Torr-level, seedless, non-resonant velocity distribution function measurement with a dual-color, single-shot coherent Rayleigh–Brillouin scattering scheme

A two order of magnitude spectral acquisition improvement in velocity distribution function measurement is demonstrated with a novel single-shot, dual-color coherent Rayleigh–Brillouin scattering (CRBS) scheme. By performing this non-resonant and seedless spectral diagnostic technique, capable of obtaining a spectrum in ∼300  ns, we demonstrate accurate temperature (ranging from 300 K to 500 K) and pressure (ranging from 760 Torr down to 1 Torr) measurement capabilities, for a variety of atomic, molecular and multispecies gases. This demonstrated gas thermodynamic characterization capability of the dual-color CRBS scheme over broad ranges of pressure and temperature for a variety of gases is anticipated to be of great interest to a plethora of fields, ranging from aerospace applications to low-temperature plasmas, providing with an accurate measurement of physical properties of neutral particles, for a range of gases.


Introduction
Non-intrusive remote sensing of gas properties is highly desirable in a plethora of scientific and engineering fields to accurately estimate the thermodynamic parameters of neutral * Author to whom any correspondence should be addressed.
Original Content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. and charged species. Resonant (such as Raman and fluorescence) and non-resonant (such as Rayleigh) light scattering from atomic and molecular neutral and charged gas particles are widely used for remote sensing of physical properties, since the resulting scattering spectra contain information about the thermodynamic state of the scatterers. For instance, the Rayleigh-Brillouin scattering (RBS) lineshape consists of a central Rayleigh peak due to the Doppler shift by the thermal motion of gas particles, and two Brillouin side peaks which result from the acoustic motion of the gas. The spectral width and relative intensity of the RBS spectral lineshape provide information on various important gas properties such as the temperature [1][2][3][4][5][6], density [7,8], sound speed [7,9], bulk viscosity [10], flow velocity [11,12], etc and can thus be effectively used for gas diagnostics. Laser Rayleigh scattering [13] has over the last decades become one of the most popular linear diagnostic tools for RBS lineshape measurement. Depending on the employed scheme, observation of the linear RBS may be performed in different ways, ranging from spontaneous RBS (SRBS) [3,5,14,15] to filtered Rayleigh scattering (FRS) [16].
Application of gas remote sensing with RBS has often been limited to test conditions at, near or above atmospheric pressures [3,14,17,18]. However, various applications in the aerospace [19][20][21][22], combustion [1,23], materials [24][25][26], low-temperature/weakly ionized plasmas [27][28][29] fields, etc operate in pressure regimes ranging from atmospheric to single or sub-Torr, thus imposing a high demand for accurate, non-intrusive, non-resonant and seedless diagnostics of neutral and charged species at such pressure regimes. Since RBS provides comprehensive thermodynamic information of neutral particles, it is indeed an attractive diagnostic technique for those applications. First of all, as a non-resonant technique, it does not have limitations on working wavelengths or on gas species. This is one of the advantages over resonant techniques such as laser-induced fluorescence [30] or coherent anti-Stokes Raman scattering (CARS) [31], in which a specific energy level of testing gases needs to be targeted. Additionally, it can be readily utilized for various weakly ionized plasma applications. Considering the differential scattering cross-sections in 10 −32 m 2 sr −1 , 3.9 for Rayleigh (N 2 ) and 794 for Thomson (e −1 ) [32], one can expect the RBS signal to be the dominant scattered signal in applications where the ionization ratio is <10 −4 , enabling neutral particle diagnostics by RBS in such plasma devices. Noting various weakly ionized plasma applications operate at atmospheric to sub-atmospheric pressure [27,29,33], expanding capability toward low gas density applications can be greatly beneficial. In addition to neutral species measurements in low temperature plasmas, it is noteworthy that the RBS techniques would also be applicable to fully charged particle flows such as e.g. the ones encountered in a Hall effect thruster, where the corresponding pressures encountered are on the order of 10 −5 Torr [34]. Thus, pursuing spectral acquisition capabilities at such low relative densities for both neutral and charged species, will enable novel insights into the relevant processes in such measurement cases.
