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Abstract
In this work, a detailed calibration study is performed to establish non-intrusive one-dimensional (1D) rovibrational temperature measurements in unseeded air, based on air resonance enhanced multiphoton ionization thermometry (ART). ART is generated by REMPI (resonance enhanced multi-photon ionization) of molecular oxygen and subsequent avalanche ionization of molecular nitrogen in a single laser pulse. ART signal, the fluorescence from the first negative band of molecular nitrogen, is directly proportional to the 2-photon transition of molecular oxygen C3Π (v = 2) ← X3Σ (v’=0), which is used to determine temperature. Experimentally, hyperfine structures of the O2 rotational branches with high temperature sensitivity are selectively excited through a frequency-doubled dye laser. Electron-avalanche ionization of N2 results in the fluorescence emissions from the first negative bands of N2+ near 390, 425, and 430nm, which are captured as a 1D line by a gated intensified camera. Post processing of the N2+ fluorescence yields a 1D thermometry line that is representative of the air temperature. It is demonstrated that the technique provides ART fluorescence of ∼5cm in length in the unseeded air, presenting an attractive thermometry solution for high-speed wind tunnels and other ground test facilities.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
A renewed interest in hypersonic and high-supersonic research and development has resulted in increased desire for flow characterization techniques that can serve as a means of CFD validation tools. [1,2] Most facilities are built to provide flow regimes that can accurately simulate certain aspects of in-flight flow conditions. At high flow velocities the use of physical probes is detrimental, as they induce perturbations of sufficient strength that can change flow phenomena and invalidate most measurements taken in the downstream region of interest. This has led to a renaissance in non-intrusive optical techniques that minimize induced flow disturbances and leave medium chemistry unaffected.
One of the key design parameters for high-speed test beds is thermal protection as the thermal gradients present in the boundary layer becomes extremely important as surface heating dramatically increases as a direct result of increased skin-friction from reduced boundary layer heights [3]. This imparts increased aerothermal strain on the vehicle and can lead to catastrophic failure, thus the importance of characterizing the thermal gradients imparted from the boundary layer is critically important [4,5].
Some current techniques that exist for optical thermometry in low pressure, non-heated flows include Planar-Laser Induced Fluorescence (PLIF), Coherent Anti-Stokes Raman Spectroscopy (CARS), and Tunable-diode laser absorption spectroscopy (TDLAS) [6–9] etc. PLIF has to employ the use of tracer molecules such as Nitric Oxide, Hydroxide [10], or an aromatic molecule [11,12], which could negatively impact the flow chemistry resulting in nonreal flow features and altered flow dynamics [6,8,13,14]. CARS is a non-intrusive technique that does not require seeding of the flow for thermal measurement making it an attractive option [3,15]. However, CARS is susceptible to misalignment in high-noise environments typically found in wind tunnel facilities [7]. Furthermore, CARS is mostly limited to point measurements at low pressure conditions, thus rendering it inadequate to fully characterize the dynamic thermal gradients typically present in boundary layers [7]. TDLAS suffers from being limited to an average measurement that is path integrated, which can enhance the nosiness and make it difficult to get accurate measurements that represent the flow properties near the surface of a vehicle [16–18].
2. ART fluorescence from REMPI of O2 and avalanche ionization of N2
Here, we propose and demonstrate a novel laser-based line thermometry technique for use in low-enthalpy high-speed flows, which can resolve a 1D line thermal profile without particulate or gas seeding. The technique builds upon advances in Resonance Enhanced Multi-Photon Ionization (REMPI) of molecular oxygen, which has been demonstrated to have the capability to achieve high spatial and temporal resolution measurements of concentration profiles and species-specific rotational temperatures in combustion and air-discharge environments [19–23]. ART resonantly ionizes the target molecules by REMPI; since REMPI is a highly non-linear optical process, the energy deposition into the surrounding medium is sufficiently small [24]. ART differentiates from Radar REMPI, in that a weak plasma discharge is produced to yield the ART fluorescence signal. To achieve O2 ART thermometry, specifically chosen rotational bands of O2 are resonantly excited via focusing a frequency doubled dye laser of sufficient energy such that regions of high laser energy density is able to briefly populate with excited O2 molecules given by Eq. (1).
