm{S}}_2^0$ and ${{}^3\mathrm{S}}_1^0$ electronic levels of atomic oxygen at various high-temperature conditions and significantly improve the detection sensitivity over conventional single-pass shock-tube experiments. Rapid scanning of the laser output frequency (50 kHz triangular wave) helped reduce cavity noise, and enabled measurements of absorption lineshapes which were used to extract the kinetic temperature and electronic populations. The significant absorption gain of 104 and 142 for the 777.2 nm and 844.6 nm transitions, respectively, obtained with CEAS demonstrates the potential of using this scheme to study nonequilibrium electronic-excitation processes at very high temperatures. In the future, this new capability may be applied to many other electronic levels of various neutral and ionized species present in hypersonic flow fields.

APPENDIX A: EXPERIMENTAL VALIDATION OF CAVITY GAIN

A. Introduction

Precise knowledge of the gain factor $G$ is needed for quantitative CEAS. A common method for determining $G$, especially for high-finesse cavities, is to measure the cavity ring-down time $\tau =L(1+G)/c$. For the low-finesse cavity used in this study, however, photon residence times were considerably short relative to the detector bandwidth ($\tau <0.1\mathrm{\mu s}$), thereby limiting direct measurements of $\tau$. Hence, a less conventional technique was employed to tackle the difficulties of determining $G$ for a low-finesse cavity.

In recent shock-tube studies of ${\mathrm{C}}_2{\mathrm{H}}_2$ [11], a low-finesse cavity was filled with known amounts of absorbing gas and the gain was inferred by exploiting the relatively strong absorption spectra of the gas at ambient conditions and using known spectroscopic parameters of ${\mathrm{C}}_2{\mathrm{H}}_2$. In this work, however, such a technique was impractical for ${\mathrm{O}}^{*}$ due to extremely small populations in the probed excited states at room temperature. Thus, in order to conduct controlled static-cell experiments to accurately determine $G$, a different gas species with desired absorption properties in the wavelength regions of interest (near 777.2 and 844.6 nm) was needed. Nitrogen dioxide (${\mathrm{NO}}_2$) was found to be an attractive target gas as it has strong absorption cross sections from the UV to the NIR spectrum [25]. Here, a diluted mixture of 2% ${\mathrm{NO}}_2/\mathrm{Ar}$ was employed in scanned-wavelength laser absorption experiments utilizing two static cells with different effective path lengths (at the same temperature and pressure) where $G$ was determined by comparing measured absorption signals across each cell.

B. Detail of Experimental Setup

Collinear beams from each DFB laser were directed, sequentially, through a vertical multipass cell and a custom-built CEAS cell for scanned-wavelength absorption measurements of ${\mathrm{NO}}_2$; the arrangement of the experiment is shown in Fig. 10. The multipass cell used here (Infrared Analysis, Inc.) had a cylindrical body made of borosilicate glass (60 cm in length and 12.5 cm inner diameter) and a total optical path length of 35 m (64 passes with an average $54.7\mathrm{cm}/\mathrm{pass}$). Two plane transfer mirrors aimed by fine-pitch screws were used to couple the laser light into and out of the cell with two small potassium chloride windows (2.5 cm in diameter) used for optical access. The laser beam reflected multiple times by three gold-coated mirrors configured as a “white cell” system and was focused on the detector upon exiting the cell. Using flip mirrors, the beams were also aligned through an aluminum CEAS cell designed to utilize the same pressure-sealing plugs with mounted mirrors used in the shock tube, such that the cavity length was equal to the inner diameter of the tube (15.24 cm). An elliptical light pattern in the cavity with identical shape as in the shock-tube setup was carefully reproduced here using an off-axis beam alignment. The laser wavelength was tuned over a range of about $\pm 1{\mathrm{cm}}^{-1}$ at a frequency of 5 kHz, which helped suppress cavity noise and improved the scatter in our measurements. Both static cells were evacuated prior to each experiment to record the baseline laser intensity ($I_0$) for both lasers. The cells were then simultaneously filled with test gas to $P=1.84\mathrm{atm}$ and $T=297.5\mathrm{K}$ and the transmitted laser intensity ($I_t$) through each cell was recorded for both DFB lasers. Data were digitally sampled at 2.5 MHz and background signals (detector offset) were subtracted from the transmitted laser intensity. The laser beams were also directed across a solid fused-silica etalon ($\mathrm{FSR}=0.067{\mathrm{cm}}^{-1}$) to characterize the laser wavelength scanning.

