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Abstract
This article describes the development and application of hydrogen (H2) chirped-probe-pulse femtosecond coherent anti-Stokes Raman scattering (CPP fs CARS) in high-temperature and high-pressure conditions. H2 fs CARS thermometry was performed in Hencken burner flames up to 2300 K, as well as in a heated gas-cell at temperatures up to 1000 K. It was observed that the H2 fs CARS spectra are highly sensitive to the pump and Stokes chirp. Chirp typically originates from optical components or systems such as windows, polarizers, and the optical parametric amplifier. As a result, the pump delay is modeled to provide a shift to the Raman excitation efficiency curve. With the updated theoretical model, excellent agreement was found between the simulated and experimental spectra. The mean error and precision are 2.8% and 2.3%, respectively. In addition, the spectral phase of the input pulses and the pump time delay determined from the experimental spectra closely align with the theoretical predictions. It is also found that pressure does not have significant effects on the H2 fs CARS spectra up to 5 MPa at 1000 K. The collision model provides excellent agreement with the experiment. This allows the use of low-pressure laser parameters for high-pressure thermometry measurements.
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1. Introduction
Hydrogen (H2) has been on the forefront of extensive combustion research, ranging from fundamental chemical kinetics [1] to applications in gas turbine engines and rocket propulsion [2]. High-frequency measurements on key parameters, such as temperature and species mole fraction, are required to understand the coupling between fluid mechanics and chemical kinetics during H2 combustion. Coherent anti-Stokes Raman scattering (CARS) is an excellent tool for providing non-intrusive, time and spatially-resolved measurements in reacting flows [3]. CARS was first demonstrated by Régnier et al. for H2 concentration measurements in a hydrocarbon flame [4]. Since then, substantial progress has been made in advancing H2 CARS for high-fidelity measurements in gas phase media [5–9]. Rahn et al. measured the self-broadening coefficients of the H2 Q-branch lines up to 1000 K and 50 bar [5]. Tran et al. further characterized the collision linewidth of H2-N2 mixture [6]. With known broadening coefficients, H2 CARS was demonstrated in a premixed, CH4/air flame up to 40 bar [7]. Later, Hancock et al. performed H2 CARS thermometry in Hencken burner flames [8]. Traditionally, Q-switched lasers are preferred for CARS measurements due to their high output power. The sampling frequency of these nanosecond CARS system is on the order of 10 Hz, which is at least two orders of magnitude lower than the frequency required to resolve the transient dynamics of turbulent reacting flows [10]. With the advancements in femtosecond (fs) laser sources, researchers have developed fs CARS systems that are capable of achieving sampling rate on the order of 1 kHz [11–13].
The first H2 fs CARS was demonstrated by Lang et al. in a heated gas cell up to 1100 K [14]. Constructive beating patterns of the H2 Q-branch transitions were recorded with sub-picosecond time-resolution. The authors also attempted time-domain single-shot H2 fs CARS thermometry with a chirped-probe-pulse (CPP) from 150 fs to 500 fs [15]. The error at 300 K was $\approx$ 10% due to the lack of transitions at low temperature and the short probe pulse duration. Later, Bohlin et al. developed ultrabroadband two-beam CARS with a 7-fs pump/Stokes pulse and a narrowband picosecond (ps) probe pulse [16]. This hybrid fs/ps CARS system was able to cover a Raman excitation range up to 3200 cm-1, which enabled simultaneous probing of both the ro-vibrational N2 Q-branch and the pure-rotational H2 S-branch. Using this system, Courtney et al. developed pure-rotational H2 thermometry in a heated flow and a Wolfhard-Parker burner [17]. An average error of 3% was reported at temperatures up to $\approx$ 800 K. However, the acquisition rate of the system was limited by the ps laser, which had a repetition rate of 20 Hz. In addition, Ran et al. performed hybrid fs/ps CARS targeting the H2 Q-branch in a gas oven at pressure and temperature up to 1.7 bar and $\approx$ 1073 K. The error and precision were 4.9% and 2.7%, respectively [18]. Significant averaging ($\approx$ 2.5 s) was required to achieve good signal-to-noise ratio (SNR), which made single-shot measurements challenging. More recently, Retter et al. developed H2 hybrid fs/ps CARS thermometry in near-adiabatic H2/air flames at 1 kHz [19]. The reported error was $\approx$ 5%. The measurement precision was 3% for equivalence ratios ($\phi$) larger than 1.4. The authors attributed the decrease in precision to the change in non-resonant spectra throughout the test. In order to address this issue, Mazza et al. developed an ultrabroadband hybrid fs/ps coherent Raman scattering (CRS) system with in-situ referencing of the non-resonant background, which effectively mapped the Raman excitation efficiency curve at the probe volume for each laser shot [20]. The ultrabroadband pump/Stokes pulse was generated after a 22 mm thick BK7 window to simulate the optical properties of typical combustion chambers. The system targeted the H2 O-branch pure-rotational lines and was calibrated in a laminar H2/air diffusion flame. The H2 thermometry results were within 1% difference compared with results obtained by a conventional pure-rotational N2 hybrid CRS setup, which has a typical error of $\approx$ 5% [21,22]. The precision of the measurements was within 3%. Currently, N2 has been the primary target in high-pressure fs CARS diagnostics due to its abundance in air [23–25]. Miller et al. demonstrated O2 and N2 pure-rotational hybrid fs/ps CARS thermometry at pressures up to 15 bar at room temperature with error less than 5% [23]. Mecker et al. extended the N2 thermometry range to $\approx$ 71 bar at room temperature and 38.5 bar at 1000 K using the same technique [25]. The averaged absolute error across all conditions is 5.3%. In addition, Stauffer et al. applied ro-vibrational N2 hybrid fs/ps CARS in high-pressure CH4/air Hencken flames at pressures up to 10 bar [24]. In high-pressure combustors where air is not used as the oxidizer, species such as H2 is often chosen for CARS measurements [26]. High-pressure H2 measurements are therefore crucial for assessing the performance of fs CARS techniques under high-pressure conditions. Another important topic in fs CARS diagnostics is the treatment of frequency chirp, which is generated as fs pulses travel through optical components such as windows and lenses. One popular approach utilizes dispersion-compensation tools in the experiment to pre-compensate the dispersion picked up by the fs pulse from optics in the beam path [25,27,28]. Mecker et al. utilized a 4-f pulse shaper to create a phase compensation mask to compensate the dispersion generated from the high-pressure cell window in the 800 nm pump/Stokes beam [25]. Martin et al. installed a pair of dispersion compensation mirrors to pre-compensate the chirp from lenses [27]. Castellanos et al. employed an external compressor for dispersion compensation in the 800 nm pulse [28]. An alternative approach involves incorporating dispersion in the theoretical model [29]. Details of this method is presented in the theory section.
At present, all of the H2 fs CARS systems follow the hybrid approach. In this manuscript, we present the development of H2 CPP fs CARS thermometry in near adiabatic H2/air flames at 5 kHz. Due to the large frequency span of the H2 Q-branch lines, additional modeling on the pump and Stokes frequency chirp was necessary to provide accurate Raman excitation efficiency profiles. This is in contrast with the conclusion drawn for N2 [29], as the N2 Q-branch only spans over $\approx$ 100 cm-1, which is much smaller than the excitation frequency range covered by the pump and Stokes pulse. In addition, the effect of chirp from typical high-pressure combustor windows on the H2 spectra was investigated. Moreover, we performed H2 thermometry in a heated gas cell up to 1000 K at $\approx$ 0.3 MPa to examine the accuracy of this technique at low temperatures. Finally, we investigated the influence of pressure on the H2 CPP fs CARS spectra at 1000 K, ranging up to 5 MPa. This addressed the lack of high-pressure H2 fs CARS studies in the existing literature.
2. Theory
The time-domain H2 fs CARS model is adopted from the well established N2 model [12,30]. In CPP fs CARS, the pump and Stokes pulse excite a broad range of Raman transitions in the target molecule. A chirped-probe-pulse samples this Raman coherence in the time domain, and the CARS signal is generated through the four-wave mixing process. In the frequency domain, the CARS signal reflects the beating of all the Raman transitions as they dephase after the initial excitation. The CARS electric field ($E_{CARS}$) is the product between the probe pulse electric field ($E_{pr}$) and the sum of the resonant ($P_{res}$) and non-resonant polarizations ($P_{nres}$).
The non-resonant polarization is the instantaneous product between the pump electric field ($E_{pu}$) and the complex conjugate of the Stokes electric field ($E_{St}^{*}$). The resonant polarization characterizes the induced dipole moment in the excited molecule and is modeled as [12]
Figure 1 shows the H2 Raman transitions at 296 K and 3000 K. The H2 Q-branch lines are widely spaced due to its large rotational constant. This leads to the constructive beating of the H2 transitions, which corresponds to a long Raman coherence decay time. Therefore, long probe-time-delay (PTD) can be employed to avoid the interference from the non-resonant background. The typical excitation frequency range covered by the pump and Stokes pulse is $\approx$ 200 cm-1 in full-width at half maximum (FWHM), which is much less than the span of the Q-branch transitions at temperatures over 1500 K. As shown in Fig. 1, different Raman transitions have different excitation efficiencies. A Raman excitation efficiency curve is therefore required to account for this difference, and it is proportional to the magnitude of the cross-correlation of the pump and Stokes spectra [29].