where $h{\nu _{REMPI}}$ is the photon used to resonantly ionize O2 and ${e^ - }$ is photoelectron.The resulting photoelectrons are then amplified by the laser pulse to induce electron-impacted collisional excitation and electron avalanche ionizations of N2 given by Eq. (2).
The recombination of electrons and molecular nitrogen ions produces emissions of the first negative band of $N_2^ + ({{B^2}\Sigma _u^ +{-} {X^2}\Sigma _g^ + } )$, given by Eq. (3). or further decay by first positive band given by Eq. (4). [20].
where $h{\nu _{{1^ - }}}$ is the first negative band of N2, and $h{\nu _{{1^ + }}}$ is the first positive band of N2.The resulting emissions from the first negative band are at three distinct peaks (Δv0, ∼390nm; Δv2, ∼425nm; Δv1, ∼430nm), resulting from the $1 \to 0$, $2 \to 1$, and $1 \to 1$ transitions, respectively. The energy diagram and the emission spectra for N2 are shown in Fig. 1 [25]. Since the N2 emission strength is directly related to number density of liberated photoelectrons from resonantly excited and ionized O2, an in-depth analysis is required of the various O2 REMPI rotational lines and the resulting collisional rates for N2+.
Fig. 1. (a) energy diagram for N2+ first negative band (b) Normalized ART spectrum from the first negative band of N2+.
Furthermore, to apply a rotational state distribution analysis to assign temperature in O2 from REMPI, and subsequently assign temperature for resulting N2+ emissions, a rotationally resolved spectrum of molecular oxygen must be obtained and corresponding two-photon transition cross-sectional data is needed to identify suitable peaks.
The REMPI structure of O2 is described in detail in previous literature [26,23]. For this purpose, a brief summary is given. The ground state, O2(X2Σ), can be best described as Hund’s case (b), in which the splitting due to $\Sigma ^{\prime}$ = -1, 0, and 1 lead to the hyperfine structure in the ground state, which can denoted as G1, G2, and G3, respectively. The excited state O2(C3Π) can be best described as Hund’s case (a), in which Ω takes the values 0, 1, 2 respectively. The Ω values lead to the hyperfine structure in the C state, which can be denoted as F1, F2, and F3, respectively. Both the ground and excited states contribute to the hyperfine structures in the REMPI spectra, this presents a challenge in resolving the common two-photon rotational branches of O, P, Q, R, and S. There is an adopted convention of adding subscripts of the hyperfine structures to the rotational branch, for example, S21 represents the S branch which originates from G1 and transits to F2. The focus of this study is the two-photon transition line strength $T_{f,g}^{(2 )}$ between the excited state C3Π and the ground state X3Σ of their respective Hund’s cases and has been modeled in detail in literature [27] and can be expressed by Eq. (5).
The S21 branch transitions were selected for this analysis due their spectral distinctness and position that made them readily accessible via frequency double dye laser emissions. It should be noted the S21 branch transitions used in this study are acceptable for gas temperatures <700K, as above this the lines become congested due to overlap of multiple branches between 286 and 287.5 nm [21].
A theoretical O2 REMPI spectral model capable of resolving the S-branch transitions has been previously developed, studied, and described in literature [21]. It was shown the model exhibited high accuracy when compared to experimentally obtained spectra, and was validated up to 1700 K [19,21]. This model was used to replicate the REMPI spectra at various temperatures and used with Eq. (1). to identify suitable two-photon transitional line strengths to test for ART. An example of the REMPI spectra produced by the model at 180, 293, and 473 K is shown in Fig. 2. The model indicates that as the temperature rises from 180K, population distributions of molecular oxygen shift towards higher rotational states, resulting in increased structure in the spectrum. Thus, the peaks that could be suitable contenders for O2 ART change depending on the temperature of the test medium. A more in-depth look at the model reveals that certain peaks signal does not vary as a function of temperature (i.e., band heads), furthering the importance of peak selection.
