1. Introduction

In recent years, laser-induced breakdown spectroscopy (LIBS) has been proven to be a powerful technique for the in-situ measurement of gas properties. A pulsed laser is focused to dissociate, excite, and ionize gas molecules, producing a plasma with high temperature and elevated pressure in the focal region. In combustion research, the spectra emitted during the plasma cooling phase can be used to infer the local equivalence ratio or mixture fraction after careful calibration [1–3]. In comparison with other laser-based techniques, LIBS has unique advantages in system robustness and signal intensity [4]. Moreover, LIBS signals are insensitive to molecular types and reaction processes, which is well suited to deployment in harsh environments, such as furnace and boiler exhaust [5,6], internal combustion engines [7], and supersonic combustors [8].

To prompt the successful implementations of LIBS in practical combustion systems, numerous research was conducted, covering a wide variety of combustion conditions and fuel types. Do and Carter [4] pioneered the use of short-gated LIBS featuring a nanosecond gate window and delay, which can minimize the impact of high-speed fluid on measurements. The method was further used to map fuel concentrations in a supersonic flow with a Mach-2 freestream [9]. By establishing a calibration scheme ranging from only air to only fuel, Kotzagianni et al. [10] measured the mean mixture fraction in a turbulent diffusion flame. Wu et al. [11] conducted one-dimensional fuel–air ratio measurements under 1-11 bar using line-LIBS. Lee et al. [12] developed a predictive model that detected the equivalence ratio and gas pressure using machine learning-assisted LIBS in a variable-pressure combustion chamber. Besides, some works employed LIBS to study flame structures. Kiefer et al. [13] determined the spatial distribution of Hydrogen/Oxygen atomic ratio in a laminar methane/air flame sustained by a Bunsen burner nozzle. Combining LIBS and acoustic-based laser-induced breakdown thermometry (LIBT) [14], our group [15] simultaneously measured the mixture fraction and flame temperature in a ethylene counterflow diffusion flame. The preferential diffusion of Hydrogen relative to Carbon was well captured. Li et al. [16] investigated the effects of mixture fractions on the structure and soot formation of a laminar oxy-ethylene inverse diffusion flame using LIBS.

In gaseous environments, the collision-dominated plasma excitation is strongly influenced by the gas density distribution around the focal region [17]. The local gas temperature can be measured by analyzing the energy deposition behaviors during plasma excitation [9,14,18]. Previous literature [19–21] reported that, under atmospheric pressure, the plasmas propagated toward the incoming laser beam, while under reduced pressure, the plasmas propagated bi-directionally from the focal point. These observations suggested that the shape of plasma will be different when the gas temperature was varied. As a result, the measurement locations of LIBS, which are determined by the plasma locations, will be unstable when the temperature was varied dynamically. The instability in measurement locations led to fluctuated collection solid angle and light collection efficiency [22], which could deteriorate signal stability, limiting the LIBS applications in unsteady flows. Besides, when LIBS was used to profile a non-uniform temperature field, such as a flame edge, the variations in measurement locations can cause nonnegligible measurement biases. However, despite its significant influence on measurement accuracy, the method to improve the stability of measurement location is still lacking. In Sun’s work [23], a beam-crossing configuration based on a single laser source was successfully used to control plasma positions. Kim [24] reduced the variations in plasma center locations using an electron seeding technique.

It has been revealed that, the laser pulse duration significantly affected the plasma properties and the LIBS measurements [25–28]. In the work by Gragston et al. [29], the continuum emission of picosecond LIBS spectra was weaker than that of nanosecond LIBS due to the limited avalanche ionization. Feng et al. [30] observed that femtosecond laser-induced plasmas did not show significant expansion and internal composition transport, which can yield high spatial resolutions in a 1D measurement. These previous studies opened the door for tailoring plasmas with desired properties by adjusting the pulse duration. Considering the widespread application of nanosecond LIBS, adjusting the pulse duration within the nanosecond regime to stabilize the LIBS measurement locations is of significant interest, yet remains unexplored under combustion environments.