In Eq. (9), $A_{\omega }^0$ is the amplitude of each frequency component and $\eta$ accounts for the width of the spectrum. The imaginary component is related to the spectral phase, with $\beta$ and $\gamma$ defining the quadratic and cubic phase, respectively. As a fs pulse goes through optical components such as lenses and windows, it picks up frequency chirp, which leads to an increase in pulse duration. As evident from Eqs. (8), (9), the pump and Stokes quadratic phase are closely coupled in the calculation of the Raman excitation efficiency curve. The determination of these parameters is discussed in Section 4.2. In addition, a time delay between the chirped pump and Stokes pulse induces a frequency shift to the Raman excitation efficiency curve. This frequency shift (cm-1) is defined as [37]
where $\Delta \tau$ is the relative time delay between the pump and Stokes pulse. Overall, accurate Raman excitation efficiency curve is crucial for high-fidelity H2 fs CARS thermometry measurements.
Fig. 1. Simulated H2 Q-branch Raman transitions at 296 K and 3000 K. Transitions from the first hot band (v$''\rightarrow$v$'$=2$\rightarrow$1) are labeled as QH. The pressure is set to 0.1 MPa and the probe linewidth is 0.8 cm-1. Spectra are generated through CARSFT [36]. The Raman excitation efficiency curve is computed using the pump and Stokes quadratic phase fitted from the averaged Hencken burner flame spectra at 2283 K.
Details of the spectral fitting routine used in our model can be found in previous literature [12]. The fitting process is divided into two parts. First, nine laser parameters were extracted from an averaged spectrum (2000 frames) through a genetic algorithm referred to as differential evolution [38]. Details on the fitting algorithm and code can be found here [39]. The nine floated parameters are: the second and third order phases of the probe pulse, the second order phases of the pump and Stokes pulse, the pump time delay, the PTD, the instrument width scalar, the horizontal and the vertical shifts. The resonant to non-resonant ratio ($\alpha$) is set to a constant since long PTDs (> 6 ps) were used in the experiment to suppress the non-resonant background. For the same reason, the phase shift term $\phi$ is set to zero. The cubic phase of the pump and Stokes pulse are set to constant since their values are small, and therefore do not have significant impact to the H2 CARS spectra. After the laser parameters were known, they were fixed in the simulation and a synthetic spectra library was created with three variables: the H2 temperature, the horizontal shift, and the vertical shift. Single-shot spectra were compared with theoretical spectra in the library with the same fitting algorithm and the best-fit temperatures were extracted.
3. Methodology
3.1 CPP fs CARS system
The fs CARS system employed in this experiment is based on a prior design [40], and is illustrated in Fig. 2. The Ti:Sapphire amplifier (Legend Elite Duo, Coherent Inc.) amplifies 800 nm fs seed pulses from $\approx$ 6.5 nJ/pulse to $\approx$ 2.2 mJ/pulse with a repetition rate of 5 kHz. The output from the amplifier is near Fourier-transform-limited (FTL) with a pulse duration of $\approx$ 87 fs. The pulse duration is provided by the laser manufacturer and verified with a multiphoton intrapulse interference phase scan (MIIPS) system. An 80:20 (R:T) beam splitter is used to direct 80% of the 800 nm output to an optical parametric amplifier (OPA, OPerA Solo Light Conversion), which generates 603 nm output with a pulse energy of $\approx$ 102 $\mu$J. The compressor grating inside the amplifier is adjusted to maximize the OPA power. The OPA output is sent through a telescope lens pair (-50 mm/+125 mm) to match the beam diameter of the Stokes pulse ($\approx$ 10 mm), and is further split into the pump and probe pulse with a 70:30 ratio. The other 20% of the 800 nm output is used as the Stokes pulse. The Stokes pulse is sent through a delay line to account for the optical path length of the OPA. The pump and Stokes pair create a Raman shift of $\approx$ 4080 cm-1, which targets the H2 Q-branch transitions. A 30 cm SF-10 glass rod is used to chirp the probe pulse to $\approx$ 6.7 ps. Both the pump and probe pulse beam paths include linear translation stages to achieve optimal timing with the Stokes pulse. In addition, two half-wave plate and polarizer assemblies are employed to provide power attenuation function for the pump and Stokes pulse. After each power attenuation assembly, another half-wave plate is installed to control the polarization angle. The pump, Stokes, and probe pulse are focused with a +300 mm lens using the BOXCARS geometry [41]. The probe volume is approximately a cylinder that has a length of $\approx$ 936 $\mu$m and a diameter of 31 $\mu$m [42]. The probe volume length was measured by scanning a 0.1 mm thick BBO crystal with a step size of 0.1 mm. The integrated intensity of the non-resonant spectrum was calculated and the probe volume length was defined as the distance between the points that are 10% and 90% of the maximum intensity. For a conservative estimation, the probe volume diameter was calculated based on the Stokes pulse assuming a Gaussian beam profile and a beam diameter of 10 mm. The CARS signal is generated at 484 nm and focused into a spectrometer (1200 g/mm grating) with a +125 mm lens. A bandpass filter (490/60 nm) was installed before the slit to filter out the scattered light from the input beams. Finally, the CARS signal is collected by an electron-multiplying CCD (EMCCD, Andor iXon Ultra 888) at 5 kHz. A xenon calibration lamp is used to provide pixel-to-wavelength mapping for the CARS spectra. In addition, a frequency dependent instrument response function (IRF) is calculated based on the linewidth of the covered xenon transitions.
