Temperature imaging in low-pressure flames using diode laser two-line atomic fluorescence employing a novel indium seeding technique

The use of diode lasers for spatially resolved temperature imaging is demonstrated in low-pressure premixed methane–air flames using two-line atomic fluorescence of seeded indium atoms. This work features the advantages of using compact diode lasers as the excitation sources with the benefits of two-dimensional planar imaging, which is normally only performed with high-power pulsed lasers. A versatile and reliable seeding technique with minimal impact on flame properties is used to introduce indium atoms into the combustion environment for a wide range of flame equivalence ratios. A spatial resolution of around 210 µm for this calibration-free thermometry technique is achieved for three equivalence ratios at a pressure of 50 mbar in a laminar flat flame.


Introduction
The temperature in thermochemical processes, such as combustion, is one of the major governing physical properties due to the strong relation between temperature and reaction rates. Chemical kinetic models striving to understand, explain and model the combustion process are highly dependent on accurate experimental data for validation and optimization, where temperature information is a crucial parameter. For the development of kinetic models, low-pressure flat flames are frequently used due low-pressure nanoparticle synthesis flames offering a temperature range between 600 and 1500 K [7]. A substantial amount of NO has to be seeded into the gas flow to achieve a decent signal-to-noise ratio, which may have non-negligible effects on the flame chemistry.
With the recent advances in hybrid femto/picosecond coherent anti-Stokes Raman spectroscopy (CARS), the technique previously limited to point measurements has been expanded to 1D and even 2D measurements at atmospheric pressures [8,9]. CARS is, however, expected to have decreased usability in low-pressure environments as the signal is proportional to the square of the number density. Even so, measurements in low-pressure hydrogen flames have been reported successfully [10]. The CARS technique also suffers from an experimentally complicated set-up involving expensive and bulky equipment.
Absorption-based techniques benefit from experimental simplicity and straightforward data evaluation, and numerous papers present temperature measurements utilizing absorption techniques based on either near infrared diode lasers or quantum cascade lasers [11,12]. Commonly, a tunable diode laser is scanned over either one or a few well-known absorption lines. For the twoline approach, the lines are usually chosen so the ratio of the intensities of two lines is temperature sensitive and the temperature can be extracted if the line strengths are well known. A one-line method can also be used where a recorded line shape is fitted and the Doppler broadening due to thermal molecular motion is calculated. Absorption-based techniques are limited to path-integrated temperatures along the line of sight and even in one-dimensional flames edge effects may contribute to errors in measured temperatures, although this can be minimized with proper precautions [11].
With the introduction of laser diodes in the blue wavelength region, temperature measurements using atomic fluorescence of indium have been reported, both a two-line method [13,14] and a one-line scanning method, termed OLAF [15]. Both methods will be described in detail in the next section. The two-line method is especially suitable for sooty and particle-laden flames as elastic scattering can be filtered. However, even detection of resonant fluorescence has been shown to work well for low-pressure sooty flames [13] due to the high quantum yield of the atomic fluorescence. In these papers, indium was seeded into the flame using InCl 3 dissolved in water. The introduction of a few per cent water vapour will potentially influence the flame chemistry, and a temperature uncertainty of ±20 K has been estimated to be caused from this seeding method [16]. Previous work has been limited to point measurements due to weak powers of the diode lasers, and mapping of the flame temperature has been a somewhat time-consuming process. As evident, there is still room for developing a diagnostic method that can image the temperature with good accuracy and spatial resolution using diode lasers.
In this work, we present the development of a temperature imaging technique with diode lasers using two-line atomic fluorescence in low-pressure flames. Imaging is possible due to the development of higher-power diode lasers in combination with a state-of-the-art intensified high-speed camera, working in the linear regime. A novel indium seeding system, previously described in [16], with negligible impact on flame properties is used to access temperature information from the reaction zone to the product zone for a wide variety of equivalence ratios at pressures of 50 mbar. The seeding system also allows for seeding through sintered porous plug burners commonly employed in low-pressure flame studies for kinetic modelling [17], and the temperature measurements conducted here are included in a broader effort striving to perform accurate quantitative measurements of species concentrations in low-pressure flames using infrared polarization spectroscopy (IRPS) for model validation and kinetic simulations [18,19].
The theory of the two-line atomic fluorescence method is explained, and temperature measurements for different equivalence ratios are presented. The demonstrated technique is shown to be a valuable tool for temperature measurements that can be expanded into sooty flames and higher pressures.

