1. Introduction

Laser Rayleigh scattering provides a remote and accurate diagnostic technique that can be applied to the measurement of temperature, density and composition in flow fields and flames. For example, it has been used for quantitative flow visualization in unseeded flows [1], for temperature and density measurements in flames [2] and in high speed flows [3,4]. Coherent Rayleigh scattering (CRS) is a relatively new technique in which a volume density grating is created in a gas via electrostrictive forces from two pump beams. The CRS signal is a phase matched scattering of a probe beam from this volume density grating. Like spontaneous Rayleigh scattering in the low density limit, CRS for a single species gas is characterized by a particularly simple analysis due to the near-Gaussian spectral profile of the signal. The CRS signal is, however, a coherent beam that is orders of magnitude stronger than the spontaneous signal which leads to high signal to noise ratios at low densities and has been used to measure the temperature of single species plasmas and gases [5, 6]. CRS is a promising technique for temperature measurement in a variety of gas phase environments primarily because of its particularly simple analysis and the high signals intensities that can be obtained. CRS and the closely related coherent Rayleigh Brillouin scattering have been studied extensively in single species gases where it has been used to measure temperature in a plasma. In this paper, we describe the first application of CRS to a multispecies gas in a cell subsequently to a flame indicating its utility for measurements in this and other multispecies gas phase environments.

2. Coherent Rayleigh scattering

In CRS, two nearly counter propagating pump beams having electric fields E ₁(x,t) and E ₂(x,t) and frequencies ω ₁ and ω ₂ interfere within the sample to produce an interference pattern. The interaction of the periodic intensity profile with the polarizability of the gas species gives rise to a periodic electrostrictive force that perturbs the spatial velocity distribution of particles moving close to the velocity υ = Ω/q. The beat frequency of the electric field is given by Ω = ω ₁ - ω ₂, and q=∣k ₁-k ₂∣ is the wave vector of the induced grating, where k ₁ and k ₂ are the wave vectors of pump beam 1 and 2, respectively. The CRS signal is produced by phase-matched scattering from this volume density grating that moves at the same speed. The magnitude of the perturbation at each beat frequency (velocity) is proportional to the square of the density at that frequency (velocity) in the distribution function. The intensity of the scattered CRS signal is proportional to [5],

where L is the interaction length, I ₁, I ₂ and I ₃ are the intensities of pump beam 1, pump beam 2 and the probe beam respectively. In CRS, we operate in a regime where essentially no collisions occur during the interaction. In this limit the perturbation to the velocity distribution function to each species in a mixture is independent and thus the total induced density perturbation for n species is given by

where δf_i is the perturbation to the velocity distribution function f _0,i for each species density ρ_i. The variation of δρ with velocity, and therefore beat frequency, determines the spectral profile of the scattered light. In this work, the importance of collisions to the spectral profile is quantified by the y parameter, which compares the molecular collision time with the grating vector and is defined as [7,8]

where k_b is the Boltzmann constant and τ is the molecular collision time at temperature T. In the collisionless limit where y ≪ 1, the perturbation for each species is calculated from the one-dimensional, collisionless Boltzmann equation [6]. A periodic electrostrictive force creates a perturbed distribution function given by f = δf + f₀. When δf_i ≪ f _0,i, the perturbation for each species is given by [5]

where α_i is the polarizability of each species and E ₁ and E ₂ are the amplitudes of the pump fields. Using Eq. (1), (2) and (4) the spectral profile of CRS can be modeled for multi-component gases. This enables CRS to be applied to more complex environments, such as flames, when the main constituents and their respective mass and polarizabilities are known.

3. Experiment and analysis

To study CRS in gas mixtures we used two narrowband pumps to induce a grating that was probed by a narrowband probe as shown in Fig. 1. Pump beam 1 and the probe were created from an injection seeded frequency doubled Q-switched Nd:YAG. A narrow band cw Nd:YAG laser was pulse amplified and frequency doubled to produce pump beam 2. The pump and probe beams had pulse durations of ~ 10 ns and each pump pulse had an energy of 15 mJ at a repetition rate of 10 Hz. The probe beam had a pulse energy of ~40mJ and the polarization was rotated to be orthogonal to that of the two pump beams. The two pump beams were focussed into the flame or gas cell by two 500 mm focal length plano-convex spherical lenses producing an interaction length of approximately 10 mm. The probe beam counter propagated to the beam path of pump 1 and the resulting signal was scattered from the induced density grating and counter propagated to pump beam 2.

 

Fig. 1. Schematic of the coherent Rayleigh scattering system used to measure the temperature of a butane-air flame. BS ‒ beamsplitter.