However, detection of the linear RBS signal becomes challenging at these sub-atmospheric pressures due to (a) its inherent small Rayleigh cross-section and (b) the existence of less scatterers. For SRBS and FRS, where spontaneous light scattering occurs in a 4π solid angle as a result of random gas fluctuations, most of the scattered light intensity decays proportional to 1/r 2 at distance r away from the scattering volume. This weak signal makes measurement almost impossible in optically noisy environments. On the other hand, by operating in a coherent Rayleigh-Brillouin scattering (CRBS) scheme, a nonlinear light scattering technique, the generated RBS signal propagates coherently in a singular direction from the scattering volume, providing a much higher signal-to-noise ratio (SNR) than in linear RBS techniques. This renders CRBS as a diagnostic technique ideal for low gas density applications.
Pressure sensing measurements down to a few Torr were achieved using single-shot CRBS [7], a technique developed to obtain a full CRBS spectrum within a single laser pulse (order of ∼200 ns). However, the measurements reported in [7] were limited to acquiring the spectral integrals of the CRBS signal, not the full RBS spectral lineshapes which provide more comprehensive information about the gas particles in the measurement volume. The capability of retrieving the full single shot CRBS spectra has been limited to pressures of ∼200 Torr [35].
In this work, we reach the sub-Torr range for gas diagnostics with a novel single shot, dual-color CRBS scheme. To achieve this measurement capability, a dual-color CRBS technique utilizing 1064 nm pump beams and a 532 nm probe beam is employed to produce an improved signal to noise ratio at lower pressures versus single color CRBS (where the probe is at 1064 nm). We note that all previous single shot CRBS systems utilized 1064 nm laser beams for the pump and probe beams [7,35]. Details on the dual-color CRBS scheme and its advantages compared to the single color CRBS are given in section 2, while the capability of the dual-color CRBS technique to resolve full CRBS spectra of neutral gases is demonstrated at sub-atmospheric pressures (atmospheric pressure to 1 Torr order) and elevated temperatures (300-500 K) in sections 4.2 and 4.3, respectively. Successful acquisitions of full CRBS spectra are demonstrated for various test gases, including air, N 2 , Ar, CO 2 , Xe, and SF 6 . Altogether, this demonstrates single shot, dual-color CRBS's robustness as a non-resonant technique for the accurate estimate of temperature and density at low density conditions, for neutral or charged heavy species, irrespectively of the working gas. This scheme can thus immediately be extended and enable the thermodynamic characterization of neutral species in partially ionized gases.

CRBS overview and dual-color CRBS scheme
CRBS is a non-resonant, four-wave mixing laser diagnostic technique which, like other RBS techniques, allows for in-situ measurements of important gas properties such as temperature, sound speed, pressure, polarizability, flow velocity etc [7,14,17,35,36]. In CRBS, two interfering laser beams, termed the pumps, having a relative frequency difference ∆f and the same polarization, generate a traveling density wave in a gas, called the optical lattice. The lattice traveling speed is determined by the phase velocity v ph of the interference pattern of two pump beams, given by the equation: where λ pump is the pump beam wavelength and ϕ 2 is the half crossing angle between the pumps. A third beam, termed the probe, with its polarization set to be orthogonal to that of the pumps, is incident on the lattice at the Bragg angle, and is then coherently scattered from this induced density wave, resulting in the fourth beam, which is the CRBS signal beam. By scanning the ∆f between the pumps, the travelling optical lattice interacts with the respective portions of the gas velocity distribution function (VDF). Ultimately, the signal intensity as a function of the lattice phase velocity, results in the CRBS spectral lineshape.
The resulting wave vector of the coherently scattered signal depends on the phase matching conditions that govern the momentum conservation between the wave vectors of the pumps, probe, and signal beams, given by: The phase matching condition, equation (2), can be satisfied in various ways, including a two-dimensional (2D) coplanar backward/forward orientation, two color phase matching in 2D [17,37], or a three-dimensional (3D) folded phase matching [38]. The 2D phase matching scheme has been commonly adopted, as in [2,7,35]. In the 2D co-planar singlecolor configuration, since the probe and the signal beams are exactly counter-propagating the pump beams, the signal detection is prone to high optical noise from the high-energy pump beam even though the polarizations of the pump and signal beams are orthogonal. Additionally, potential backwards amplification of the laser beams, can be catastrophic for the laser systems employed. To overcome these issues, 3D folded configurations, where the two pump beams define a plane while the probe and signal beam form another plane that intersects the pump beams' plane where the optical lattice propagates, can be employed to eliminate them.
The 3D single-color CRBS geometry is shown in figure 1(a), where two equi-polarized pump beams counterpropagate at an angle ϕ on the x-y plane. A probe beam is incident at the Bragg angle θ on the y-z plane and is scattered, resulting in a signal beam on the same y-z plane. This 3D configuration for CRBS was successfully utilized previously for the in-situ nanoparticle detection in an arc discharge [38].