Theory
Two-line atomic fluorescence (TLAF) thermometry is a ratiometric technique, in which the temperature is derived from the ratio of the fluorescence signals from two different lower levels excited to a common upper level. For a three-level electronic system with two lower states and one excited state, as shown in Fig. 1, two different detection schemes are commonly used. In the first detection scheme  Fig. 1a), the non-resonant fluorescence is detected for each excitation. This technique is suitable in sooty and particulate laden flames as elastically scattered light can be filtered out. The major disadvantage is the need for a temperature calibration measurement to account for detector efficiencies at the different wavelengths and collection angle differences [20]. Medwell et al. [21] have conducted measurements in the nonlinear excitation regime to increase the signal-to-noise ratio with the added complexity of needing a calibration curve from a fluorescence versus irradiance plot. For the second detection scheme as shown in Fig. 1b, the fluorescence is detected at the same wavelength independent of the excitation wavelength obviating the need for two detectors and a calibration measurement. Despite an increased sensitivity to elastic scattering, this has been shown to work well in low-pressure sooty flames [13].
For a tunable light source and the detection scheme in Fig. 1b, the temperature is related to the fluorescence signal, F, as [13]: where ΔE is the energy splitting between the two ground states, k is the Boltzmann constant, I the laser power, A is the Einstein, and ν is the laser frequency. The numerical subscripts denote the transitions according to Fig. 1.
The two dominant broadening mechanisms that have to be accounted for when fitting the line shapes are the Doppler broadening and the pressure broadening, also known as collisional broadening. The Doppler broadening is due to thermal molecular motion and gives rise to a Gaussian profile. The collisional broadening is more complex and arises from the interaction between an emitting molecule and the collisional species and is thus dependent on temperature and pressure, as well as local gas composition.
To analytically express the collisional broadening requires information about the local species concentrations, temperature and pressure as well as information of the reference broadening parameters for each species, which except for nitrogen and the noble gases are unknown. The collisional broadening can be approximated using impact broadening theory, and from this the FWHM of the Lorentzian can be described as [22]: where a reference collisional broadening at a known temperature and pressure can be used to calculate the Lorentzian profile at other pressures and temperatures if the gas compositions remain the same. The impact broadening approximation assumes that the duration of collisions are much shorter than the time between collisions. For pressures of 50 mbar, relevant for this work, the mean free path is approximately 20 µm at flame temperatures, magnitudes greater than the atomic diameter, as needed for the impact approximation to be valid. The observed spectral line shapes will be a convolution of the Gaussian and Lorentzian profile, known as the Voigt profile. If the collisional broadening is known, the temperature information can be extracted from a spectral line shape by fitting a Voigt profile to the line shape using the temperature as a fitting parameter.

Experimental
The experimental set-up is shown in Fig. 2. Two external cavity diode lasers (ECDL) (Toptica, DL100pro and DL100) were used to probe the two indium transitions 5 2 P 1/2 → 6 2 S 1/2 and 5 2 P 3/2 → 6 2 S 1/2 at 410 and 451 nm. The lasers had a power of 5 mW and were wavelengthmodulated to scan the hyperfine structure of each transition. Using a dichroic mirror, the two lasers were spatially overlapped and sheet forming optics were employed to produce a 4-mm-high laser sheet, thickness 0.2 mm, focused over the burner. A chopper wheel rotating at 10 Hz alternated between the lasers in synchronicity with the laser wavelength scanning. A reflection of the laser beam from a flat glass plate was directed to a high-finesse confocal Fabry-Perot etalon (Toptica, FPI 100) to measure the relative frequency when tuning the lasers and to ensure that the wavelength scans were mode-hop free. Two photodiodes, before and after the flame, measured the laser power during a scan and recorded the amount of absorption of the lasers, respectively. Perpendicular to the incident laser sheet, an intensified high-speed camera (Photron, SA-X) recorded the laser-induced fluorescence signal. Wavelength scans were performed with each laser sequentially, and fluorescence spectra were thus acquired at each pixel of the high-speed camera. An interference filter centred at λ = 450 nm and Δλ ± 10 nm was used to reduce background chemiluminescence and detect fluorescence from the excited state to the upper level of the spin-orbit split ground state as this transition has approximately two times stronger transition cross section than the transition to the lower ground state. The camera was mounted with an objective f# = 1.4, and imaging of a 1951 USAF resolution test card and applying the Rayleigh criterion resulted in a spatial resolution of 210 µm and a pixel size corresponding to 70 × 70 µm 2 . A power meter (Thorlabs S110) was used to calibrate the power measured on the photodiode before the flame.
The thermometry measurements were conducted on a McKenna burner with a diameter of 30 mm fitted in a low-pressure chamber. A co-flow of N 2 prevented entrainment of ambient gases, and through a translation stage, the burner was adjustable in height. Mass flow controllers regulated the flow of methane, oxygen and nitrogen to the burner, and the pressure of the chamber was stabilized to 50 mbar with a rotary vacuum pump. Conditions of the three flames are listed in Table 1. For richer flames, N 2 was decreased in relation to O 2 to prevent blow-off. The flame conditions investigated in this paper are targeted for further study by other measurement techniques such as infrared polarization spectroscopy [23] for modelling purposes, and the temperature measurements are crucial for the wider efforts to characterize these flames.
