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Abstract
We have developed a diagnostic that uses time-domain spectroscopy to measure transient infrared absorption spectra in gases. Using a time-stretch Fourier transform approach, we can determine pressure, temperature, and gas concentrations with sub-microsecond time resolution for over two milliseconds. We demonstrate high-resolution (0.015 nm), time-resolved spectral measurements in an acetylene-oxygen gas mixture undergoing combustion. Within a 5 µs period during the reaction, the acetylene line intensities decrease substantially, and new spectra appear that are consistent with the hydroxyl (OH) radical, a common by-product in the combustion, deflagration, and detonation of fuels and explosives. Post-reaction pressures and temperatures were estimated from the OH spectra. The technique measures spectra from 1520 to 1620 nm using fiber optics, photodetectors, and digitizers. No cameras or spectrometers are required.
1. Introduction
Laser-based spectroscopic techniques that probe the rotational and vibrational spectra of molecules are often used to measure temperatures, pressures, concentrations, and material composition on short timescales to examine events such as shock waves in high pressure research, during the detonation of explosives, or in combustions studies. In many cases, a method that records high-resolution spectra on a sub-microsecond timescale under dynamic conditions is required. Conventional high-speed recording methods map the spectrum into the spatial domain using a grating or prism to disperse the various wavelengths, and a streak or framing camera records the spectra [1]. Such techniques have an inherent trade-off between high time resolution and long recording times. Furthermore, high-speed streak and framing cameras that can record in the short wave infrared (SWIR), where many vibrational spectra exist, are uncommon. Time-stretch spectroscopy is an alternative approach that overcomes these limitations. Time-stretch spectroscopy, also referred to as dispersive Fourier transform spectroscopy or photonic time-stretch, [2,3] disperses spectra into the time domain by creating different temporal path lengths for different wavelengths. The spectra can then be recorded with a single-point photodiode and oscilloscope. In our case, the system operates at wavelengths ranging from 1520 to 1620 nm, where many rotational-vibrational spectra exist.
Time-domain spectroscopy based on dispersion in optical fiber [3,4] has led to recent advancements in optical ranging [5,6], high-speed velocimetry [7,8], laser science [9,10], digitizer technology [11], spectroscopy [3,12–20], and other topics [21–22]. Much of the recent progress made in this area is summarized in a review article on photonic time-stretch techniques and their applications by Mahjoubfar et al. [2]. Our work examines time-domain spectroscopy as a potential method for measuring temperature, pressure, and concentration of gases undergoing combustion, where transient events can occur on microsecond timescales. In this work we optically dispersed (chirped) pulses from a broadband femtosecond laser into the time domain using dispersive optical fibers. The pulse train is passed through a gas of interest, and the absorption spectra are superimposed on the chirped pulse and recorded every 160 ns on a fast digital oscilloscope. We detected the spectra with a single-point photodetector rather than a camera. With high-bandwidth digitizers and detectors, we can measure the rotational-vibrational infrared absorption spectra in gases at 160 ns intervals for tens of milliseconds with a spectral resolution of ∼0.015 nm. We demonstrate the system’s capability to make dynamic temperature, pressure, and concentration measurements at a rate of 6.25 MHz during the combustion of acetylene (C2H2) in oxygen (O2). Repetition rates in the 10-100 MHz range could also be realized with some spectral bandwidth trade-offs.
Combustion often occurs during deflagrations and detonations. Deflagration is the propagation of combustion reactions at sub-sonic speeds while detonation occurs at hyper-sonic speeds. Often deflagration proceeds detonation, and accurate modeling of the deflagration to detonation transition is desired [23] to advance research in pulse detonation engines [24] and the safe storage of explosives [25]. This technique is well suited for observing the dynamics that occur during the microsecond time frames typical of this transition.
This work also demonstrates a new method for high-speed pressure, temperature, and concentration measurements in OH. Other approaches for monitoring OH, such as laser induced fluorescence, [26] cannot easily provide temperature and pressure. The use of standard IR absorption [27] or frequency combs [28] can provide accurate thermodynamic measurements from OH spectra. However neither of these methods can typically exceed megahertz rates for extended times because of limitations in the camera and/or lasers.