Fig. 2. Schematic diagram of the CPP fs CARS system. BPF: bandpass filter; BS: beam splitter; BT: beam trap; GR: glass rod; HWP: half-wave plate; I: Iris; L: lens; LTS: linear translation stage; M: mirror; P: Glan-laser polarizer; TFP: Thin-flim polarizer.
3.2 Hencken burner and the heated gas cell
In this experiment, a Hencken burner was used to produce near-adiabatic H2/air diffusion flames. Hencken burner flames have been well-characterized in past literature [8] and are used as standard calibration flames for this study. The Hencken burner features a central square (25 mm $\times$ 25 mm) and a surrounding 7 mm thick honeycomb co-flow. In the central square, each 1 mm diameter fuel needle is surrounded by six oxidizer honeycomb cells. Digital mass flow meters were calibrated and used to reach equivalence ratios from $\phi$=0.8 to 2.0. Good single-shot signal-to-noise ratio (SNR) was achieved with $\phi$>1.28. The probe volume was placed at 28 mm above the burner surface to ensure the fuel and oxidizer were fully mixed and reacted [8]. The air volumetric flow rate was set to 40 lpm, and the co-flow was turned off. In addition, two windows were installed before and after the Hencken burner to study the effect of window to the H2 spectra. These two windows have the same dimension as the gas cell window. The distance from the focusing lens to the outer surface of the first window is set to 200 mm. The spacing between the two windows was also set to the gas cell window configuration (175 mm). The pump and Stokes energy were attenuated to $\approx$ 23.2 $\mu$J/pulse and $\approx$ 4 $\mu$J/pulse to avoid self-phase modulation (SPM) [43].
The gas cell used in the experiment is designed to operate up to 1000 K at 10 MPa. The design of the gas cell is detailed in Fig. 3. The gas cell is constructed using Hastelloy-X to provide sufficient strength at the target operating conditions reported in the study. Optical access is provided at the ends of the cell with fused quartz (Heraeus TSC-3) windows, which have a thickness of 19 mm. The windows are sealed using either flexible graphite (Grafoil) or elastomeric seals depending on target temperature for the test and material compatibility. The gas cell has eight ports that are available for pressure and temperature instrumentation, a gas inlet, exhaust and relief valve. During operation, the cell is purged and filled to target pressure with pure H2. A radiant electrical heater (Thermcraft Inc. RH274) with feedback from a temperature regulator is used to heat the gas cell to the prescribed temperature. An array of k-type thermocouples (GKMQIN-062G-06) are used to ensure uniform temperature distribution in the gas-cell and to verify the fs CARS measurements. One of the thermocouples provides feedback to the PID control loop of the radiant heater. At each temperature set point, effort was made to ensure the gas cell temperature was stabilized for at least 5 minutes before data collection. The pressure in the gas-cell is measured using a GE-Sensing UNIK50E6 pressure transducer with a full-scale output of 13.8 MPa (2000 psia) with an error of 0.04% of the full-scale output.
4. Results and discussion
4.1 Effect of chirp to the Raman excitation efficiency
As mentioned earlier, the pump and Stokes pulse pick up positive chirp from optical components such as windows and lenses. The pump pulse has significantly higher chirp than the Stokes pulse since it was generated through the OPA. In addition, the pump pulse was sent through a $\approx$ 25 mm long $\alpha$-BBO Glan-laser polarizer, which added significant chirp. Frequency chirp leads to increased pulse duration, as the red frequency components travel faster than the blue frequency components. According to Eq. (10), any difference between the pump and Stokes timing could result in a shift to the interacting pump and Stokes frequencies at the probe volume. In the experiment, the Stokes pulse was used as a reference and only the pump and probe timing were adjusted. A positive pump delay ($\Delta \tau$) corresponds to an increase in the optical path length of the pump beam and a blue-shift of the pump spectrum relative to the Stokes spectrum at the probe volume. This means the Stokes pulse starts to interact with pump frequency components that have higher wavelength as the pump delay increases. High temperature H2 fs CARS spectra at two different pump delays are shown in Fig. 4(a-b). Two windows were installed before and after the Hencken burner to simulate the dispersion caused by the gas cell windows. H2 spectra were recorded at 100 Hz due to the reduced pump and Stokes pulse energy. Each spectrum is an average of 2000 frames. The Raman excitation efficiency curves in Fig. 4(c) are calculated from experimentally measured pump and Stokes power spectra. The peak of the Raman excitation efficiency curve decreases slightly as the pump delay increases. The Raman excitation efficiency curve is normalized in the spectral fitting routine. As the pump delay increases, the beating depth between the spectral features increases. This is expected since a positive pump delay corresponds to a negative shift to the Raman excitation efficiency curve, as shown in Fig. 4(c). The transition frequency of the H2 Q-branch lines decreases with increasing $J$. Therefore, the higher $J$ lines receive better excitation efficiency as the pump delay increases, leading to the increase in the beating depth between spectral features. For the case of hybrid CARS, a change in pump delay directly translates to a change in the relative line intensities. In Fig. 4(a-b), the theory shows excellent agreement with the experiment. The estimated pump delay difference between the two spectra in the experiment is $\approx$ +90 fs, which matches with the theoretical prediction (87 fs). The corresponded frequency shift is $\approx$ -58 cm-1. The estimated PTD from the experiment is $\approx$ 8.5 ps, which agrees well with the theory ($\approx$ 8.8 ps). Spectral phases of the pump, Stokes, and probe pulse are also consistent between the two spectra. This shows our model is able to provide an accurate estimate of the pump delay. In the following experiment, the pump delay is set to values that enable better excitation for the higher $J$ lines.