A newly developed indium seeding system was used to deliver indium atoms to the flame [15]. The working principle of the seeding system is as follows. A flow of inert gas is passed through a bubbler filled with crystallized trimethylindium (TMIn). The inert gas acts as a carrier of TMIn, where the bubbler temperature, controlled with a thermalized bath, determines the vapour pressure and thus the concentration of TMIn in the flow. The TMIn thermally decomposes when heated to produce free indium atoms. The carrier gas is mixed with the unburned gases to introduce TMIn to the combustion environment. As only a small amount of carrier gas is needed for a sufficiently high concentration of indium in the flame, it is reasonable to assume that the added constituents to the flame have negligible effects on the flame properties. The investigated flames had a total flow of approximately 2 L/min, whereas the TMIn flow was 0.03 L/min consisting mostly of N 2 carrier gas. The TMIn seeding level was adjusted to achieve strong LIF signals while ensuring that the high concentration did not affect the temperature measurement. Detection of the fluorescence to the same level, as shown in Fig. 1b, circumvents problems with self-absorption at high seeding concentrations. Instead, these measurements may suffer from line-shape distortions if the concentrations are too high.
Scanning the lasers with 20 Hz, a recording was made during one second with a frame rate of 6 kHz. The singlemode scanning range was 20 GHz for the 5 2 P 1/2 → 6 2 S 1/2 transition and 15 GHz for the 5 2 P 3/2 → 6 2 S 1/2 transition. At every measurement height, each pixel had an excitation scan of the two transitions averaged over ten scans, each scan consisting of 300 data points. A flat-field correction for differences in beam profile between the two lasers was made by measuring the fluorescence of the beam sheets at the highest position in the flame, where it was assumed that the temperature was uniform, and extracting a beam profile for each laser. The extracted profiles agreed well with the profiles acquired from a beam profiler allowing the use of the beam profiles measured from the indium fluorescence for flat-field corrections.

Results
Typical normalized excitation scans of the two transitions for a single pixel are presented in Fig. 3. Wavelength tuning of the lasers is accompanied by an intensity modulation that is corrected for by the base line recorded with the reference photodiode. A least-squares fitting routine is adapted to fit the measurement data to the well-known hyperfine structure of indium [24]. Voigt profiles for each of the hyperfine transitions are simulated, and the complete line shape is achieved after summation of the separate profiles. To account for a nonlinear frequency response in the laser tuning, a quadratic polynomial is fitted to the peaks of the etalon trace. A peak signal-to-noise ratio (SNR) of 60 was achieved evaluated by dividing the peak value by the standard deviation of the residual. Almost background-free measurements are observed for the line shapes indicated by both the fitting parameter and the observable line shape as shown in Fig. 3 when the laser is off the absorption line. The two-line atomic temperature is insensitive to the collisional broadening due to the low pressure which allows for a two-step iterative fitting scheme to be employed to calculate the reference collisional broadening, increasing the precision of the TLAF measurement. In the first step, the temperature is calculated from Eq. 1 after fitting the two line shapes with the floating parameters temperature, background and amplitude. In the second fitting step, the previously floating parameters are locked and only the reference collisional broadening is fitted. The fitted broadening parameter is used in the next iteration, and after typically three iterations, the temperature and broadening parameter has converged. The temperatures obtained from the line-shape fits, the OLAF temperature, are in this iterative scheme locked to the TLAF temperature. As shown in Fig. 3, a good agreement between the fits and the measured line shapes is achieved. The good agreement between the experimental and simulated line shapes indicates that the indium concentration is low enough so as to not distort the line shapes.
Two-dimensional TLAF temperature maps of the three flames are shown in Fig. 4 with corresponding temperature profiles along a single pixel line in the centre of the burner plotted to the right. As expected, the temperature profiles show a steep gradient in the reaction zone followed by a plateau at high temperature in the burnt gas region. The temperatures of the flames were simulated with CHEM-KIN using the GRI 3.0 mechanism under the assumption of a burner stabilized flame, and the result is plotted as the lines in the temperature profile plots. The TLAF temperature is observed to consistently have a lower temperature than the simulations attributed to heat losses not included in the model. For Φ = 1.16 and Φ = 1.42, the experimental temperature is approximately 120 K lower than the simulations, and for Φ = 1.68, the difference is 60 K.