Additionally, while ART is driven by O2 REMPI and vibrationally excited N2+; comparison of REMPI spectra of air by coherent microwave scattering (Radar REMPI) [19] and N2+ fluorescence from the $1 \to 0$ transition at atmospheric pressure and room temperature has shown great similarity, showing all major ro-vibrational lines of molecular oxygen [21]. Furthermore, the intensity of nitrogen fluorescence ($\Delta {v_0},\Delta {v_1},\Delta {v_2}$) closely follows the (2 + 1) REMPI excitation of molecular oxygen. The prominent band representing 2 + 1 REMPI with the initial 2-photon transition O2(C3Π (v = 2) ← X3Σ (v’=0)) lies between 285-289nm. This relationship allows direct utilization of the modeled spectra along with a previous study of the calculated rotational strengths of the S21 branch transitions based on Eq. (1). to find multiple resonant wavelengths of interest for the calibration of ART. The selected resonant wavelengths for this study are listed in Table 1 and were chosen due to population distributions being relevant across the selected range of calibration temperatures.
Table 1. Selected rotational line of S21 branch for temperature measurements
Table 2. Tabulated ART results for N2+ fluorescence bands Δv0, Δv2, and Δv1
Using the values from Table.1, the O2 two-photon transition from state g to f will produce a theoretical resultant fluorescence intensity ${I_{{\lambda _n}}}$ of the first negative band of vibrationally excited N2, which can be expressed by Eq. (6).
When a region of the spectrum including multiple rotational lines is measured, a statistical fit of the Boltzmann plot gives an accurate measurement of the rotational populations and thus the rotational temperature, i.e., the slope of the Boltzmann plot as shown in the Eq. (7).
3. Experimental setup
To identify specific rotational peaks most suitable for statistical fits of the Boltzmann plots, a calibration study was conducted at 180, 233, 293, 367, and 460 K in a gas cell. A general rendering for the calibration experiment for O2 ART is shown in Fig. 3. The second harmonic of an Nd:YAG Laser (Continuum Surelite SL-10) with a pulse width of 8ns, repetition rate of 10 Hz, and 220mJ/pulse lasing energy was used to pump a dye laser (Continuum ND6000) that utilized a mixture of Rhodamine 590 and Rhodamine 610 to produce lasing light around 574nm (0.02 cm-1 linewidth).
The dye laser was frequency doubled to generate ultraviolet (UV) beam using an auto-tracker (Continuum UVT-1) to maintain a constant conversion efficiency from the frequency doubling crystal. The UV beam had energy of ∼10 mJ/pulse from 285 to 287.5nm. The UV beam was focused using a fused-silica spherical lens with focal length of +150mm, which generated a fluorescence line. The line was centered in a cylindrical, fused-silica glass cell. The emission spectra were collected via two +100mm spherical fused silica lenses that served to focus the light onto the slit of a spectrometer (Princeton Instruments, 600gr/mm blazed at 500nm) with a 50µm slit width. The spectrum was captured via an intensified scientific camera (PI-MAX4 1024f) with the sensor size of 1024 × 1024 pixels. To avoid local heating and maintain a uniform species number density in the area of interest, a constant flow of standard air was provided to the cell at a rate of 0-50 L/min via an electronic flow controller (OMEGA). Depending on the desired calibration temperature the air passed through either a flow heater (OMEGA) or through a custom-built flow-chiller to achieve temperatures ranging from 180 to 470 K and cell temperature was monitored by a K-type thermocouple and maintained within a tolerance of ±1% of the set point.