Fig. 4. H2 fs CARS spectra at two different pump delays and their corresponding Raman excitation efficiency curves. The equivalence ratio is set to $\phi =1.8$, which corresponds to an adiabatic flame temperature of 2128 K. (a) Spectra with pump delay of 86 fs. (b) Spectra with pump delay of 173 fs. (c) Raman excitation efficiency curves as of the two H2 CARS spectra as calculated using Eqs. (8), (9).
4.2 Hencken burner thermometry
Single-shot H2 fs CARS spectra were acquired in Hencken burner flames from $\phi$=1.28 to 2.0 at 0.1 MPa (1 atm). In addition, spectra were collected in a room temperature, non-reacting H2 jet. No windows were placed before and after the probe volume to achieve high SNR at 5 kHz. At $\phi$=1.28, the acquisition rate was reduced to 2.5 kHz to further improve the SNR. Nine laser parameters were determined by fitting averaged spectra obtained from 2000 individual laser shots. As shown in Fig. 5, the theoretical spectra agree well with the experiment. At room temperature, only a few transitions were populated and relatively simple beating patterns were observed. The shape of the spectra reflects the constructive interference between these transitions. At flame relevant temperatures, most transitions covered within the excitation frequency curve were populated, which leads to more complex beating patterns. The laser parameters from both the flame and room temperature fits are summarized in Table 1. Adiabatic flame temperatures are cited as the reference temperature for flame conditions.
Fig. 5. Averaged H2 fs CARS spectra and their theoretical fit. Spectra taken at 0.1 MPa with temperatures set to: (a) room temperature (296 K); (b) 2203 K ($\phi =1.6$).
Table 1. Summary of selected fitting parameters for measurements without windows.
The listed laser parameters exhibit excellent consistency across the five flame conditions. In addition, both the horizontal and vertical shifts remain consistent across the listed conditions. Non-resonant spectra taken in room air were used to further validate the laser parameters. The fitted laser parameters, except the PTD, were used to fit the non-resonant spectra. Good agreement was found between the experiment and theory. However, it was observed that the non-resonant spectra were not sensitive to changes in the pump delay and pump quadratic phase due to the lack of molecular response. In Table 1, the spectral phases at room temperature are slightly different from that for the flame conditions. The laser parameters at room temperature are less accurate due to the limited number of transitions available. This increased the difficulty for the fitting algorithm to determine the correct shape of the Raman excitation efficiency curve, which directly relates to the pump quadratic phase. In addition, the lack of transitions results to the lack of spectral features, which increased the uncertainty in the probe spectral phase.
It was observed that the Stokes quadratic phase tends to converge to the upper limit, even if it is not physical. The Stokes quadratic phase is coupled with the pump quadratic phase since they both affect the shape of the Raman excitation efficiency curve. The Stokes quadratic phase is thus fixed to -426.8 fs2, which is the theoretical estimation based on the optical component it interacts in the experiment. This estimated value is fairly accurate since the Stokes beam is directly taken from the FTL amplifier output. In addition, the dispersion from all the optical components were taken into account, except for mirrors since low group delay dispersion (GDD) mirrors were used. The thickness, GDD, and third-order dispersion (TOD) of each transmissive optical component in Fig. 2 are summarized in Table 2 for the pump, Stokes, and probe pulse. The material dispersion properties are taken from a online database by Light Conversion [44]. The dispersion from the OPA was not included due to its complex design.
Table 2. Dispersion properties of optical components used in the experiment.
In addition to the dispersion estimation, the pump delay and PTD were estimated from the delay stage travel lengths. These theoretically estimated values, as well as their upper and lower bounds in the fitting routine, are summarized in Table 3.