In this work, we temporally modulated the laser pulse to improve the stability of nanosecond LIBS measurement locations under large gas temperature gradients. When the focal point was moved across a hot-cold gas flow interface, the plasma formation process was investigated to reveal the cause of instability in measurement locations. Then, a pulse duration was modulated using a pressurized chamber to suppress this instability. The benefits of stabilized measurement locations were demonstrated by comparing the measured and simulated equivalence ratio distribution across the interface.

2. Experimental setup

2.1 Optical system

The schematic experimental setup is shown in Fig. 1. A 532 nm laser beam was generated from a Nd: YAG laser (Quantel, Q-smart 850) operating at 2 Hz. The output energy was optimized to 260 mJ (shot-to-shot fluctuations were less than 3%) to minimize the fluctuations of modulated pulse width. A 1-inch UV fused silica plano-convex lens #1 (f = 200 mm) was used to focus the laser beam into a stainless-steel chamber. This chamber is 75 mm in inner diameter, 200 mm in height, and equipped with four 2-inch optical windows on its periphery. Compressed air was used to fill the chamber and then evacuated through a vacuum pump (Edwards, RV3). By adjusting the needle valves on the air inlets and outlets, the chamber pressure P can be regulated from 0.001-10 bar. The gas pressures within the range of 0.001-1 bar and 1-10 bar was accurately monitored using Panasonic DP-101A and DP-102A pressure sensor, respectively. The laser beam exiting from the chamber was collimated to its original diameter using another f = 200 mm plano-convex lens #2. Using a pair of beam splitters (Thorlabs BSF10-A), the energy and temporal profile of this pulse can be simultaneously monitored shot-to-shot, by a pyroelectric energy meter (Ophir, PE25BF-DIF-C) and a fast photodiode (Thorlabs, DET025A, rise/fall time < 0.15 ns), respectively. The signals from photodiode were fed into a digital oscilloscope (Teledyne, LeCroy WavePro 404HD, 10 GS/s sampling rate). Then, the laser beam was refocused by a 1-inch plano-convex lens #4 (f = 75 mm) to generate probe plasmas in a hot-cold gas flow interface.

 

Fig. 1. The schematic experimental setup.

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Using a back-scattering optical configuration, plasma spectra generated in the interface were collected with a compact spectrometer (Avantes, ULS2048XL-EVO), which covers the wavelength range of 580 nm-790 nm and has a 1200 lines/mm grating. The spectral resolution was 0.25 nm (FWHM). The spectrometer was triggered 1 µs ahead of laser initiation time and ran at the integration time of 100 µs. The plasma self-emissions were imaged with an intensified complementary metal oxide semiconductor (ICMOS) camera (Photonis, iNocturn HI-QE UV) coupled with an objective lens. A calibration target was used to determine the spatial resolution of the camera, which was 6.45 µm/pixel. Both in the spectra and images acquisitions, 532 nm notch filters were inserted to suppress the elastic scattering. In the absence of breakdown and notch filter, Rayleigh scattering images of 300 K air were recorded with a delay time of 0 ns and a gate width of 20 ns. The plane where the beam diameter was smallest was registered as the focal plane in images. The laser, energy meter, oscilloscope, camera, and spectrometer were synchronized by a digital delay generator (Stanford Research Systems, DG645).

2.2 Hot-cold gas flow interface

The hot-cold gas flow interface was generated using a water-cooled McKenna flat-flame burner, which is composed of a 60 mm-diameter sintered stainless steel porous plug, a concentric 8.8 mm-diameter central tube, and a porous shroud ring, as schematically shown in Fig. 2(a). Stoichiometrically mixed methane (1.5 L/min, purity > 99.99%) and synthetic air (14.28 L/min, 21% oxygen and 79% nitrogen) generated a laminar flame above the plug, while the room-temperature air (5 L/min) flowed out from the central tube. The high-temperature after-burn gas flow and the central cold air flow constructed the hot-cold interface above the tube-plug boundary. 20 L/min nitrogen was used as the shroud gas. The flow rates of methane, nitrogen, and air were set by pre-calibrated mass-flow controllers (Alicat Scientific) with fluctuations less than 0.3%. The plano-convex lens #4 was held in a fixed position. Using a computer-controlled translational stage installed below the burner, the location of focal point was moved from $X$=-8 mm to X =+8 mm with an increment of 0.5 mm, in the symmetry plane and at a height Z of 6 mm above the burner surface.