Although this 3D configuration with a single-color system provided a great improvement to the resulting SNR for the reasons mentioned previously, it is still not the optimal solution for lower pressure applications where the signal can be several orders of magnitude weaker.
To improve on this, in this work we adopt, for the first time to our knowledge, a dual-color single shot CRBS scheme to further push the measurement envelope of CRBS towards low pressure applications. Here, we make use of a 532 nm probe beam in a dual-color CRBS scheme, which offers several advantages over the single-color CRBS scheme. First, the geometric configuration for the dual-color CRBS scheme, e.g. a configuration where the pump's second harmonic is used as a probe beam, as is shown in figure 1, prevents the high-energy pump beams from sharing the same optical path as the probe and signal beams. Any remaining unwanted background from the pump beams can be spectrally filtered out on the measurement photodiode with a notch filter. In addition, RBS, which is proportional to λ −4 , enhances the intensity of the scattered signal from the 532 nm probe by sixteen times compared to that from a 1064 nm beam of the same power. Finally, the 532 nm signal takes advantage of high-sensitivity photocathodes combined within high-gain photo-detectors such as photomultiplier tubes (PMTs) when the signal can be extremely weak as going toward low-pressure applications (for high-pressure cases where a signal photon influx is large, photodiodes can outperform PMTs [39]). It should also be noted that PMTs offer a much higher gain at 532 nm in comparison to similar detectors for 1064 nm. Additionally, typical quantum efficiency for 532 nm photocathodes is ∼20%, while photocathodes for 1064 nm experience a ∼2% quantum efficiency [40].
In a dual-color CRBS scheme, the phase matching condition, equation (2), is simplified into, Rearranging equation (3), the half crossing-angle for the probe ψ/2 is obtained as, which represents the angle at which the probe beam must be incident onto the resulting optical grating to fulfill the Bragg condition. Figure 2 presents the required 532 nm half crossing angles ψ/2 as a function of the half angle ϕ/2 formed by the 1064 nm pump beams. It is noteworthy that the approximation ψ ≈ ϕ λ probe λpump only holds for a narrow crossing angle (co-propagating pumps configuration). In the present work, where the pump beams counter-propagate at an angle of ϕ/2 ≈ 88 • , a halfcrossing angle of ψ/2 ≈ 30 • for the probe beam is obtained.

Experimental setup
In this work, we aim to establish the measurement capability of gas thermodynamic properties in low pressure and high temperature conditions with single shot CRBS. To achieve this goal, CRBS was applied in a hexagonal gas chamber which provided a controlled gas pressure and temperature environment. A 3D CAD model of the chamber and the propagation directions of the four CRBS beams are shown in figure 3 where a schematic of the four wave vectors is inset. Three input laser beams (two 1064 nm pump beams and a 532 nm probe beam; all beams operating at a 10 Hz repetition rate) were generated by a custom-built frequency agile dual-color laser system, which is described in detail in [41]. Here we provide a short description of its operation. The system first generates two 1064 nm beams having a pulse duration of ∼300 ns (temporal duration adjustable from 10 up to 1000 ns), energy of ∼450 mJ per pulse per beam. The system provides with a frequency chirp rate, which denotes the laser frequency change over the As briefly explained in section 2, this phase velocity scan range basically corresponds to the resolving range of the gas VDF in the form of the CRBS spectral lineshape. In practice, by increasing the frequency chirp rate or by adapting a longer pulse duration, the scanning range can be expanded to accommodate a specifically required scanning range depending on the conditions of test articles.
Part of one 1064 nm beam is sampled to produce the second harmonic 532 nm probe beam, which keeps the temporal and spatial profiles of the original 1064 nm beam. The resulting 532 nm CRBS signal in the dual-color scheme is detected by a PMT (H14601-20, Hamamatsu) operated with a power supply (C10709, Hamamatsu). It is noted that, in the reference singlecolor scheme, the 1064 nm signal is detected by an InGaAs PIN photodiode (5G6854-01, Hamamatsu) having a spectral response range 0.9-1.7 µm. Both signals are recorded through an oscilloscope (Wavesurfer 510, Teledyne Lecroy) with a sampling rate of 10 GS s −1 . With this setup, two main experiment campaigns were carried out to demonstrate dual color CRBS capabilities: (a) gas pressure measurements, where the chamber pressure was scanned from 1 atm to sub-Torr, and (b) temperature measurements, where the temperature of the gas was scanned from ∼300 K to ∼500 K. Note that the number of laser shots averaged in the oscilloscope are 5/20/100 shots at 100/10/1 Torr orders in the pressure scanning experiment campaign, and 5/10 shots in the temperature scanning experiment campaign. The chamber pressure was monitored by a capacitance manometer (ACG-HT-1-1, KJLC) having a typical accuracy of ±0.2%.
