Is rotational CARS an alternative to vibrational CARS for thermometry ...

Appl. Phys. B 51, 25-30 (1990)

Applied "physi ° ' ° - cs Physics B and laser Chemistry © Springer-Verlag1990

Is Rotational CARS an Alternative to Vibrational CARS for Thermometry? S. Kriill, P.-E. Bengtsson, M. Ald6n, and D. Nilsson Combustion Centre, Lund Institute of Technology, P.O. Box 118, S-221 00 Lund, Sweden Received 2 January 1990/Accepted 8 February 1990

Abstract. Recent developments in rotational CARS thermometry and critical issues when comparing vibrational and rotational CARS thermometry are described. In particular, the development of dual broadband rotational CARS and the noise characteristics of this approach are emphasized. The difficulty with unambiguous temperature determination in vibrational CARS with unknown parameters, in particular the nonresonant background susceptibility, and the lower sensitivity of rotational CARS thermometry at flame temperatures are also discussed. PACS: 42.65 Dr, 82.40 Py

The application of coherent anti-Stokes Raman scattering (CARS) to combustion studies almost always implies the use of vibrational CARS, i.e. probing of the population difference between vibrational energy levels to determine temperatures and/or number densities. Since it was first applied to a combustion situation by Taran and co-workers in the early seventies [1], considerable knowledge has been gained about thermometry using vibrational CARS and it has found numerous applications including e.g. studies of discharges [2], MHD combustors [3], convective flow and heat transfer [4], jet engine exhausts [5] and power plants [6]. To develop an alternative technique which has the same reliability in thermometry is expected to be a demanding project and consequently the need for such a task must be carefully judged. One must first identify situations where vibrational CARS thermometry is insufficient. Then one must consider whether an alternative with better properties in this particular aspect performs comparably to vibrational CARS thermometry in other situations. In this paper we describe some recent developments in rotational CARS thermometry and discuss its advantages and disadvantages with respect to vibrational CARS thermometry.

1. The Dual Broadband Rotational CARS Approach Although rotational CARS, i.e. probing of the population difference between rotational levels within a vibrational state, seems to have certain advantages for diagnostic purposes, e.g. larger Raman cross-sections and narrower linewidths, this technique has, with a few exceptions, not been applied for combustion diagnostics. The first demonstration of rotational CARS for flame diagnostics was reported by Zheng et al. [7] who used the frequency-tripled 355nm output of a Nd:YAG laser to pump a Coumarin dye laser. A major problem with this approach is the use of the inherently bad Coumarin dye, which has large shot-toshot spectral fluctuations, low efficiencyand short time stability. This problem can be avoided by using dual broadband techniques, demonstrated on rotational CARS by Eckbreth et al. [8] and Ald6n et al. [9]. Although the dual broadband technique was demonstrated rather recently, it was proposed as early as 1979 by Yuratich [10]. The dual broadband technique utilizes two broadband (typically 100-300 cm- 1) dyelaser beams originating from one or two dye lasers and one pump-laser beam, conceptually illustrated in the energy level diagram in Fig. la. Each rotational tran-

26

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N~~

"F

~b

c

I&\'~tY

V 1.0:

0,5

O 1.0:

(15

0

200

150 100 Rarnt~n shift / cm-1

50

Fig. 1. a Energyleveldiagramillustratingschematicallythe dual broadband technique.Broadbandlasers withfrequenciesco.and cob induce Raman coherencesbetween the molecular rotational states representedby solidhorizontallines. The radiationfrom a narrowband laser with frequency coc couples to the Raman coherences generating the CARS frequencies coCARS,b Experimental CARS spectra of room-temperature (above) and flametemperature (below) oxygen illustrating the temperature dependence of the spectral signature in rotational CARS sition is driven by multiple pairs of dye-laser photons where, assuming a BOXCARS phase-matching arrangement [11], each of the two photons within each pair originate from separate dye-laser beams. Once the transition is excited, photons from the pump laser are scattered off the coherently vibrating molecules and spectra are generated at the Stokes (CSRS) and antiStokes (CARS) rotational Raman frequencies around the pump laser frequency. With the dual broadband technique and using a Nd:YAG-laser-based system one can now, instead of pumping Coumarin dyes at 355 nm, use stable Rhodamine dyes pumped at 532 nm for rotational CARS.