 

Fig. 2. (a) The schematic McKenna burner and the simulated temperature field. (b) The simulated gas temperatures across the interface at the height of 6 mm above burner surface and the measured results using the Rayleigh scattering thermometry (RST). (c) The temperature gradients along the X direction.

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To provide a benchmark for the measurements, the combustion field was simulated using the ANSYS Fluent software. The GRI-Mech 2.11 [31] was used as the full kinetic mechanism, which contains 277 elementary chemical reactions of 49 species. Radiation was estimated by the discrete ordinate (DO) model. A laminar model was applied. The simulated gas temperatures across the hot-cold interface at $Z$ = + 6 mm are shown in Fig. 2(b), together with the measured results using the Rayleigh scattering thermometry (RST). The good agreement between them validated the simulation. When the focal point was moved across the interface. The largest temperature gradient along the X direction is estimated to be ±612 K/mm, occurring at $X$ = ±4.2 mm (Fig. 2(c)).

3. Results and discussion

3.1 Key factor to the instability in measurement locations

When the chamber was vacuumed to 0.001 bar, no breakdown was observed inside the chamber. In this case, the laser pulse exited the chamber without any change in its original temporal profile (4 ns FWHM and 12 ns total duration), and the laser energy just behind the plano-convex #4 was 197.2 mJ. With this original pulse (referred to as original pulse 1), the plasma formation process was investigated in the hot-cold interface by imaging the plasma self-emissions with a short integration time of 3 ns. By increasing the delay time with an increment of 3 ns, four time-sequential plasma images were obtained during the total laser duration and displayed in Fig. 3. Each image is an average of 50 breakdown events and then normalized by the maximal intensity. ${t_w}$ is the acquisition window relative to the laser initiation time. Laser propagates from left to right. The focal plane is indicated by the vertical dash line.

 

Fig. 3. The normalized plasma self-emission images with the original pulse 1 when the focal point was moved across the hot-cold interface.

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Figure 3 shows that the location of initial plasma core within 0-3 ns was insensitive to changes in gas temperature and gradient. Nevertheless, the following plasma expansion differed significantly, resulting in unstable plasma shapes at the laser ending time. For $X$ = -8 mm, the plasmas expanded bi-directionally, because with a reduced gas density, the initial plasma core was not totally opaque to the incoming laser pulse, and part of the laser energy was transmitted through this initial plasma core to excite the gas on the right region of focal plane. The fast divergence of hot spots generated a two-lobe structure, which shown consistency with the observation in Alberti’s work [32] with the focal length of 75 mm and 100 mm under reduced gas pressures. Such two separated lobes resulted in two probe volumes, which was also unwanted in a point-measurement technique like LIBS. When the focal plane was moved to $X$= -5 mm, where a strong negative gradient exists, the laser pulse transmitted through the initial plasma core was then absorbed by the lower-temperature gas in the right region, thereby generating a much brighter right lobe. For -2.5 mm ≤ $X$ ≤ + 5 mm, the increased gas density in the left region of focal point was able to sustain an opaque initial plasma core. Thus, the plasma emission in the left region dominated the total plasma luminosity throughout the laser duration.

For more detailed analysis, the location of plasma was determined by the weighted centroid of plasma image. Using the focal plane as a reference, the changes of plasma location over time are plotted in Fig. 4. A positive value denotes that the location is at the right of focal plane. Initially, in 3 ns, the locations were close regardless of changes in temperature gradient, with a maximal location difference of 0.13 mm. Afterward, the locations quickly diverged which indicated significant instability. In 9 ns, the location at $X$ = -5 mm shifted to +1.16 mm, while at $X$ = + 2.5 mm, it moved to -0.67 mm, resulting in a maximal location difference of 1.83 mm, which represented a 14-fold increase compared to that at 3 ns. The divergence of locations continued to develop after 9 ns, but at a slower rate due to the reduced laser irradiance. Therefore, the experimental observations indicated that, the instability in plasma locations was a result of plasma expansion behaviors in the later stage of laser pulse duration.