 

Fig. 10. Left panel (a) Schematic of the experimental setup illustrating the two-static-cell method used to determine the CEAS gain factor. Laser beams from both DFB lasers were aligned across a multipass cell and a CEAS cell with different effective path lengths. Both cells were filled with the same gas mixture of 2% ${\mathrm{NO}}_2/\mathrm{Ar}$ at $P=1.84\mathrm{atm}$ and $T=297.5\mathrm{K}$. Right panel (b) Single-sweep raw scan data showing measured transmitted signals across the multipass (bottom) and CEAS (top) cells with ($I_t$) and without ($I_o$) absorbing gas. Data averaging of 100 successive scans helped improve overall signal-to-noise, especially for the CEAS scheme.

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C. Results

Multipass and CEAS absorbances were obtained directly using the Beer–Lambert relation [Eq. (1)] and the results are shown in the top panel of Fig. 11. This strategy allowed us to directly determine the absorption gain factor $G$ for both transitions from the measured multipass (${\alpha }_{\mathrm{MP}}$) and CEAS (${\alpha }_{\mathrm{CEAS}}$) absorbances by rearranging Eq. (6),

(A1)$$G=\frac{\exp ({\alpha }_{\mathrm{CEAS}}(\nu ))-1}{{\alpha }_{\mathrm{SP}}(\nu )},$$

with

(A2)$${\alpha }_{\mathrm{SP}}(\nu )={\alpha }_{\mathrm{MP}}(\nu )\left(\frac{L}{L_{\mathrm{MP}}}\right),$$

where $L_{\mathrm{MP}}=35\mathrm{m}$ is the optical path length in the multipass cell and $L=15.24\mathrm{cm}$ is the CEAS cavity length. Though the measured spectra represents a blended contribution of several lines, note that this method for determining the gain factor did not require accurate knowledge of ${\mathrm{NO}}_2$ spectroscopic parameters (broadening coefficients, linestrength, etc.). Results are shown in the bottom panel of Fig. 11; gain factors of $104\pm 1.5$ and $142\pm 2$ were determined for the transitions near 777.2 nm and 844.6 nm, respectively. In addition, we found that measured gain factors were insensitive to small changes in beam alignment (ellipse shape) across the CEAS cavity. The average values of $G$ measured here were found to be in excellent agreement (within 0.1%) with the values obtained from quoted mirror reflectivities discussed in Section 2.C of this paper.

 

Fig. 11. Top panel: Measured ${\mathrm{NO}}_2$ absorbance near (a) 777.2 nm and (b) 844.6 nm for both the multipass and CEAS static cells. Both cells were filled with identical mixtures of 2% ${\mathrm{NO}}_2/\mathrm{Ar}$ at $P=1.84\mathrm{atm}$ and $T=297.5\mathrm{K}$. Bottom Panel: Measured CEAS gain factors near (a) 777.2 nm and (b) 844.6 nm. Gain factors were found to be constant across the frequency range of the laser scan with an average value of 104 (777.2 nm) and 142 (844.6 nm). The standard deviation between average and measured values of $G$ were approximately 1.4% for both transitions.

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Funding

Air Force Office of Scientific Research (AFOSR) (FA9550-12-1-0483).

Acknowledgment

We thank Professor Mark Cappelli at Stanford University for useful discussions on excitation of atoms and particle gas dynamics at high temperatures.