The custom-made hexagonal heating box, figure 4(a), was used to provide a controlled gas temperature at the CRBS measurement point which is located at the center of the box. The heating box was thermally isolated from the main chamber by a ceramic rod. A heater was attached at the top of the box, and wall temperatures at the top and bottom were measured by respective K-type thermocouples. The mean temperature between the top wall and bottom wall is denoted as T wall . Figure 4(b) presents an example data set of the monitored wall temperatures during a temperature scanning experiment. T wall is assumed to be the gas temperature at the CRBS measurement point. This assumption was verified by a finite element thermal analysis performed by an open software, Finite Element Method Magnetics (FEMM 4.2) [42]. Therefore, this T wall is used to verify the theoretical relation that the features of the CRBS lineshapes (Brillouin peak shift or Rayleigh fullwidth half-maximum (FWHM)), which contain gas temperature information, should follow. This will be demonstrated in section 4.3, confirming the thermometry capability of dualcolor CRBS. Additional justification is provided by comparison of the experimentally obtained CRBS lineshapes with the simulated ones using the Tenti s7 code [2], showing a good agreement (see appendix). It is noteworthy that in the present work, as the temperature is measured by means of tracing the Brillouin peak location or the FWHM of the Rayleigh scattering, analysis of the spectral lineshape is involved. Thus, the uncertainty of the measurement largely depends on the SNR level on resolving the full lineshape, meaning that at low pressure, where the signal is weak, a larger uncertainty results.

Comparison of single-color and dual-color CRBS
As discussed in section 2, several factors greatly improve the SNR in dual color CRBS compared to the single-color CRBS scheme. Here, the pressure scanning experiment was performed where the CRBS spectral lineshapes were obtained with both single-color CRBS and dual-color CRBS schemes for a direct comparison between the two schemes: the gas pressure was varied within the chamber and single shot CRBS spectra were recorded with each CRBS scheme. The resulting spectra are compiled into spectral maps to demonstrate the evolution of CRBS lineshapes as a function of pressure. Figure 5 presents the resulting CRBS lineshape spectral maps for (a) single-color CRBS and (B) dual-color CRBS; working gas is CO 2 at 300 K in both cases, where (a) depicts the spectra measured using a 1064 nm probe beam in the 3D phase-matching configuration (see figure 1(a)) and (b) shows the spectra resulting from the 532 nm probe beam in the dual-color configuration (see figure 1(b)). The corresponding colormaps indicate the normalized CRBS signal intensity at each pressure.
First, it is worth noting that the good agreement of the two CRBS spectral maps obtained by the two different schemes at higher pressures confirms that the dual-color scheme accurately resolves CRBS spectra. Importantly, the main difference between the two schemes can be found at the low pressure regime. Approaching the low pressure regime, the signal in the single color scheme is largely dominated by the noise floor. While the detection of the CRBS spectra by the single-color 1064 nm scheme is limited to a pressure of ∼200 Torr, similar to the reported limitation of the past single-color CRBS system [35], full CRBS lineshapes down to a pressure of 1 Torr are successfully resolved using the dual-color CRBS scheme. Apart from CO 2 , we reached similar detection levels with other atomic or molecular gases of comparable polarizability, such as air, argon, xenon, and SF 6 as shown in section 4.2. To quantify the SNR of the experimentally obtained CRBS signals, we use the relative root mean square error (RRMSE), defined as where X i is the ith experimental data point and f i is the ith value from the fitted function. A lower value for the RRMSE suggests a higher SNR for the obtained experimental data. Figure 5(c) presents the RRMSE as a function of gas pressure for the single-color CRBS scheme (1064 nm probe-red dot) and the dual-color scheme (532 nm probe-green dot). It is noteworthy that the dual-color scheme greatly enhances the SNR; the RRMSE is suppressed to under 20% for pressures on the order of 1 Torr (the RRMSE at lower pressure ranges can be seen more clearly in figure 7). We note that the discontinuity on the RRMSE curve for the 532 nm probe is due to the PMT gain change. Importantly, we also note that this result is ultimately limited by the performance of the photodetector used: a detector with the same bandwidth and better gain should allow for accurate measurements at even lower pressures.