 

Fig. 4. The plasma location relative to focal point over time with the original pulse 1.

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3.2 Suppressing plasma expansion with temporally modulated pulses

Based on the observations in Fig. 3 and 4, i.e., the instability in plasma location was a result of different plasma expansion behaviors, gaseous LIBS measurement locations can potentially be stabilized by suppressing the plasma expansion. For this purpose, a pulse modulation technique [33] was employed to chop the original laser pulse. When the chamber pressure was above 0.03 bar, stable breakdowns were observed inside the chamber. The gas in the chamber was nearly transparent to the laser pulse in the time prior to the breakdown initiation; whereas, after the breakdown was initiated, the generated plasmas led to an abrupt decrease in the temporal profiles of transmitted pulse [34], which modulated the laser pulse to a reduced duration. The chamber pressure was optimized to ensure that the temporal profiles of modulated pulse were well separated, as shown in Fig. 5. Additionally, to isolate the effects of pulse modulation, the energy level of original pulse was adjusted to the same as that of modulated pulse 5, when the chamber pressure was kept at 0.001 bar. This pulse was referred as the original pulse 2. The properties of these pulses are listed in Table 1.

 

Fig. 5. The temporal intensity profiles of original and modulated laser pulses after averaged over 50 pulses.

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Table 1. Properties of original and modulated pulses

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With an acquisition window of 0-12 ns, Fig. 6 shows the normalized images of plasmas induced by original and modulated pulses in the interface, demonstrating the pronounced effects of pulse modulation on suppressing plasma expansion. Modulated pulse 1, represented by the yellow curve in Fig. 5 with a FWHM of 2.5 ns, was generated with the breakdowns initiated at 4.5 ns inside the chamber. Using this modulated pulse, the plasma expansions with the original pulse 1 can be suppressed after 4.5 ns. Figure 3(b) and (c) show that, at $X$ = -2.5 mm and with the original pulse 1, the two-lobe structure formed 6 ns after laser initiation time. Thus, at a proximate location $X$ = -2 mm, employing modulated pulse 1 eliminated the two-lobe structure (Fig. 6(b)). By increasing the chamber pressure to initiate breakdowns earlier, the plasma expansions with the original pulse 1 were further suppressed. At other locations, such as $X$ = -8 mm, the two-lobe structure with the original pulse formed during 3-6 ns (Fig. 3(b)), therefore it can be eliminated using the modulated pulse 5, which was generated with a breakdown initiated at 3 ns under 8 bar (Fig. 6(f)). Comparing the plasma morphology generated by the modulated pulse 5 and original pulse 2, we can also conclude that simply decreasing the energy of laser pulse without the temporal modulation cannot eliminate the two-lobe structure under high temperature, as shown in Fig. 6(g).

 

Fig. 6. The normalized plasma self-emission images with the original pulse and modulated pulses when the acquisition window was adjusted to 0-12 ns.

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We further analyzed the location of hot spots in plasmas for different pulse durations. When the two-lobe structure exists, the location of hot spot was determined from the weighted centroid of corresponding lobe; otherwise, its location was from the whole plasma. With the original pulse 1, the divergence of hot spots under high temperatures was significant, having a maximum of 3.8 mm at $X$ = -5.5 mm (Fig. 7), which further led to considerable ambiguity in LIBS measurement location, which is not suitable for the measurement under large temperature gradients. The separation of hot spots reduced with the original pulse 2 but was still non-negligible. For the modulated pulse 5, the hot spots did not diverge as original pulses, which eliminated the two-lobe structure and thus stabilized the plasma morphology across the interface. As a result, the plasma location relative to focal point were constrained within a narrower range, which varied between +0.01 mm and -0.85 mm relative to the focal point, with a standard deviation of 0.27 mm, indicating an improved stability in LIBS measurement locations.