2. Experimental setup
Figure 1 shows a simplified schematic of the system to measure spectra in the time domain. We built a pulse picker from a Mach-Zehnder modulator [29] and in-house electronics to extract individual pulses from a 100 MHz, fiber-based, mode-locked laser (Menlo T-Light). The pulse picker has 40 dB extinction. The pulses have a center wavelength of 1550 nm, bandwidth of 100 nm, and pulse length of 100 fs. The pulse picker produces a train of pulses at a 2−6 MHz rate. The pulses are then stretched in a spool of highly dispersive optical fiber [30] and amplified with a series of Raman amplifiers, each with a slightly different frequency to keep the spectrum relatively flat and broad. The Raman pumps are combined with the mode-locked laser in a Wavelength Division Multiplexer (WDM) and amplified in the dispersive fiber. The dispersive fiber has a second order dispersion of 252 ps2/km and third order dispersion of −1.44 ps3/km near 1550 nm. Another WDM is not needed after the dispersive fiber because most of the pump light is absorbed in the dispersive fiber. A fraction of the pulse is diverted and recorded as a reference spectrum. The signal pulse is coupled into free space with a small collimating lens (AC Photonics), passed through a gas cell, and coupled back into another fiber; the signal pulse is then detected on a 10 GHz bandwidth photodiode and digitizer.
Fig. 1. Experimental setup for time-domain spectroscopic measurements of temperature, pressure, and composition of gases during the combustion of C2H2 in O2. A mode-locked 1550 nm laser is chirped and Raman amplified in highly dispersive fiber before passing through the combustion cell and being recorded by a photodiode. WDM is a wavelength division multiplexer.
There is a trade-off between spectral bandwidth, spectral resolution, and laser repetition rates (frequency of recorded spectra). For example, it is possible to use longer lengths of dispersive fiber to stretch the pulse out to hundreds of nanoseconds to attain spectral resolutions on the order of 0.001 nm if needed. However, as spectral resolution is increased, the pulse width also increases, and it becomes necessary to decrease the repetition rate to keep pulses from overlapping in time. Alternatively, if high frame rates are desired, shorter dispersive fiber lengths can be used for smaller dispersive stretching, and recording rates from 50 to 100 MHz can be realized, but shorter dispersion lengths reduce the spectral resolution. Other time-stretch methods have been demonstrated where the trade-off between repetition rate and dispersion is different [19]. We can obtain high resolution and fast recording speeds simultaneously by configuring the system to have more dispersion, but over a narrower spectral range to prevent pulse overlap. Here we configure the system differently depending on the objective of the experiment.
3. Experiment and results
3.1 Static measurements
We conducted initial static measurements to test the system in a 2 m long cell filled with carbon dioxide (CO2) and trace amounts of C2H2. The results are shown in Fig. 2. For these measurements, the laser pulse was stretched to 600 ns with a chirp of about −6.6 ns/nm, obtained by double passing the pulse through 21.4 km of dispersive fiber. The repetition rate was pulse picked down to 2 MHz. We used four Raman pump lasers with wavelengths of 1445, 1465, 1485, and 1500 nm to amplify the full bandwidth of the laser pulse to maintain a wide spectrum. Figure 2(a) shows the signal (blue) superimposed on the reference spectrum (red). Figures 2(b)–2(d) show the transmittance obtained after normalizing by the reference pulse; time is shown on the lower x-axis, and wavelength is displayed on the upper x-axis.
Fig. 2. Static time-domain spectral measurements in a mixture of CO2 and C2H2 gases. Spectra at wavelengths longer than 1560 nm are from CO2; spectra at wavelengths shorter than 1550 nm are from C2H2. (a) Transmission through the cell shows absorption lines (blue) superimposed on the pulse envelope (red). (b) (1 − transmission) with the pulse envelope subtracted. (c) Spectrum is expanded to show a magnified view of one of the rotational branches in CO2. (d) A further magnified view shows a single rotational line.