Pressure measurement with dual color CRBS
One major advantage of CRBS is that as a non-resonant technique it can be applied to nearly any gas without having to change at all the optical setup. Figure 6 shows the normalized CRBS spectral maps for a variety of gas species as a function of the gas pressure. These include gases ranging from monatomic to diatomic/polyatomic as well as a mixture of gas species (i.e. air). We note that the experimentally obtained lineshapes become Rayleigh dominant (i.e. primarily dependent on the gas thermal motion) and approach a Maxwell-Boltzmann lineshape as the pressure reduces. As anticipated, the SNR decreases at lower pressures: lower number density of scatterers results in less useful signal. Although the signal depends on density, measuring the temperature and knowing the gas composition allows for the determining of pressure through the ideal gas law.
The RRMSE at sub 100 Torr pressures for the spectral maps of figure 6 is shown in figure 7. We note again that the discontinuities in the plots are due to the change in the detector gain. RRMSE difference between gases are notable. As mentioned in section 4.1, the RRMSE is the indication of the SNR. The signal strength largely depends on the polarizability of gases, as given in table 1, therefore one can expect a weaker signal for gases with low polarizability. Note that the polarizability of air may be approximated to be a volume-weighted average of N 2 and O 2 , the primary gas species it is composed of, as demonstrated in [37]. For gases with relatively low polarizability (here air, N 2 , and Ar), full CRBS lineshapes are resolvable down to 10 Torr with RRMSE <20%. Meanwhile, for gases of relatively high polarizability (CO 2 , Xe, and SF 6 ), the full CRBS lineshapes are resolved at pressures on the order of 1 Torr. This is a significant improvement of two orders of magnitude in the detection limit compared to the prior single-shot CRBS schemes used in the recent past [7,35].

Temperature measurement with dual-color CRBS
In this section, the capability of dual-color CRBS for temperature measurements is demonstrated. Depending on the spectral features of the CRBS lineshapes, gas temperature information can be extracted by either the location of the Brillouin  Sub 100 Torr RRMSE comparison between each gas for air, N 2 , Ar, CO 2 , Xe, and SF 6 . Depending on the gas polarizability, a CRBS lineshape at pressures even lower than 1 Torr can be resolvable with an RRMSE of <20%.
peak (corresponding to the temperature dependent gas sound speed), or the FWHM of the Rayleigh peak (corresponding to the thermal motion of the gas). For example, in the highpressure (i.e. above ∼300 Torr) range, where the Brillouin features are clear and traceable, the sound speed is determined by finding the spectral center of the Brillouin peaks on the phase velocity domain. In a gas medium of known composition, the temperature may then be obtained through the relation given in equation (6). On the other hand, in the lowpressure range (i.e. below ∼300 Torr), where Rayleigh scattering is dominant, the broadening of the Rayleigh spectrum, measured through its FWHM can be utilized to extract the temperature since the FWHM is determined by the Doppler shift of the probe beam's photons due to the thermal motion of the individual gas particles. In the present work, these two temperature estimation methods are demonstrated over a temperature range from ∼300 K up to ∼500 K.
Thus, the Brillouin peak in the phase velocity domain v Brillouin follows the relation given by, which can be used to estimate the gas temperature. Figure 8(a) shows the changes of the experimentally obtained, normalized CRBS lineshapes for SF 6 gas as a function of heatbox temperature under the same heatbox gas pressure. Importantly, we note that the peak intensity decreases with elevated temperature due to the decrease in gas density, as expected from ideal gas law. It is also worth noting that the detector gain did not need to be increased under the tested temperature range, hence no discontinuities in the recorded signals are observed. It is clear that the improved detection limit achieved by the dual-color CRBS scheme enables resolving full spectra at elevated temperatures where the signal becomes much weaker. From the top view of the map shown in figure 8(b), the shift in the Brillouin peak location is also clearly notable. Figure 8(c) shows the gas v sound extracted from the location of the Brillouin peaks in the CRBS lineshapes, with an overlapped a √ T fitting curve, where a is a proportional coefficient. The estimated sound speed follows the theoretical  relation given in equation (7). Thus, in a condition where Brillouin features are seen in the CRBS lineshape, gas temperature can be accurately estimated by tracing the Brillouin peak location on the CRBS lineshape.