The precision of the TLAF measurements is 0.7 % calculated as the standard deviation in a region of the flame with a uniform temperature distribution, in this case using a box at 13 mm height above burner (HAB) with dimensions 9 pixels in the vertical direction and 60 pixels in the radial direction in the centre of the burner. An increased temperature is observed for the richer flames which, as explained previously, is due to the lower relative concentration of N 2 in the O 2 -N 2 gas mix for these flames. An estimated accuracy based on the error sources is presented here. The evaluated TLAF temperature is dependent on the relative power response of the power meter for the two wavelengths, 410 and 450 nm. A reasonable assumption of a relative error of 5 % for the power calibration results in an error of the TLAF temperature by 3 %. A more accurate power meter, such as a thermopile-based power meter, would drastically increase the accuracy [13], and the error given here is not a fundamental limitation of the technique. Other notable error sources are, as previously mentioned, the reference collisional broadening, beam profile compensation and the goodness of the fit. The error of the beam profile compensation results in slight distortions in the vertical temperature profile which is otherwise expected to be smooth. Assuming the errors are independent and normally distributed, the accuracy of the technique can be estimated as the square root of the sum of squares and is for this measurement 4 %.
The horizontal temperature profile for a single pixel line at a height of 10 mm above the burner surface is shown in Fig. 5. The flat flame nature of the porous plug burner holds true between −10 and 10 mm in the radial direction of the flame, thereafter a temperature decrease is seen due to the entrainment of cold co-flow gas. The smoothness of the radial cross section is seen as an indication of the robustness of the fitting model.
The concentration of indium atoms in the flame is determined from the recorded absorption profile by the photodiode located after the flame. The recorded transmission through the flame is shown in Fig. 6 as well as the best fit to the recorded data. According to the Beer-Lambert law, the transmitted intensity I is related to the concentration N as where σ is the absorption cross section, L the length and I 0 the intensity before the flame. The absorption length L is measured from the recorded LIF images, and the ratio I/I 0 is the resulting transmission presented in Fig. 6. The absorption cross section is calculated from the Einstein A coefficient.
Here λ is the wavelength of the transition, φ is the normalized line shape function and g n and g m are the degeneracies of the upper and lower states, respectively. Integration over the line shape for both the cross section expression and absorbance data and applying Eqs. 3 and 4 yield a concentration of 0.27 ppm indium in the flame. This is a substantial fractional absorption, but a fairly high seeding concentration was chosen in order to demonstrate the principle of diode laser TLAF imaging. For axis-symmetric flames like the one studied here, the effects of absorption can be compensated for by calculating the local laser power at the measurement volume. It has been shown previously that temperature measurements by the single-detector TLAF scheme are insensitive to signal trapping. Nevertheless, strong fluorescence signals are evident from the spectra as shown in Fig. 3, meaning that much lower seeding concentrations could be used in future to avoid any influence of laser absorption on the measured temperature. Similar concentrations have been shown for atmospheric flames under the same seeding conditions [16].

Conclusions
In this work, we have demonstrated two-dimensional imaging of flame temperature using diode lasers for the first time. Previous work on diode laser two-line atomic fluorescence was restricted to point measurements, but advances in diode laser output power and camera technology have allowed mapping of the temperature field in low-pressure methane flames to provide data for validation of chemical kinetic models. This demonstration of planar laserinduced fluorescence imaging with compact, inexpensive, low-power light sources is a significant step forward since such measurements have been performed in the past with high-power, pulsed dye lasers. The spectral purity of the diode lasers allows a fully resolved indium spectrum to be recorded at every camera pixel. A novel indium seeding system providing more flexibility than conventional arrangements allowed indium seeding through a sintered porous plug McKenna-type burner while avoiding the addition of water vapour to the premixed gases. Diode lasers were shown to give a peak SNR of 60 for imaging purposes, which highlights the future potential to make temperature measurements more quickly and/or at lower seeding levels than that has been reported here. The accuracy of the measurements reported in this first demonstration of TLAF imaging was estimated to be ±4 % at flame temperatures, but this is by no means a limitation of the technique and would be drastically improved by using a laser power meter that is insensitive to wavelength. More accurate beam profile compensation will further increase the accuracy and the precision of the technique and reduce the spread in vertical direction. These improvements may be expected to lead to measurement uncertainty similar to that previously demonstrated for single-point diode laser TLAF studies. The temperature measurements were shown to compare well to chemical kinetic simulations. Thanks to the simplicity of the set-up, the technique is expected to be applicable to a wide range of other laminar flames and particularly well suited to fuel-rich and sooting flames, including those with sharper and more complex spatial gradients than the one studied here. Transmission of the laser tuned over the 5 2 P 1/2 → 6 2 S 1/2 transition recorded on a photodiode after the flame and the best fit