4. Results and discussion
4.1 ART signal dependence on laser power
To find the point of saturation and confirm the dependence of fluorescence on (2 + 1) O2 REMPI, a dye-laser of similar design was used that achieved per pulse energies up to 38mj. Figure 4(a) shows the ART power dependence with a 287.33-nm laser beam in ambient air. It clearly shows that the signal intensity scales quadratically with laser power in the range from 0–30 mJ/pulse for a 300-mm focal length lens. It confirms that the driving mechanism is from O2 (2 + 1) REMPI, because of a quadratic dependence of the ART signal on the laser power at the resonant excitation wavelength. When the laser pulse energy is beyond ∼30mJ/pulse, saturation effect occur which is consistent with the typical multiphoton absorption phenomenon. Figure 4(b) shows a typical ART image in ambient air in false color. The laser pulse energy of 30mJ/pulse focused by a lens with 300mm focal length, showing a strong fluorescence line of almost 50mm long.
Fig. 4. Laser power dependence of ART signal (a); ART fluorescence emission line from 287.33 nm resonant wavelength (b); Line average intensity profile of the 287.33 nm resonant emission line (c).
The measurement was conducted to quantify the amount of energy deposited into the flow using a scientific grade, high-sensitivity thermopile meter (1mW detection at ±0.5% repeatability), the sensor was unable to detect any change in output energy from pre-focal spot to post-focal spot of a 300mm spherical lens with input wavelength of 287.5nm at 30mJ/pulse.
4.2 N2+ emission spectra by ART at various excitation wavelengths
Visualized in Fig. 5 are the imaged N2+ emissions at 293K for all resonant wavelengths listed in Table 1. The spectra at the selected wavelengths over the range of temperatures showed similar features, changes in the bands emitted signal intensity was the only observable change. Spectra of all ten wavelengths at the remaining calibration temperatures are given in Supplement 1 and are Fig. S1, Fig. S2, Fig. S3, and Fig. S4 for 180, 233, 367, and 460 K, respectively. To minimize shot-to-shot laser fluctuations and remove background effects, the captured emission signals are 200-image averaged and background subtracted. The use of the spectrometer allowed for discrete analysis of each emission peak in the first negative band of N2+,(Δv0, ∼390nm; Δv2, ∼425nm; Δv1, ∼430nm) of a high spectral accuracy.
To confirm the resonantly excited O2 and the resulting N2+ emissions were temperature sensitivity, a study was conducted that compared signal intensity at various rotational bands that were temperature dependent or independent. It was found that when non-temperature sensitive peaks of the O2 REMPI spectra were selectively excited the resultant N2+ emissions were also independent of medium temperatures. The reciprocal relationship also holds true. This result is visualized in Fig. 6(a) where a 287.28nm O2 resonant line is directly excited and resultant fluorescence signal is temperature insensitive; while in Fig. 6(b) the 286.51nm directly excited resonant line and resultant fluorescence signal is temperature sensitive. This behavior is foreshowed by the aforementioned theoretical REMPI spectrum in Fig. 2 and for ease of comparison shown again in Fig. 6(c). A visual inspection of the 286.51nm peak signal varies drastically at various temperatures, whereas the 287.28nm signal exhibits small intensity variation. This further highlights the importance of peak selection, as certain resonant wavelengths are suitable for thermometry applications.
Fig. 6. (a) 287.28 nm excited non-temperature sensitive peak. (b) 286.51 nm excited temperature sensitive peak. (c) Theo. REMPI spectrum.