Table 3. Typical values of the upper bound, the lower bound, and the theoretical estimation of key floated variables in the fitting routine.a
From Table 3, it can be observed that all the fitted laser parameters are well within the bounds. The fitted pump and probe quadratic phase are $\approx$ 1900 fs2 larger than the theoretical estimates in general. This difference is likely due to the dispersion from the OPA, which is not considered in the theoretical estimation. This also explains the small discrepancy in the probe cubic phase. The pump delay and PTD calculations are very close to the fitted values. This further demonstrates that the fitting algorithm is able to provide accurate laser parameter estimations.
Another important finding in the H2 CPP fs CARS spectra is that the temperature sensitivity at temperatures over 2000 K mainly comes from the beating depth between spectral features. At 2000 K, all the transitions covered by the pump and Stokes pulse are populated. Higher temperature only affects the relative intensities between these transitions, which corresponds to the change in beating depth in the CARS spectra. Since the temperature is fixed during the laser parameter fitting routine, the parameters that only change the beating depth are the pump delay and the IRF scalar. The IRF scalar tends to converge to the lower limit for all flame cases. This lower limits corresponds to an instrument width of $\approx$ 0.3 cm-1, which is near the theoretical limit. With the IRF scalar correctly constrained, the fitting algorithm is able to provide accurate prediction to the pump delay. One might argue that the pump delay is also coupled with the pump quadratic phase, as shown in Eq. (10). However, the pump quadratic phase also controls the shape of the Raman excitation efficiency curve. Therefore, the pump quadratic phase is not directly coupled with the pump delay and IRF scalar.
With known laser parameters, single-shot spectra were compared with theory by the fitting routine, and the H2 temperature was retrieved. All experimental single-shot spectra were smoothed by a Savitzky-Golay filter to reduce CCD noise as well as etalons created by neutral density filters. Example single-shot fits at room temperature and $\phi =1.28$ are shown in Fig. 6. Laser parameters from the $\phi =1.6$ spectra were used for all the single-shot fits. In general, the fit temperature matches closely with the reference temperature. Good agreement was also found between the theoretical and experimental spectra. The room temperature fit has slightly higher residual due to the difference between the $\phi =1.6$ and room temperature laser parameters, especially the pump quadratic phase and probe cubic phase. Since the Raman excitation efficiency curve is centered to the high $J$ lines, the low $J$ lines fall under the slope part of the curve. A slight difference in the pump quadratic phase can induce a large change to the slope of the curve, creating high fitting residual at room temperature. Figure 7 shows the histogram statistics of all the six conditions listed in Table 1. Reference temperatures are labeled in the plot as Tref. The accuracy and precision of the thermometry, along with the mean temperatures, are listed in Table 4. The error is calculated by comparing the difference between the mean and reference temperatures. The precision is characterized by the standard deviation. Both the error and precision are presented as a percentage of the reference temperature.
Fig. 6. (a) Room temperature and (b) Hencken burner ($\phi =1.28$, 2330 K) single-shot fits using laser parameters from the $\phi =1.6$ spectra.
Fig. 7. Histograms of 2000 single-shot fit for each condition listed in Table 1 using laser parameters from the $\phi =1.6$ spectra. The bin size is 5 K at room temperature, and is 20 K at flame temperatures. Reference temperature is labeled as Tref.
Table 4. Accuracy and precision of the H2 thermometry in Hencken flames.
From the histograms, excellent precision is observed for all the experimental conditions. The $\phi =1.28$ case has the highest standard deviation due to its relatively low SNR. The mean precision is 3.3%, which is similar to the values reported by others using hybrid CARS systems [18–20]. The histogram also shows excellent accuracy for all cases. The $\phi =1.8$ case has the highest error, which is 4.4%. The overall single-shot error of the system is 2.8%, which is $\approx$ 2% better than previously reported values [19,20]. The histogram of $\phi =1.28$ and 2.0 are slightly bimodal. This is likely due to fluctuations in laser parameters. The OPA alignment tends to drift after several hours of operation. This is reflected as a fluctuation in the relative peak intensities of the spectra and could lead to the bimodal distribution in temperature measurements.
4.3 Hencken burner measurements with windows
In order to investigate the effect of windows to the H2 fs CARS spectra, Hencken burner measurements were repeated with windows installed before and after the flame. The window before the flame adds extra dispersion to the pump, Stokes, and probe pulse, and thus affects the CARS spectra. The window after the flame does not have a direct impact on the CARS signal, but it does affect the alignment of the signal, and is therefore included to fully simulate the setup of the heated gas cell. Spectra were taken at 100 Hz due to the reduced pump and Stokes pulse energy. The pump delay is carefully set in the experiment to reach similar Raman excitation efficiency profile as previous tests for better comparison between the two scenarios. The laser parameters from both the flame and room temperature spectra are summarized in Table 5. Using the spectral phase in Table 5, the estimated pulse duration of the pump, Stokes, and probe pulse at the probe volume are approximately 759 fs, 97 fs, and 6.7 ps, respectively.