1.1. Experimental The experimental arrangement for rotational CARS is similar to that used in vibrational CARS. In the dual broadband concept the basic difference compared to conventional vibrational CARS 1-12] is that an additional dye laser beam is used instead of one of the two frequency doubled YAG laser beams. We have used a Nd:YAG-based system. (A Quantel YG581-C Nd:YAG laser and a Quantel TDL-50 dye laser.) Normally 20% of the frequency-doubled light at

532 nm was split offto serve as the 09~ beam in Fig. la with a pulse energy of about 50 mJ. The rest was used to pump the dye laser where typically 60 m J/pulse at 630 nm could be obtained using DCM as the dye. The dye laser was used in a broadband configuration producing a linewidth of 280 cm-1 (FWHM). The dye laser beam was split into two components, co, and cobin Fig. 1a, and together with the green beam arranged in a BOXCARS phase matching configuration and focused into the flame with an f = 500 mm lens. The created rotational CARS beam is superimposed and collinear with one of the red beams, but is spectrally isolated by dichroic mirrors and colored glass filters before entering a I m spectrograph with a dispersion of 2.9 A/ram. The rotational CARS spectra were detected with a PARC OMA III diode-array detector and stored on floppy disks for subsequent data analyses. The experiments showed that the rotational CARS intensity could be very large. In pure nitrogen at room temperature the peak signal single-shot intensity was more than 106 counts. Even at flame temperatures the peak signal intensity exceeded 10 a counts in a single laser pulse. As an example of rotational CARS spectra at different temperatures, Fig. I b illustrates experimental spectra of O2 molecules at room temperature (above) and at flame temperature (below). The latter spectrum was recorded in a lean C H J O a flame at atmospheric pressure. As can be seen the peak intensity in the high temperature spectrum is shifted towards higher Raman shifts and the envelope of this spectrum is also considerably broader compared with the spectrum at room temperature. Both spectra have been normalized to the same height, although the flame spectrum has a lower signal intensity.

1.2. Accuracy Besides the simpler operation one might also anticipate lower single-shot spectral noise (and consequently better temperature accuracy) for the dual broadband techniques. The reason for this is that, even on a singleshot basis, a spectral averaging effect is obtained, since essentially all dye-laser frequency components participate in the generation of each CARS frequency. At a quite early stage there were already speculations that such a reduction could occur for the dual broadband techniques [8, 9, 13, 14] and in theoretical work concerning the influence of laser statistics on noise in nonlinear processes, specifically CARS, it was shown that with the conventional assumption of the pulsed multimode lasers having Gaussian (chaotic) statistics, the dual broadband techniques would have lower noise (better temperature accuracy) than the conventional approaches for single-shot CARS thermometry [15]. The dye laser spectral noise is mainly caused by

27

Is Rotational CARS an Alternative to Vibrational CARS for Thermometry?

Table 1. Singleshot signal strength and temperature accuracyfor differentapproaches to rotational CARS thermometry Rotational CARS technique

Dye(s)

Peak signal Temperatureaccuracy strength in [-%] flame [counts] Experiment; Theory Average of flame and room temp. result

Dual broadband Dual broadband (2 dye lasers) Conventional Conventional (2 dye lasers)

DCM Rh610+Rh640

3 x 103 5 x t02

5 6

C500 Rh6t0+Rh610

6 x 10 z 4 x 102

10

8

6

6

random fluctuations in the laser mode amplitudes. This noise source is essentially eliminated in the dual broadband CARS spectrum. In the dual broadband CARS spectrum the noise is instead caused by random fluctuations in the laser mode phases. Why this is the case, and its implications for CARS and CARS thermometry, is extensively discussed in Refs. [15, 16]. One of the more remarkable consequences pointed out in that work is that the spectral noise in the signal can be lower than the spectral noise in the sources generating the signal. This is indeed a very attractive property for a measurement technique. Support for the claim of lower noise in the signal than in the sources can be found even among the first papers on dual broadband rotational CARS where lower noise was reported in the CARS signal than in the dye laser generating the spectra [9]. At this point a more detailed investigation of the possibilities of the dual broadband techniques was motivated. In Ref. [16] the signal strengths and temperature accuracies at room temperature and flame temperature were investigated for different CARS techniques. Some of the results from that investigation are collected in Table 1. A full discussion including all the results is given in the original work. It is clear, however, from Table 1 that the dual broadband technique in practice can offer a significant improvement over conventional rotational CARS, not only regarding ease of operation, but also in terms of its significantly larger signal strength and better temperature accuracy.