 

Fig. 7. The location of hot spots when the focal point moved across the hot-cold interface. The regions where the hot spots diverged with original pulses were indicated by blue dash area.

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The total plasma lengths with original and modulated pulses were compared in Fig. 8, which can be used to estimate the measurement spatial resolutions in the axial direction. With the original pulse 1, the average plasma length was 4.17 mm, while with the modulated pulse 5, it decreased to 1.69 mm, a reduction of 2.47 times. The improved measurement spatial resolution is also beneficial for the LIBS implementations in interpreting a fine flow structure. It is worth noticing that in Fig. 8, the total plasma length for original pulse 2 and modulated pulse 5 looks close; however, considering the hot spot is contributing the majority of emission, the diverged hot spot in original pulse 2 actually introduces a lower spatial resolution than the modulated pulse 5. Moreover, our recent work [35] suggested that the two-lobe structure had a negative impact on energy deposition under high temperatures. The deposited energy with the modulated pulse 5 was significantly higher than that of original pulse 2 even the incident energy level was the same, which greatly improved LIBS signal intensity by almost 3 times, as shown in Fig. 9.

 

Fig. 8. The plasma length with the original and modulated pulses when the focal point moved across the hot-cold interface.

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Fig. 9. Comparison of (a) deposited energy, (b) O 777 nm intensity, and (c) N 746 nm intensity between modulated pulse 5 and original pulse 2

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3.3 Demonstration in the hot-cold interface

To demonstrate the benefits of stabilized measurement locations and improved spatial resolution on the LIBS measurements, the equivalence ratio distribution across the hot-cold interface was profiled using the original pulse 1 and the modulated pulse 5. Figure 10 shows the typical raw spectra in a single-shot measurement at $X$ = -8 mm and at $X$ = 0 mm, the two locations corresponding to the highest temperature of 1807K and the lowest of 300 K, respectively. To correct the continuum background in raw spectra, an algorithm developed by Sun et al. [36] was used. The observed atomic emission lines in the corrected spectra were indexed using the NIST Atomic Spectra Database [37]. Here we used the Hydrogen line at 656 nm and the Oxygen line at 777 nm. Given that the Stark broadening dominated the line broadening [38], the Lorentzian profile was used to fit the lines. Then, the area beneath the profiles were registered as the line intensity. The signal-to-background ratios (SBRs) were calculated and compared between the original pule 1 and modulated pulse 5. The signal refers to the atomic emission lines, and the background refers to the continuum emission beneath the atomic lines. Even though the modulated pulse 5 had a reduced energy level of 31.7 mJ, which was 6.2 times lower than that of the original pulse 1, the SBR with the modulated pulse 5 was not significantly decreased. For example, at $X$ = -8 mm, the average SBR at O 777 nm was estimated to be 14.2 with the original pulse and 13.2 with the modulated pulse, while at $X$ = + 0 mm, it was 9.0 and 11.2, respectively.

 

Fig. 10. Typical raw spectra normalized by the peak height of O777 nm with the original and modulated pulse 5 in (a) 1807K and (b) 300 K

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The equivalence ratio can be represented by $(H/O)/{(H/O)_{stoi}}$, where $(H/O)$ is the atomic number ratio of Hydrogen to Oxygen at the measurement location, and ${(H/O)_{stoi}}$ is the atomic number ratio of Hydrogen to Oxygen under the stoichiometric condition. The calibrations were conducted on the same McKenna burner with the equivalence ratio of premixed methane-air mixture varied from 0.65 to 1.10 at a 0.05 increment. When the calibration was performed, there was no gas flow from the central tube, so the hot-cold interface was not generated. The breakdowns were generated at the height of 15 mm above the burner surface and on the central line. 200 shots were averaged for each equivalence ratio. As shown in Fig. 11(a), linear correlations can be established between H/O peak area ratios and equivalence ratios with good accuracy (R² were above 0.999). Because the equivalence ratio was progressively reduced to zero in the air side of the hot-cold interface, which was below the lower operation limit of the premixed calibration burner, these linear correlations were extrapolated to serve as calibration curves in the measurement.