Table 5. Summary of selected fitting parameters for measurements with windows.
Similar to previous Hencken flame thermometry measurements, the laser parameters show superb consistency across different flame temperatures. The room temperature laser parameters are less accurate due to the limited number of transitions populated. The pump and probe spectral phases are greater than their corresponding values for the scenario where no windows were installed. The pump quadratic phase shows an increase of $\approx$ 584 fs2, and the probe quadratic phase shows an increase of $\approx$ 777 fs2. From Table 3, the theory predicts that the front window could result in 525 fs2 extra quadratic phase to the pump and probe pulse. The increase in the quadratic phase of the pump and probe pulse agrees well with the theoretical prediction. The pump delay shows a slight decrease with the addition of windows. This is expected since higher dispersion results in larger delay on the red frequency components in the pump pulse. Therefore, less pump delay is required in the experiment to reach the same Raman excitation efficiency profile.
Example Hencken burner flame fits using laser parameters from $\phi =1.4$ are shown in Fig. 8. The theoretical spectra show excellent agreement with the experiment. As mentioned earlier, the temperature sensitivity of the H2 fs CARS spectra at temperatures over 2000 K mainly comes from the increase in the beating depth between the spectral features. This can be observed at the peak and valleys of the spectral features in Fig. 8(a), where the fit temperature is $\approx$ 200 K higher than that for Fig. 8(b).
Fig. 8. Hencken flame fits with the addition of windows. Laser parameters from $\phi =1.4$ spectra were used. Each spectrum is an average of 50 single-shots. (a) $\phi =1.32$; (b) $\phi =1.8$
In line with previous measurements, 2000 frames were recorded and the H2 temperature was determined from the fit. The accuracy and precision of the measurements are reported in Table 6. The statistics shows similar precision as previous results. The $\phi =1.32$ case has the largest precision (5%) due to its low SNR. As the equivalence ratio increases, the precision improves. The error is $\approx$ 1% lower than that for the measurements without windows. This is likely due to the 50-shot averaging implemented during the data acquisition. In general, the addition of window before the probe volume does not have a significant impact to the shape of the H2 fs CARS spectra. This does not mean that the H2 spectra is not sensitive to chirp, since the dispersion from the window is only $\approx$ 12% of the total pump quadratic phase. The pump beam has experienced significant chirp from other optical components before reaching the window. As discussed in Section 4.1, due to the high sensitivity to chirp, the H2 CARS model requires detailed treatment on the pump delay. These results suggest the improved model can effectively predict the dispersion of the input pulses and provide excellent measurement accuracy and precision.
Table 6. Accuracy and precision of the H2 thermometry in Hencken flames with windows.
4.4 Heated gas cell thermometry near 0.3 MPa
A heated gas cell was used to characterize the precision and accuracy of the system at temperatures below 1000 K. The gas cell pressure is kept constant at $\approx$ 0.3 MPa to improve seal and the SNR. Spectra were acquired every 100 K at 5 kHz. The fitting parameters from each temperature set point are listed in Table 7. The laser parameters become more consistent once the temperature is over 600 K and more transitions are populated. One might notice the spectral phase of the input pulses are smaller than the spectral phase of the Hencken burner with windows measurements. This is likely a result of the OPA alignment change. The heated gas cell measurements were taken with a slightly different pump/probe wavelength. The crystal angle, delay line settings, and optical alignment inside the OPA were also different from the Hencken burner measurements. These factors could result in a smaller spectral phase. The laser parameters at 1001 K also deviate from the laser parameters of near by temperatures. This is due to a small change in the relative intensity of the H2 spectra. At 1000 K, the gas cell leak rate is high enough that the regulator periodically feeds cold H2 gas into the cell, which sometimes creates a density gradient in the probe volume and impacts the shape of the spectra. Effort was made to only acquire data when the gas cell reached thermal equilibrium, and when the relative intensity fluctuation was at the minimum.
Table 7. Summary of selected fitting parameters for heated gas cell measurements.
Excellent agreement was found between the simulated and experimental spectra. Single-shot fits using laser parameters from the 802 K spectra are shown in Fig. 9. The fit temperature is labeled as Tfit in each plot. As temperature increases, the peaks in Fig. 9(a) divide into small peaks. This indicates more transitions are populated and the relative transition intensity has changed. The change in beating depth between spectral features become more pronounced as the temperature increases from 700 K to 1000 K, as most transitions within the excitation frequency are populated.
Fig. 9. Heated gas cell single-shot spectra with theoretical fit using laser parameters from the 802 K spectra. All measurements were acquired near 0.3 MPa. The reference temperatures are: (a) 500 K; (b) 701 K; (c) 1001 K.
Histograms of 2000 single-shots at selected temperatures are plotted in Fig. 10. The histograms show excellent precision for all the target temperatures. The error and precision at each temperature set point are listed in Table 8.