The measurements demonstrate how this approach can provide simultaneous high spectral resolution over a broad range of wavelengths at megahertz rates. The digitizer and photodetector used for these measurements have a 10 GHz recording bandwidth, and the time stretch maps the spectrum into the time domain with a nearly linear chirp. This provides 100 nm wide spectra with 0.015 nm resolution recorded every 500 ns. Figure 2(c) shows a magnified view of part of the spectrum, demonstrating full rotational branches in CO2. Further magnification (Fig. 2(d)) illustrates that the spectral resolution is sufficient to resolve the shape of a single absorption line. This makes it possible to measure spectral line broadening effects. The slight asymmetry of the line profile in Fig. 2(d) is from the non-linear response of the detector. If a more accurate record of the line shape is required, the detector response could be calibrated.
3.2 Dynamic measurements and results
To test the system under dynamic conditions, we adjusted the system to target C2H2. To enhance the short-wavelength side of the spectrum, we turned off three of the four Raman pumps with longer wavelengths (1465, 1485, and 1500 nm) so that we could increase the power of the one with the shortest wavelength (1445 nm) to obtain more signal near the C2H2 lines around 1520 nm. This adjustment also made the temporal length of the pulse shorter so that we could pulse pick at a higher repetition rate (6.25 MHz) without pulse overlap effects. We measured the time-wavelength relationship by comparing the room temperature C2H2 spectra to the theoretical spectra obtained with SpectraPlot and mapped time to wavelength by fitting to the function
which gives A2 = −2.124 ns/nm and A3 = −0.00379 ns/nm2 at λ0 = 1599.35 nm, obtained with 11.3 km of dispersive fiber. The use of this formula provides a spectrum that overlaps the theoretical spectrum to within 0.3 nm where deviations from the second order curve appear as non-monotonic fine structure in the dispersion curve. In order to obtain better than 0.3 nm agreement we matched every peak in the measured C2H2 spectrum with the theoretical spectrum and created a wavelength axis by interpolating between peaks. This method adjusts for the fine structure in the dispersion and resulted in agreement between the measured and theoretical data to within 0.01 nm. We filled the cell with a mixture of 29% C2H2 and 71% O2 (molar equivalence ratio φ = 1) at a total combined pressure of 1 atm and installed a spark generator inside the cell. The gas cell for the dynamic measurements had an optical path length of 20 cm. The spark generator was located at the base of the cell, and the probe laser beam passed about 20 mm above the base. The digitizer was triggered when the spark was initiated, and the digitizer recorded for 1.6 ms. The gas cell was not destroyed in the experiments, and it was reused several times. The results provide a time record of the combustion process. A summary of the observed dynamics follows.The spark generated a weak, nearly sonic, shock wave that took ∼60 µs to propagate to the probe’s field of view. As the shock wave passed the probe, there was a brief reduction in the transmitted laser intensity because of beam steering from light refraction near the shock front. However, there was no noticeable broadening or shifting in the lines, suggesting that the temperature, pressure, and gas concentrations did not change appreciably during or immediately after the passage of the shock wave. Instead, the system remained stable for another 50 µs, at which point we began to see fluctuations in the intensity of the transmitted signal. We believe these fluctuations are turbulence in the form of small pressure waves running ahead of a deflagrating combustion front. At 110 µs there was some slight broadening (∼0.08 nm FWHM) of the C2H2 lines, indicating small changes in the thermodynamic properties of the gas, probably a small increase in pressure. Otherwise, the system remained relatively stable for another 27 µs during this turbulence. In future experiments we could add Schlieren imaging to better understand the nature of this turbulence. At 137 µs after the spark, the C2H2 concentration started to decrease as the combustion wave front passed through the probe beam. Over a period of 2 µs, the C2H2 concentration rapidly decreased, and hydroxyl (OH) radical lines appeared. The OH spectra persisted with little change for the remaining 1.5 ms. Figure 3 shows four plots that illustrate the process at various times.
Fig. 3. Dynamic combustion of 29% C2H2 in O2. Absorption spectrum in the gas cell at four different times: (a) before any reactions have occurred (t < 136 µs), (b) 137 µs after the spark, (c) 138 µs after the spark, and (d) 139 µs after the spark. Beginning at ambient temperature and pressure, the transmission spectrum is largely unchanged for the first 136 µs after the spark. At 137 µs the transmission increases as the C2H2 concentration begins to decrease. Examination of individual peaks shows no broadening or shifts, indicating that the temperature and pressure remain relatively unchanged. At 138 µs the C2H2 concentration is further reduced, and OH lines begin to emerge. Complete reduction of C2H2 near room temperature occurs over a period of 2 µs, and hot, high-pressure OH radical lines appear. By 139 µs all of the C2H2 has disappeared, and only OH lines are present. The OH spectral features remain present and stable for the remaining 1.5 ms of the record.