4.3 Excitation wavelength selection for temperature determination
4.3.1 Temperature determination using single fluorescence band
The N2+ emission spectra similar to the ones depicted in Fig. 5 were captured and post-processed. The raw images were averaged and background subtracted to remove any light scattering or artifacts present. Integration was performed under each band, with care taken to not include any contributions that were not associate with the band emission. The resultant signal was then plotted for each temperature, this allowed for identification of possible groups that would yield a high coefficient of correlation and thus an accurate temperature. The peak signals for 293K are visualized in Fig. 7 with potential groups shown via the red dashed line, which results in a poor fit. It should be noted, potential groups for other temperatures and peaks were not as easily found from a visual inspection; thus, a more iterative selection process was used till a fit with high correlation was found. In the conservation of space, the responsible reader is directed to the Supplement 1 for 390, 425, and 430nm peaks signal intensities visualized in fig. S5, fig. S6, fig. S7, and fig. S8 for 180, 233, 367, and 460K in the Supplement 1, respectively.
Fig. 7. Integrated peak signal values for Δv0, ∼390 nm (a), Δv2, ∼425 nm (b), Δv1, ∼430 nm (c) at 293 K.
From the signal intensity plots, four wavelengths are selected that have the highest fit metrics at each calibration temperature. The slope of the fit in the Boltzmann plot is applied to Eq. (7) to yield a temperature. The ART reading for 293K is shown in Fig. 8 for the 390, 425, and 430nm peaks. Each emission peak yields an approximate temperature close to the actual measured cell temperature of within ±10 K, and all have a high coefficient of correlation >98% suggesting a very linear relationship exists between N2+ emissions from resonant excited O2. ART. Measurements for 180, 233, 367, and 460K are found in in the Supplement 1 and are visualized in fig. S9, fig. S10, fig. S11, and fig. S12, respectively. The acquired ART temperatures at each emission peak for all calibration temperatures are tabulated in Table 2.
Fig. 8. Temperature determination by N2+ emissions at Δv0 (a), Δv2 (b), and Δv1 (c) for actual temperature of 293 K.
Table 3. Referenced and measured temperatures in air from full spectrum integration study.
Through the studies of the individual emission peaks from the first negative band of N2+, it is proven that ART is a viable non-seeded, non-intrusive thermometry method for resolving temperature gradients with sufficiently high accuracy. The high accuracy and low error of the calculated temperature suggests the vibrational N2+ temperature is useable for temperature determination. The excited vibrational temperature of a molecule is typically slower to respond to medium temperature changes, this inherent characteristic is due to the fundamental physical time required for molecular collisional rates to occur and enter a vibrationally excited temperature state. However, the results show the N2+ fluorescence that is generated and resultant measurements are outside this time requirement and the vibrational read emissions has achieved near true medium temperatures.
The data in Table 3 suggests an accurate temperature reading of the gas medium across the calibration temperatures can be extracted from the unique peaks of the emission spectrum. The Δv0 (390nm) exhibits the best capability of accurate thermal measurements, with the highest percent error difference between actual and measured being 2.94%. Additionally, Δv1 (430nm) and Δv2 (425nm) yield decent results for all ranges except at the coldest cell temperature of 180K. Since these transitions are of higher rotational states, it is expected the signal would weaken at low temperatures as the populations distributions will trend more towards the ground state thus, less energy will be imparted as the transitional strengths diminish directly reducing the collisional rates.
4.3.2 Temperature determination using integrated fluorescence bands
To expand ART measurement applicability and practical useability, a study is conducted; here the signal is found via integrating along the captured spectrum (370 to 435nm). This simulates the removal of the spectrometer and direct imaging of the emission fluorescence through an optical bandpass filter that blocks light outside of the N2+ spectral region.
Figure 9 visualizes the peak intensity values found from the aforementioned integration for the calibration wavelengths at 180, 293, and 460K. An inspection of Fig. 9 and Fig. 7 suggest the summed peak intensity values trend towards the Δv0 emission. This is expected as its emission intensity strength dominates the Δv1 and Δv2 bands. Using the aforementioned approach for finding peaks that could related temperature well for the individual emissions bands, the best fit was found from a selected group, and fitted to a Boltzmann plot to yield a temperature measurement.