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The signal was extracted by a thin film polariser, passed through a polariser and detected unamplified on a silicon photodiode. The signal was then integrated on a boxcar averager before being passed to the LabView program via a computer interface module. The CRS signal was recorded as a function of the difference in frequency between the two pump beams. The frequency of pump beam 1 was scanned by incrementing the voltage applied to the seeder laser which temperature tuned the output frequency. The frequency difference between the two lasers was measured by mixing fractions of the two infrared seeder outputs and measuring the beat signal on a fast InGaAs photodiode. Frequency to voltage conversion of the photodiode signal produced a DC voltage that was recorded for each scan. This system enabled us to measure frequency differences of up to 10 GHz at 532 nm.

 

Fig. 2. Measured CRS spectral profiles from 100 mbar mixtures of N₂ and Xe with the corresponding modeled data at 298 K. A good fit with the multi-component model was found for all mixtures.

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Measurements were made on binary mixtures of gases to compare with the multi-component CRS model. These measurements were carried out at 100 mbar and at 298 K leading to a y parameter of approximately 0.02. We show results in Fig. 2 for mixtures of nitrogen and xenon. Although pure Xe and N₂ have near-Gaussian spectral profiles, the line shape of the mixtures cannot be approximated by a simple Gaussian because they have very different masses. For these and other mixtures, very good agreement with the model was found [9]. This allows us to model CRS spectral profiles from a flame when the major species fractions are known.

 

Fig. 3. CRS signal taken from a butane-air flame as a function of pump laser frequency difference. Also shown is the best fit from the model that gives a flame temperature of 1740 K.

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We have made measurements of the spectral profile of CRS from a butane-air flame with y = 0.035 and compared these measurements with a model. This model was based on the major species down to 0.005 molar fraction but only N₂, H₂O and CO₂ contributed significantly to the CRS profile in the butane-air flame. A laminar butane-air flame was produced by a slot burner that was 45 mm long. The flame conditions were constant over the 10 mm interaction region of the crossed pump and probe beams. Two successive CRS scans in the flame are shown in Fig. 3. The scan taken at 16 MHz intervals was averaged over 20 laser pulses. The noise in this scan was found to be primarily due to the variation in the beam pointing of the pump and probe beams. A second scan at intervals of 800 MHz shows much less noise due to increased averaging at each point (1000 shots). The solid line is the simulated profile for a temperature of 1740 K using the major species described above. The temperature of 1740 K with a 3 % uncertainty was determined by simulating the CRS spectra over a range of temperatures with the best fit found by reducing the sum of the squares of the residuals between the 800 MHz interval data and the simulated CRS spectrum. Unlike the line shapes for the Xe/N₂ mixtures, we find that the experimental and simulated CRS line shapes are very well approximated by a Gaussian profile. The simulations confirm that the CRS signal width, which is related to the thermal velocity profile, varies as the square root of temperature. The same flame temperature can also be found by fitting a Gaussian profile, Δυ _m, to the data and by comparing its width with the CRS simulation for this mixture, Δυ _s, at any simulated temperature T_s. The temperature is determined, as in single species, CRS by

For this flame the model was found to be insensitive to the exact stoichiometry of the flame. For fuel equivalence ratios φ from 0.6 to 2.5, the CRS signal changed by a maximum of 5% in the wings of the spectrum with a negligible change in the full width half maximum, which is dominated by scattering from N₂.

4. Conclusions

We studied CRS from multi-component mixtures and have used these results to measure the temperature of a flame from the spectrally resolved coherent Rayleigh scattering signal. A multi-component CRS model has been demonstrated by measurements in Xe/N₂ mixtures allowing temperature measurement of a butane flame modeled as a three species high temperature gas. Although the collisionless approximation is valid for y ≪ 1 there is not a clear physical interpretation for the exact y value in which the model will no longer accurately predict the spectral profile. For our experiments there was no measurable difference between our spectra and the simulations which assume collisionless conditions for y < 0.035. However, we stress that this is not an upper limit and further work is required to establish this limit for the spectral resolution of our experiments. We have found that, providing the major species are known and y < 0.035, this technique can be applied to multi-component flows and to flames where the stoichiometry is not well known. The use of narrowband laser sources for the pump and probe beams has been demonstrated for the first time. For typical energies used in CRS, the use of narrowband pumps creates larger density perturbations for a particular velocity group and therefore we have found higher signal-to-noise ratios when compared to broadband CRS [5–7, 10]. As high signal to noise ratios can be attained with CRS, single shot measurements of flame temperature may be feasible using a broadband pump such as a modeless laser [11]. We have shown that the measurement of the CRS line shape and the analysis to determine temperature of multi-species mixtures is straightforward and can now be applied to flames, high speed flows and plasma environments using either a narrow bandwidth or broad bandwidth approaches. In light of these and earlier CRS single species studies, CRS can now be seen as an alternative method to coherent anti-stokes Raman spectroscopy or LIF in these environments.