2. CARS Temperature Determination with Inaccurately Known Input Parameters; Example for the Nonresonant Third-Order Susceptibility The computer codes used to determine CARS temperatures generally contain a set of parameters that are, if

5 6

not unknown, known only to a limited accuracy [12]. These parameters are typically the nonresonant thirdorder susceptibility ()~NR), the laser linewidths, the spectral dispersion of the detection system, the absolute frequency scale of the recorded spectra and the functional form of the spectral distortion imposed by the detection apparatus. There have been several investigations on how inaccurate knowledge of these and other parameters can yield systematic errors in the determined temperature in vibrational CARS [3, 12, 17, 18]. A general problem for vibrational CARS is that in a parameter space formed by the temperature and the parameters mentioned above, changes induced by varying one parameter may not be strictly orthogonal to changes induced by varying the other parameters [12]. As an illustration of this, Fig. 2a shows vibrational CARS spectra for 1800 K (curves 1 and 2) and 2000 K (curve 3) where the curves 1 and 3 have a XNRof I (units are 10-17 esu) and curve 2 has a )~NRof 3. (Pure N 2 has a XNRof 0.74 at a temperature of 298 K and a pressure of 1 atm. Divide with the nitrogen molecule number density to obtain )~N~molecule in units of cm6/erg.) In Fig. 2b envelopes of rotational CARS spectra are shown for the same parameters. It can be seen that an increase in temperature and an increase in XNR have a similar effect on the vibrational spectra. Specifically curves 2 and 3 have a remarkably good overlap in the interval 2290-2330 cm- 1 although their temperatures differ by 200 K. In the rotational spectra, however, the temperature is determined from the position and width of the envelope of the peaks (as discussed in connection with Fig. lb), while a high ZNR mainly results in an overall background signal. (This background signal has been subtracted in Fig. 2b. From Fig. 2 one may possibly infer that the temperature determined from vibrational CARS spectra is more sensitive to errors in ZNR than those determined from rotational spectra and indeed this

28

S. Kr611et al.

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1 t

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2270

2300 2330 Romon shiff / cm-I

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100

200 300 4-00 Roman shiff I cm-I

Fig. 2a, b. An increased temperature (T) and an increased nonresonant susceptibility (Zs~) have similar effects on the spectral shape in vibrational CARS but less so in rotational CARS. a Vibrational CARS spectra: curve 1, T= 1800 K, ZNR= 1; curve 2, T= 1800 K, ZNR-----3;curve 3, T=2000 K, ZNR= 1. The spectra have been normalized such that the peak values are 1. b Envelopes of rotational CARS spectra, same parameters for the different curves as above. The spectra have been normalized such that the lowest value corresponds to 0 and the largest to 1

same premises changes by about 30%. Clearly the error in vibrational CARS can be significantly reduced, e.g. by weighting different parts of the spectra. It is our impression that the partial nonorthogonality is to some extent related to the overlapping of spectral lines in the vibrational CARS spectrum and, using detection equipment of higher resolution [12], it could probably be significantly reduced, although at higher pressure there is an intrinsic overlap between the Raman lines which cannot be resolved. As an illustration of the above problem we may consider CARS thermometry in sooty environments, a situation frequently encountered in combustionrelated applications. It has been shown that the nonresonant third-order susceptibility can undergo large variations in fuel-rich and sooty regions [19] and XNR consequently has to be fitted simultaneously with the temperature. In sooty environments there is also the additional complication of spectral interference with the CARS signal from C2 molecules produced by laser ablation of soot particles [20-22]. It has recently been shown that, together, these effects can readily introduce temperature errors of several hundred degrees, but also that the errors can be largely eliminated by appropriate data analysis [22]. It is, however, still interesting to note that no interference from soot was observed in rotational CARS spectra recorded in a sooty flame in connection with the work in Ref. [16].