 

Fig. 11. (a) The correlations between H/O peak area ratios and equivalence ratios. (b) Comparison between the measured equivalence ratio distribution across the interface and simulations.

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The experimental and simulated results are plotted together in Fig. 11(b). Each data point is an average of 50 measurements. The measurement uncertainties, represented by error bars, were evaluated by the standard deviations. Overall, better measurement accuracy was achieved with the modulated pulse. At the region with a large temperature gradient (-6 mm ≤ $X$ ≤ -3 mm and +3 mm ≤ $X$ ≤ + 6 mm), the equivalence ratios measured with the original pulse were noticeably lower than the simulated result. This was because the excited plasmas tend to reside in the low-temperature side (Fig. 6(a)), and the low-temperature side had lower local equivalence ratios, which led to a systematical bias. The maximum bias of measurement location happened around $X$= -4.5 mm, where the spatial resolution was also at its worst. The measurement errors were estimated by the measured equivalence ratios minus the simulated equivalence ratio. At $X$ = -4.5 mm, the measured equivalence ratio with the original pulse 1 was 0.18, while the simulated equivalence ratio was 0.44. The error was -0.26, which is the largest across the interface. As a comparison, with the modulated pulse 5, the measured profiles of equivalence ratio agreed well with the simulated results across the interface. The measurement errors were always below 0.05, demonstrating the great potential of pulse modulation in interpreting the structure of a hot-cold interface. On the other hand, the error bars with the original pulse were significant at -6.5 mm ≤$X$≤ -4.5 mm, which were also suppressed after pulse modulation. The improved measurement accuracy in the region with a large temperature gradient is critical for the deployment of LIBS in practical combustion systems, like in a turbulent flame.

The plasmas and shockwaves generated by breakdowns disturbed the flow field. To minimize measurement errors, it was crucial to ensure that, the disturbances induced by the previous breakdown do not interfere with the subsequent laser pulses [4]. This requirement could potentially restrict the temporal resolution achievable in measurements. Nevertheless, by suppressing plasma expansions with modulated pulses, which reduced plasma size and shockwave intensity, these disturbances can be effectively mitigated. Thus, modulated pulses also have the potential to improve the temporal resolution in LIBS measurement.

4. Conclusions

In summary, we improved the stability of LIBS measurement location by temporally modulating the laser pulse to a shorter duration. The experiment was performed in a hot-cold gas flow interface with large temperature gradients. With a standard nanosecond laser pulse (4 ns FWHM), the plasma formation dynamics were investigated across the interface through plasma imaging, revealing that the instability of measurement locations was mainly attributed to the plasma expansion behaviors in the later stage of laser duration. The plasma expanded uni-directionally towards the laser propagation direction under the room temperature, while under high temperature, the hot spot of plasma diverged bi-directionally, resulting in a two-lobe structure and unstable plasma morphology across the interface. Based on this observation, a chamber was pressurized to initiate breakdowns, chopping the laser pulse to a shorter duration, which further suppressed the plasma expansion. Using a modulated pulse with a FWHM of 1.9 ns, the standard deviation of measurement location relative to focal point was reduced to 0.27 mm. Compared to the original pulse duration with same energy level, the modulated pulse eliminated the two-lobe structure when a large temperature gradient was experienced across the hot-cold interface, increasing the deposited energy as well as LIBS signals intensity significantly. The equivalence ratio distribution measured with the modulated pulse showed better agreement with the simulation, especially in the regions where large temperature gradients present. This work contributed to a better understanding of the plasma formation dynamics under large temperature gradients, demonstrating the great potential of a shortened pulse in stabilizing measurement locations and improving measurement spatial resolutions, which can be further beneficial to the implementations of LIBS both in fundamental combustion research and in industrial applications.