Since the OH lines arise at substantially elevated pressures and temperatures (40 atm and 4000 K from OH spectrum analysis) while the C2H2 still appears to be at near ambient conditions, there is clearly a pressure discontinuity at the combustion front. From the time of flight we know that the combustion front did not propagate across the entire distance from the spark gap to the probe as a detonation wave, but it very likely underwent a transition from deflagration to detonation before reaching the probe beam. During the times when the C2H2 lines are disappearing, the spectra represent a combination of reacted and non-reacted gases with uncertain relative path lengths. This is likely caused by detonation front curvature resulting from the point initiation, so the laser beam is passing through ambient gas and simultaneously also passing through some of the combustion products. Therefore, the path length of ambient gas decreases with time during the ∼2 µs period that the C2H2 lines disappear.
Figure 4 shows the recorded data overlaid with theoretical OH spectra generated with the open-source online spectrum generator SpectraPlot [31]. The figure shows an obvious match between features in the theoretical OH and measured data. Note that in Fig. 4(a), there are two parts in the spectral range from 1542 to 1551 nm where no OH spectral data are measured; this is because these parts were blocked by notch filters we placed in the system to help with the wavelength-time calibration. In Fig. 4(b), the section of the data with the highest signal-to-noise ratio is overlaid with theoretical plots of spectra at temperatures of 3000, 4000, and 5000 K. It is clear that the temperature is well within the 3000–5000 K range, with excellent agreement at 4000 K. We used a similar, best-fit-by-eye approach to determine the pressure (40 atm) and OH molecular concentration (3.1%). We did not rigorously determine the best-fit spectra and associated errors due to the complexity involved in generating spectra and developing nonlinear fitting algorithms. We leave this for future work and present what we have here as a sufficient means to demonstrate the technique and give a sense of the potential that this technique has for measuring thermodynamic properties. Furthermore, as we did not anticipate seeing OH spectra, we did not optimize the system for measuring OH spectra. In future experiments we will optimize the system for the measurement of OH spectra, instead of C2H2, by using more probe beam passes to increase the path length. We will also shift the laser wavelength to where the OH lines are the strongest.
Fig. 4. (a) Full recorded spectrum of C2H2 + O2 detonation products (blue) and theoretical OH radical spectrum (red) at temperature 4000 K, pressure 40 atm, and concentration 3.1%. The off-scale peaks near 1542 and 1551 nm are from notch filters used to help with the wavelength-time calibration, and thus there are no experimental data in these two ranges. (b) Theoretical spectra at 3000 K (green), 4000 K (red), and 5000 K (purple) overlaid on the recorded data (blue) over a region of the spectrum with the highest signal-to-noise ratio, illustrating that the temperature lies within this range. The same approach was used to estimate the pressure to be 40 ± 10 atm.
The experiment was carried out three times with different molar equivalence ratios, φ: one with the ideal O2:C2H2 ratio of 2.5 (φ = 1), one with a rich mixture (O2:C2H2 = 1, φ = 2.5), and one with a lean mixture (O2:C2H2 = 4, φ = 0.625). The total ambient pressures of the resultant mixtures were kept the same at 1 bar. Spectrograms of each experiment are provided in Fig. 5, where the vertical axis is wavelength, the horizontal axis is time, and the colors represent transmittance.
Several features are noticeable in the spectrograms. At early times, the group of horizontal lines that extend from the upper left corner (1520–1540 nm range) are from the C2H2 absorption spectra. The fainter horizontal lines that appear as the C2H2 disappears are predominately OH lines in the combustion products. The white horizontal areas have no data because of spectral notch filters. Vertical lines that occasionally appear are temporary reductions in signal levels, likely caused by turbulence that causes beam steering from refraction and a loss of coupling. These signal reductions most frequently appear shortly before the presumed detonation reaches the probe and continue occurring for ∼200 µs after the detonation passes; after that, the OH persists at a stable pressure, temperature, and concentration until the end of the ∼1.6 ms long recording time. Since the cell remains sealed during the experiment, high temperatures and pressures persist for much longer than this recording time. It is also interesting to note that in the rich mixture case (Fig. 5(b), φ = 2.5) there does not appear to be any OH formation, at least within the detectable limits of the system. In the stoichiometric (ideal) mixture case (Fig. 5(c), φ = 1), the time between initiation with a spark (time = 0) and the detonation wave passing the probe is significantly shorter than the other two cases.