The Boltzmann plots in Fig. 10 show the temperature determination for the integrated signals at all calibration temperatures. Only the most temperature sensitive rotational lines were chosen and are listed in Table 4 additionally, the error between the actual and measured cell temperatures is given. The plots show high linearity among the four selected rotational lines for temperatures of 180, 233, 293, 367, and 460K, thus allowing for accurate thermal measurements. Furthermore, this suggests that direct imaging of the N2+ emission is a viable method for ART, and direct imaging will reduce experiment setup time, complexity, space, and expense.
Fig. 10. Boltzmann plots for 180, 233, 293, 367, 460 K calibration temperatures using fully integrated spectra of N2+ fluorescence.
Table 3 suggest as temperature decreases, the resonant wavelength selection trends towards lower rotational states of molecular oxygen. This is expected, as temperature decreases there is less structure in the REMPI spectrum as population distributions trend towards lower rotational levels. Thus, the lower rotational states become the most viable for maintaining collisional rates for sufficient N2+ emissions and maintain measurement repeatability. Furthermore, the integrated signal measured temperature only differs slightly from actual cell temperatures, thus there is relatively low error between them. By comparing the integrated result with the per peak results, the integrated signal maintains accurate measurements over a greater thermal range than Δv1 or Δv2. The integrated signal measurement capability and accuracy closely resembles the Δv0 emission band, but differs in that the integrated signal will have a great SNR ratio, as the emission signal will be sufficiently stronger as it is a contribution from all three bands. There is only a ±1% difference between the fully integrated signal and Δv0 signal measured and actual cell temperatures, further suggesting the majority of the emission light intensity is a direct result of the Δv0 band.
5. Conclusions
In this study, air REMPI thermometry (ART), a novel, non-intrusive, non-seeded technique is established and verified through a detailed calibration analysis. By weakly ionizing a medium gas that contains oxygen molecules, ART utilizes resonant wavelengths to selectively excite various rotational bands of O2. Through avalanche ionization process, the first negative band of N2+ is weakly vibrationally excited, producing spectral emissions in the visible region from 395 – 430nm. The resulting emissions are processed and fed into a Boltzmann relationship that yields a 1D line temperature measurement. The emissions have been extensively studied that resulted in ideal peak selections and thermal relationships, for individual emission bands (Δv0, ∼390nm; Δv2, ∼425nm; Δv1, ∼430nm) and fully integrated emissions (Δv0 + Δv1 + Δv2). It has been shown through individual band analysis, the dominating emission Δv0 produces accurate reference temperature measurements with a max total error of ±4% for <700K medium temperatures. While Δv1 and Δv2 emissions are not ideal for standalone thermal measurements, having total errors of 14% and 25% respectively. The high measurement error from the Δv1 and Δv2 primary stems from the 180K test-point, suggesting that the bands may be more suitable for higher temperature applications.
The fully integrated emissions analysis yielded temperature measurements with accuracies similar to the Δv0 bands; having max total error of ±5%. Additionally, the ideal resonant peaks found are given for each temperature setpoint in Table 4. ART though direct imaging of the emission will reduce experiment setup time, complexity, space, and expense and helps realize the techniques full potential. It is the suggested method for ART measurements of <700K, as the SNR is higher as contributions from Δv0, Δv1, and Δv2 result in sufficiently greater signal intensity per shot. The main drawback to ART is currently four wavelengths are needed to achieve an accurate and repeatable thermometry fit. Furthermore, a dye laser that is capable of generating at least ∼10mj/pulse is needed to achieve an ART 1D line of sufficient length. It was shown that a 3-inch emission line is possible with a 30mj-pulse, with the measurement distance and lasing energy being the main limiting factors of emission line length.
Funding
National Science Foundation (2026242); U.S. Department of Energy (DE-SC0021382.).
Acknowledgments
This work is supported by University of Tennessee, NSF-2026242 and DOE DE-SC0021382.
Disclosures
The authors declare no conflicts of interest.
Data Availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
Supplemental document
See Supplement 1 for supporting content.
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