Gas temperature measurement by Rayleigh peak
broadening. As mentioned earlier, temperature information can also be extracted from the broadening of the Rayleigh peak in addition to the Brillouin peak location. In low-pressure applications (<∼200 Torr), CRBS spectra approach Rayleigh dominant lineshapes which follow a Maxwellian distribution. Since the Maxwellian distribution is in a Gaussian form (e −mv 2 /2kBT ), the FWHM of the lineshape follows the relation which exhibits the same √ T relation between temperature and the spectral location of the Brillouin peak as in equation (7). Thus, utilizing the same method described in section 4.3.1, temperature information from CRBS spectra can also be extracted using the Rayleigh peak. Figure 9 demonstrates CRBS lineshapes vs. temperature maps for various gases at a constant 100 Torr pressure. As also seen with the Brillouin peak tracing in section 4.3.1, the CRBS signal intensity decay is notable as the temperature increases. Additionally, with increased temperatures, lineshapes spectrally broaden. It should be noted that, during the spectral acquisition, the pump beam intensities are monitored to ensure that the observed intensity decay is not resulting from a drift in pump energy per pulse (see section 'Signal intensity dependency check'). The measured FWHMs from the single shot, dual color CRBS spectral maps shown in figure 9 for each gas are plotted in figure 10 together with the fitted theoretical curves following the expression a √ T (solid lines). Each fitted curve has a different curve shape due to the varying proportional coefficient a. The coefficient a relates to the gas atomic mass (see equation (8)) through: which must be satisfied for each of the tested gases. The proportional coefficient a as a function of the gas mass is shown in figure 10(b). The dashed line indicates the relation between a and m, i.e. a ∝ 1/ √ m, confirming that the physical relation between the mass of a gas particle and a is well satisfied.

Conclusion
In this work, significant, two order of magnitude improvement in the temperature and pressure detection capabilities of CRBS from atmospheric pressure to sub-atmospheric pressure has been achieved by utilizing a novel dual-color CRBS scheme. The capability of resolving the CRBS spectra at such gas pressure range is highly desirable since it delivers information about the gas VDF, and thus enables for a variety of gas properties to be extracted. The dual-color, single shot CRBS scheme which has been utilized here for the first time to the best of our knowledge, has greatly improved the detection limit by approximately two orders of magnitude, enabling the system to resolve CRBS spectra in pressures down to 1 Torr, which previously had been limited to a 100 Torr order. As a non-resonant technique, it has been successfully applied to various gas types from monatomic and diatomic/polyatomic to a mixture of gas species.
Summarizing, non-resonant, seedless and non-perturbative thermometry with CRBS has been demonstrated, successfully deriving gas temperature from CRBS spectra for a calibrated gas temperature range from 300 K to 500 K. Depending on the spectral features of the CRBS spectra, temperature measurement can be made either by tracing the Brillouin peak location that corresponds to the gas sound speed or by evaluating the FWHM of the Rayleigh broadening that is proportional to the thermal motion of the gas. We note that there exist suitable pressure ranges over which either method is preferable. Both methods have reproduced the theoretical relation of the traced features to the gas temperature (∝ √ T) with good agreement. It has also confirmed that the observation well follows the physical relation between the mass of the gas particles and the proportional coefficient a. It should be noted that the maximum resolved temperature by the experiment presented here was limited by gas temperatures achieved by the heating box setup, not by the dual-color CRBS scheme's temperature resolving capability. For the scanned temperature range, fixing the detector gain at a single setting was enough to resolve the full spectra with a good SNR.
The demonstrated capability of the dual-color CRBS scheme over broad ranges of pressure and temperature is expected to greatly advance neutral particle thermodynamic characterization in various applications, including weakly ionized plasma sources, wind tunnels, shock tubes, etc. Additionally, it is envisaged that further extension of the techniques presented here to lower relative densities will enable the thermodynamic characterization of heavy charged species in a variety of low temperature plasma applications, such as Hall effect thrusters or magnetron sputtering. It is noteworthy that the capability of direct mapping of the VDF can provide information in determining departures from local thermodynamic equilibrium conditions in such test articles, and that various measurement such as manometry, velocimetry, and thermometry can be realized simultaneously using the dual-color CRBS techniques presented here.

Data availability statement
The data that support the findings of this study are available upon reasonable request from the authors.   Figure B1 shows an example of the intensity monitoring of the pump and signal beams performed over each measurement presented in this manuscript. It can be seen that the pump beam intensity remains constant over the whole data acquisition period.