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10. K. Sun, S. Wang, R. Sur, X. Chao, J. B. Jeffries, and R. K. Hanson, “Sensitive and rapid laser diagnostic for shock tube kinetics studies using cavity-enhanced absorption spectroscopy,” Opt. Express 22, 9291–9300 (2014). [CrossRef]  

11. K. Sun, S. Wang, R. Sur, X. Chao, J. B. Jeffries, and R. K. Hanson, “Time-resolved in situ detection of CO in a shock tube using cavity-enhanced absorption spectroscopy with a quantum-cascade laser near 4.6 μm,” Opt. Express 22, 24559–24565 (2014). [CrossRef]  

12. J. B. Paul, L. Lapson, and J. G. Anderson, “Ultrasensitive absorption spectroscopy with a high-finesse optical cavity and off-axis alignment,” Appl. Opt. 40, 4904–4910 (2001). [CrossRef]  

13. E. J. Moyer, D. S. Sayres, D. G. Engel, J. M. Clair, F. N. Keutsch, N. T. Allen, J. H. Kroll, and J. G. Anderson, “Design considerations in high-sensitivity off-axis integrated cavity output spectroscopy,” Appl. Phys. B 92, 467–474 (2008). [CrossRef]  

14. G. S. Engel, W. S. Drisdell, F. N. Keutsch, E. J. Moyer, and J. G. Anderson, “Ultrasensitive near-infrared integrated cavity output spectroscopy technique for detection of CO at 1.57 μm: New sensitivity limits for absorption measurements in passive optical cavities,” Appl. Opt. 45, 9221–9229 (2006). [CrossRef]  

15. K. Owen, D. F. Davidson, and R. K. Hanson, “Measurements of the dissociation rate coefficient for oxygen in argon with laser absorption spectroscopy in a shock tube,” J. Thermophys. Heat Transfer (submitted, 30 May 2014).

16. Y. Ralchenko, A. E. Kramida, and J. Reader, and NIST ASD Team, “NIST Atomic Spectra Database (ver. 4.1.0),” http://physics.nist.gov/asd3 (Accessed 08/24/11).

17. K. Owen, D. F. Davidson, and R. K. Hanson, “Measurements of vibrational relaxation times for oxygen with laser absorption spectroscopy in a shock tube,” J. Thermophys. Heat Transfer (submitted, 18 May 2014).

18. Z. Hong, G. A. Pang, S. S. Vasu, D. F. Davidson, and R. K. Hanson, “The use of driver inserts to reduce non-ideal pressure variations behind reflected shock waves,” Shock Waves 19, 113–123 (2009). [CrossRef]  

19. M. N. Martin, L. S. Chang, J. B. Jeffries, R. K. Hanson, A. Nawaz, J. S. Taunk, D. M. Driver, and G. Raiche, “Monitoring temperature in high enthalpy arc-heated plasma flows using tunable diode laser absorption spectroscopy,” in 44th Plasmadynamics and Lasers Conference (AIAA, 2013), pp. 2013–2761.

20. G. Colonna and M. Capitelli, “A few level approach for the electronic partition function of atomic systems,” Spectrochim. Acta Part B 64, 863–873 (2009). [CrossRef]  

21. H. A. Chang, D. S. Baer, and R. K. Hanson, “Semiconductor laser diagnostics of kinetic and population temperatures in high-enthalpy flows,” in Shock Waves @ Marseille II (Springer, 1995), pp. 33–36.

22. M. Panesi, T. Magin, A. Bourdon, A. Bultel, and O. Chazot, “Fire II flight experiment analysis by means of a collisional-radiative model,” J. Thermophys. Heat Transfer 23, 236–248 (2009). [CrossRef]  

23. C. O. Johnston, B. R. Hollis, and K. Sutton, “Non-Boltzmann modeling for air shock-layer radiation at lunar-return conditions,” J. Spacecr. Rockets 45, 879–890 (2008). [CrossRef]  

24. C. S. Goldenstein, J. B. Jeffries, and R. K. Hanson, “Diode laser measurements of linestrength and temperature-dependent lineshape parameters of H₂O-, CO₂-, and N₂-perturbed H₂O transitions near 2474 and 2482 nm,” J. Quant. Spectrosc. Radiat. Transfer 130, 100–111 (2013). [CrossRef]  

25. A. C. Vandaele, C. Hermans, P. C. Simon, M. Carleer, R. Colins, S. Fally, M. F. Mérienne, A. Jenouvrier, and B. Coquart, “Measurements of the NO₂ absorption cross-sections from 42000 cm⁻¹ to 10000 cm⁻¹ (238–1000 nm) at 220 K and 294 K,” J. Quant. Spectrosc. Radiat. Transfer 59, 171–184 (1998). [CrossRef]