Fig. 5. Spectrograms of C2H2 + O2 mixture showing combustion. The color represents optical transmission through the cell: high transmission is represented by yellow and low transmission by blue. White areas are where spectral notch filters prevented the accumulation of spectral data. Horizontal lines are absorption lines in the spectrum. The short horizontal blue lines at early times between 1520 and 1540 nm are from absorption in C2H2, and they disappear after detonation. The weaker horizontal lines that show up after the C2H2 disappears are predominately from the OH radical. (a) Molar equivalence ratio of 0.625 (lean mixture). OH is present after the C2H2 disappears; however, the combustion process takes the longest to complete compared to the rich and ideal mixtures. (b) Molar equivalence ratio of 2.5 (rich mixture). No detectable OH lines after C2H2 combustion probably indicates a different reaction pathway for this case. (c) Molar equivalence ratio of 1 (ideal mixture). Earlier disappearance of C2H2 lines shows combustion finishes earlier, followed by the appearance of strong OH lines.
To further illustrate the dynamic capabilities of this approach we extracted the optical absorption vs. time from C2H2 and OH separately for each of the 3 measurements. Figure 6 shows the optical absorption for C2H2 in blue and for OH in red. The values shown for C2H2 are the peak absorption (defined as 1 − transmittance) of 10 lines from 1534-1541 nm. For OH the values shown are for the average peak absorption of lines in the range from 1550-1560 nm (where there are no C2H2 lines).
Fig. 6. Optical absorption of OH (RED) and C2H2 (BLUE) for 3 different equivalence ratios (a) φ = 0.625 (b) φ = 1 (c) φ = 2.5. A thumbnail with an expanded view is shown for the φ = 1 case illustrating how the process of OH forming and C2H2 disappearing was time-resolved over the course of a few microseconds. Each point represents a single spectral measurement. Smoothed curves (bold) are plotted on top of the shot data for clarity.
There are some interesting things to note from Fig. 6. The scaled up thumbnail in Fig. 6(b) shows that the 5 µs transition is time resolved, a task that would be difficult using other approaches. As noted earlier, no OH forms in the fuel rich case. In the other 2 cases, OH formation occurs on the same time scale as C2H2 depletion. In the rich and lean cases the C2H2 disappears in 150-160 µs while in the φ = 1 case the transition occurs in 5 µs. After the OH has formed, the absorption and spectral shape remains constant for over 1600 µs, indicating there is not an appreciable change in the OH pressure, temperature, or concentration during this time.
To demonstrate the capability to measure thermodynamic properties we used the C2H2 spectra to calculate temperature. The results, shown in Fig. 7, show the temperature rises steadily up to around 500 K as the concentration is decreasing over the 150 µs time frame for the non-ideal mixture cases, and the temperature rises slightly faster in the rich mixture than the lean. For the ideal mixture, the temperature rises the fastest but only reaches about 350 K before sudden depletion occurs.
Fig. 7. Temperature-time profile of C2H2 in 3 shots with different equivalence ratios. The plots end when the C2H2 is depleted. Smoothed curves (bold) are plotted on top of the shot data. Temperature is calculated from the ratio of 3 peaks in the C2H2 spectrum.