Fig. 10. Histograms of 2000 single-shot for selected conditions listed in Table 7. The bin size is 5 K. Reference temperature is labeled as Tref.
Table 8. Accuracy and precision of the H2 fs CARS thermometry in the heated gas cell.a
The mean precision is 1.2%, which is $\approx$ 60% better than the precision of the Hencken burner measurements. This is expected since the single-shot SNR of the heated gas cell measurements is higher due to the higher number density. Furthermore, the gas cell environment is well-controlled, which leads to smaller temperature standard deviations. Most of the measurements have errors less than 5%, except for the room temperature spectra. The mean error is 2.8%, which is the same as the error of the Hencken burner measurements.
4.5 High-pressure gas cell measurements near 1000 K
The effect of pressure on the H2 fs CARS spectra is presented in this section. H2 spectra were acquired in the gas cell at pressures and temperatures up to 5 MPa and 1000 K. The gas cell temperature was kept constant while the spectra were measured with 1 MPa intervals. As shown in Fig. 11(a), the effect of pressure to the H2 spectra is negligible at 3 MPa. The 1 MPa and 3 MPa experimental spectra agree well with each other. Small differences can be observed at wavenumbers over 20800 cm-1, where the 3 MPa spectra have slightly lower intensities than the 1 MPa spectra. This is confirmed by theory, as shown in Fig. 11(b). The spectra at 5 MPa have similar trends as in Fig. 11. This can be explained by considering the characteristics of the chirped-probe-pulse in the experiment. The probe frequency components with higher wavenumber interact with the Raman coherence later than the red frequency components. As time increases, the H2 Raman decay term decreases. Therefore, the intensity differences are more pronounced for frequencies with higher wavenumber. In addition, the collision width of the H2 molecule is small. The collision width of the Q(1) line at 14 amagat (5 Mpa, 1000 K) is 0.074 cm-1, which corresponds to a value of 0.76 for the exponential decay term (Hph) at 20 ps. This explains why pressure does not have a significant impact on the H2 spectra up to 5 MPa.
Fig. 11. Experimental (a) and simulated (b) H2 fs CARS spectra at 1 and 3 MPa near 1000 K. Experimental spectrum is an average of 2000 single-shots.
Using laser parameters from the 1 MPa spectra, single-shot fits at 3 MPa and 5 MPa are shown in Fig. 12. Good agreement was found between the theoretical and experimental spectra. The accuracy and precision of the high-pressure measurements are listed in Table 9. It is observed that the standard deviation starts to increase at pressures over 4 MPa. As discussed earlier in Section 4.4, this is due to the small leak in the gas cell at 1000 K. As pressure increases, the magnitude of the density gradient increases, which changes the shape of the spectra and leads to higher temperature standard deviations. The mean error and precision are 2.9% and 2.6%, which are consistent with the Hencken burner and gas cell thermometry results. This suggests that it is feasible to use laser parameters retrieved from low-pressure spectra for high-fidelity thermometry measurements in high-pressure environments. Consequently, Hencken burner flames operating at ambient pressure can be used as calibration flames for measurements in high-pressure combustors.
Fig. 12. High-pressure H2 single-shot spectra with theoretical fit at (a) 3 MPa and (b) 5 MPa. Laser parameters from 1 MPa spectra were used. The gas cell temperature is set to $\approx$ 1000 K. The fit temperature is labeled as Tfit.
Table 9. High-pressure H2 thermometry accuracy and precision.
5. Conclusion
In conclusion, we developed and applied H2 CPP fs CARS thermometry in Hencken burner flames up to 2300 K at 0.1 MPa. Measurements were also performed in a heated gas cell at temperatures up to 1000 K at 0.3 MPa. It is found that the H2 fs CARS spectra are highly sensitive to the pump and Stokes chirp. As a result, the pump delay plays an important role on the shape of the spectra. The effect of pump delay is modeled as a frequency shift to the Raman excitation efficiency curve in the theory. This allows the accurate measurement of the pump delay and the spectral phase of the input pulses. With the improved theoretical model, excellent agreement was found between the theoretical and experimental spectra. The mean single-shot error and precision across all the conditions are 2.8% and 2.3%, respectively. In addition, it is proved that the addition of extra windows before and after the probe volume does not have significant impact to the precision and accuracy of the H2 fs CARS spectra. Lastly, it is confirmed that pressure has negligible effect on the H2 fs CARS spectra up to 5 MPa at 1000 K. The laser parameters from low-pressure spectra can be used for high-pressure spectral fits without compromising accuracy and precision. These results build strong foundations for future measurements in high-pressure combustors, such as rocket chambers [42] and gas turbine combustors [45].
Funding
Blue Origin LLC (40003024).
Acknowledgments
The authors would like to thank Dr. Matthieu Masquelet, Dr. Steven Stanley, Dr. Ron Ungewitter, and Dr. Aman Satija for their valuable insights and discussions throughout the project.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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.
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