3. Rotational CARS at Flame Temperatures, Temperature Information from Rotational Hotbands

155

160 Roman shift / cm-1

165

Fig. 3. a Rotational CARS spectrum of CO recorded in a CO flame, b Detail of a illustrating the first and second rotational hotbands. (e) Theoretical spectra for 1400, 1900, and 2400 K illustrating the temperature dependence of the rotational hotbands

appears to be the case. F o r example, for a 2000 K spectrum an error in ZNR as large as a factor of 5 gives approximately only a one percent error in the temperature determined from a rotational CARS spectrum after subtracting the constant background. The temperature inferred from a vibrational spectra under the

Rotational CARS thermometry is less sensitive at flame temperatures than vibrational CARS (although the situation is the opposite at lower temperatures, < 1000 K). This difference in temperature sensitivity arises because rotational CARS probes the population difference between rotational energy levels whose energy separation is small compared to the average thermal energy (~-kT) at high temperatures, while the energy difference between vibrational levels, whose population difference is probed by vibrational CARS, is at least comparable to the thermal energy at flame temperatures. However, as illustrated by the rotational CARS CO spectrum in Fig. 3a, recorded in a CO flame, one can to some extent observe the ratio between the population in different vibrational states also in a rotational spectrum. The large peaks in the spectrum are rotational Raman transitions in the vibrational ground state and the accompanying smaller peaks to the fight are the same rotational Raman transition in the first vibrationally excited state. In the partial enlargement of the spectrum in Fig. 3b the second

29

Is Rotational CARS an Alternative to Vibrational CARS for Thermometry?

rotational hotband is also clearly discernible. Thus we can also determine the temperature from the intensity ratio between rotational transitions within different vibrational states. The temperature sensitivity at flame temperatures for this approach has not yet been compared with vibrational CARS. However, a direct comparison of the increase in the ratio between the peak signals in the hotband and fundamental band when increasing the temperature from 1400K to 2000 K using theoretical spectra indicate that vibrational spectra still are more temperature sensitive. In Fig. 3c theoretical CO spectra for two ground-state rotational transitions and their corresponding hotband transitions are plotted for the temperatures 1400, 1900, and 2400 K. The first to use the rotational hotbands to determine flame temperatures were Teets and Bechtel [23] although in part they obtained too high temperatures because they neglected the vibrational dependence of the polarizability change [24]. A code for generating theoretical spectra for rotational CARS is described in detail in Refs. [16, 25].

4. Discussion

A major drawback of rotational CARS is connected to its relative novelty. For example no calibration measurement for a stabilized oven has (to our knowledge) yet been performed at flame temperatures. (However, calibration up to 2000 K is presently performed at our laboratory.) In addition, the rotational Raman linewidths are (particularly at flame temperatures) not sufficiently well known for accurate temperature determination. Even if the temperature sensitivity is lower for rotational CARS than for vibrational CARS, there may still be particular areas where rotational CARS can be of interest. One such area is at higher pressures where the line overlap in vibrational CARS is severe. Although the knowledge of vibrational CARS profiles at high pressure is extensive (see e.g. 1-26] and references therein) rotational CARS may be simpler because the lines are still largely isolated. As an example, room temperature rotational CARS spectra at 5, 20, and 38 arm are shown in Fig. 4 together with theoretical fits. The linewidths were obtained from Magens [27] whose ECS calculations [-283 are based on recent experimental linewidths [29, 30]. A property of rotational CARS which can be both an advantage and a disadvantage is that the rotational Raman transitions of (essentially) all species lie in the same frequency interval. This may cause spectral interference which potentially could severely complicate the extraction of quantitative information from the signal, but it can also be very favourable for

IL

50

100 Rammn shiff I cm-~

150

Fig. 4. Experimental high-pressure rotational CARS spectra of nitrogen with theoretical fits recorded at (a) 5 atm, (b) 20 atm, (e) 38 atm

multiple species detection. Interference from the abundant flame constituents CO2 and H 2 0 generally will not be severe. The comparatively heavy molecule CO2 has small rotational Raman shifts and its spectrum resides predominantly at the low frequency side of the CARS signal [16] and for H 2 0 there is generally no discernible rotational CARS signal [31] presumably due to a low Raman cross section for rotational transitions. In conclusion, we note that rotational CARS has several properties which potentially make it an attractive alternative to vibrational CARS thermometry. This motivates further studies of the rotational CARS technique.

Acknowledgements. This work was supported by the Swedish National Board for Technical Developments and the Swedish Energy Administration.

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