Figures 6 and 7 plot single-shot results with a smoothed function overlaid in bold for clarity to provide a visual indication of the single-shot accuracy and the overall trends. Initially, before the C2H2 starts to disappear, the standard deviation of the single-shot temperature is ∼10 K, and then it increases steadily as the concentration decreases and the spectra disappear into the noise floor. Though this is a fairly accurate thermometer, there is significant room for improvement. Temperature was calculated using the ratio of 3 line pairs in the C2H2 spectrum and comparing them to the theoretical ratio calculated from SpectraPlot. There are many more lines in the spectrum that could also be used, or nominally a non-linear fit could be done to the entire spectrum to simultaneously determine temperature, pressure, and concentration. However, in this case we saturated many lines in the C2H2 spectrum to obtain higher accuracy at lower concentrations. The lines widths were also under-resolved in these experiments with the desired trade-off of covering a larger spectral bandwidth. To obtain more accuracy for a given temperature range and gas, the dispersion of the system can be tailored for a given experiment. For example, several passes of the pulses through the cell would target lower absorption levels, like those seen here in OH, or the dispersion could be increased to obtain high resolution of single lines.
The potential value of this method is its ability to time resolve dynamic transient temperature, pressure, and concentration phenomena that occur on a 1 µs to 10 ms timescale. Streak cameras are a common method for making such measurements, but they are uncommon in this spectral range, and even where they can measure spectra, they cannot practically provide the simultaneous spectral and temporal resolution shown here combined with the relatively long (1.6 ms) recording time. Swept diode lasers can achieve this resolution but are generally limited to measurement rates slower than 100 kHz. The simultaneous combination of the high temporal resolution (160 ns per spectra) and spectral resolution/bandwidth (0.1 nm/40 nm) can provide temperature, pressure, concentration, and species identification at megahertz rates in OH, C2H2, and other gases (e.g. H2O, CO2) that have IR absorption within the bandwidth of the system. Furthermore, systems like this invoking continuum generation can be used to access a broader range of wavelengths, as was demonstrated by Hult et al. [20] to measure absorption spectra in H2O and CH4. However, it should be noted that spectra of individual pulses from continuum sources vary significantly and have fine structure that can muddle the gas absorption spectra. We overcome this issue by using a reference line (see Fig. 1) to establish a baseline that can be subtracted on a shot-to-shot basis. Also, mode-locked lasers are inherently more stable and thus preferable if the spectrum is sufficient. Additionally, erbium-doped fiber amplifiers and Raman amplifiers are available at these wavelengths to make up for losses in the dispersive fiber so that larger dispersions can be realized.
With this system, we can achieve longer recording times (in the range of tens to hundreds of milliseconds) by extending the record time on the digitizer, but to keep file sizes manageable for analysis, we did not do that here. Another advantage of this method is that it is relatively insensitive to light emission from the sample. Emission is probably significant in these experiments since the temperature is ∼4000 K; however, we see no evidence of thermal emission in the data. Unlike approaches based on a diffraction grating, which would spectrally resolve the emission, with this technique light emission would appear as a relatively slow and un-structured background and would not alter the spectral content after analysis.
4. Conclusion
We have demonstrated the use of fiber-based, time-domain spectroscopy using a mode-locked SWIR laser to make dynamic pressure, temperature, and concentration measurements during the combustion of C2H2 in O2. High-resolution spectra were recorded approximately every 160 ns with a total recording time of 1.6 ms. We observed the formation of OH radicals in the reaction product gas, which allowed us to time-resolve the change in temperature and pressure throughout the process. The appearance of OH lines, a common intermediate by-product in the detonation and deflagration of combustible materials, means this technology offers the potential to measure pressure and temperature in other gases undergoing combustion (e.g., hydrogen and hydrocarbons). If better time resolution is needed, a shorter dispersion fiber or a narrower spectral range will allow the laser to run at higher repetition rates without pulse overlap. Other commonly applied approaches for making pressure, temperature, and concentration measurements (e.g., coherent Raman scattering techniques) often use expensive, high-energy, free-space lasers and fast framing cameras and can be limited to sub-megahertz-rate measurements with limited record times. It is also difficult to accurately estimate concentrations from Raman-based approaches. The method reported here uses relatively inexpensive low-power fiber-based laser equipment and offers greater speed, resolution, and record lengths without the need for complex, expensive optical systems.
Funding
National Nuclear Security Administration (DE-NA0003624).
Acknowledgments
This manuscript has been authored by Mission Support and Test Services, LLC, under Contract No. DE-NA0003624 with the U.S. Department of Energy and supported by the Site-Directed Research and Development Program, National Nuclear Security Administration, Office of Defense.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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