Abstract

A dual-pump dual-broadband coherent anti-Stokes Raman scattering (CARS) setup for simultaneous pure rotational and vibrational CARS is further developed by reducing the experimental efforts due to the use of only one detection system. With this system dual-pump CARS for probing ro-vibrational transitions of N2/CO/H2 and dual-broadband CARS for pure rotational transitions of N2/O2/CO/CO2 are applicable simultaneously. In this work the improvements to the setup and the data evaluation are described. First simultaneous temperature and concentration results from cell measurements and from a partially premixed propane flame are presented. Interference effects due to smeared vibrational CARS are investigated. It is shown that with similar experimental effort to a conventional dual-pump CARS setup considerably more information can be gained.

© 2008 Optical Society of America

1. Introduction

The investigation of technical combustion systems is in many cases a challenging task for laser-based measurement techniques. Problems arise due to difficult optical accessibility and interference from flame luminosity, fluorescing fuels, and intermediates or soot.

Coherent anti-Stokes Raman scattering (CARS) has been extensively used to measure temperature in such harsh combustion systems. However, often not only temperature but the additional information of species concentrations is helpful to gain a deeper insight into the underlying processes. But there is still a lack of multispecies concentration determination by using CARS even though there exist several approaches to enhance the number of simultaneously detectable species. For instance, in vibrational CARS (VCARS) more species can be detected if their Raman shifts are relatively close to each other. This has been exploited in a number of cases, e.g., for N2/CO [1, 2], CO2/O2 [3], and O2/C2H4 [4]. In extension it can be combined with hydrogen S-branch rotational lines; see, e.g., Refs. [1, 5, 6]. In general, three major developments for multispecies detection can be found in the literature:

  1. Multicolor CARS-techniques,
  2. pure rotational CARS,
  3. combined techniques.
The first group covers CARS techniques using at least three lasers with different wavelength. A general overview of this group is given in the textbook of Eckbreth [7]. The multicolor technique that prevailed is dual-pump CARS (DP-CARS) developed by Lucht [8]. There, the use of two pump beams at different wavelength permits the generation of CARS signals from species with Raman transitions in two different excitation regions. Since all signals are generated by a combination of the three lasers, fluctuations of the laser power and changes in the beam overlap do not affect the accuracy. Furthermore, with increasing experimental effort derivatives as, e.g., triple-pump CARS have been demonstrated in a feasibility study [9].

A second option is the use of pure rotational lines (RCARS) where a lot of different molecules are accessible due to similar Raman shifts. However, because of the partly overlapping lines from different species, it is indispensable to model the CARS spectra of these molecules. So far, modeling of gas phase molecules of N2 and O2 [10], CO [11], C2H2 [12, 13], and CO2 [14, 15] has been shown. The most common technique is the dual-broadband (DBB-CARS) approach [16, 17]. This technique utilizes two broadband dye laser beams from the same laser source. As a result, each rotational Raman transition is driven by multiple pairs of dye laser photons, reducing the influence of dye laser mode fluctuation and generally achieving a better temperature accuracy and precision [18, 19] compared to other RCARS approaches.

Thus, to achieve multispecies concentration measurements a straightforward approach is to implement a combined vibrational and rotational CARS technique, which was shown in a number of cases; see, e.g., [20, 21, 22, 23, 24]. The combination of the obviously preferential techniques, DP-VCARS and the DBB-RCARS was first shown in a proof-of-concept by Roy [9] and later termed dual-pump dual-broadband CARS (DP-DBB-CARS) [23, 25]. In the last reference this was shown for the simultaneous detection of the molecule combinations N2CO2 (VCARS) and N2O2 (RCARS). This setup consisted of two narrowband lasers, one broadband dye laser for the signal generation, and two spectrometer and CCD cameras for the signal detection. However, this is rather complex for technical applications.

In this work we present an improved DP-DBB-CARS setup by using only one detection system. This has significantly reduced the experimental complexity compared to the one previously mentioned. Cell measurements of the obtainable molecular species are shown, disturbances inherent to the technique are discussed in detail, and solutions are pointed out. It is shown that this setup can be used to detect N2, O2, H2, CO, and CO2 simultaneously. Finally, a first test in a partially premixed flame at atmospheric pressure is performed and temperatures and concentrations are evaluated.

2. Experimental

CARS is a third-order nonlinear optical process, wherein a nascent signal at a new frequency is generated by the interaction of three intense laser beams with a medium. The signal is resonantly enhanced if the frequency difference between two laser beams, termed pump and Stokes beam, corresponds to an allowed Raman transition, either ro-vibrational (Q-branch, Δν=1, ΔJ=0) or pure rotational (O- or S-branch, Δν=0, ΔJ=±2). In a standard vibrational CARS setup one narrowband laser (ω1) is used to generate two frequency degenerate pump beams and one broadband laser (ω2) is used as a Stokes beam to cover several transitions in one molecule or even transitions of several molecules with one single laser shot. This is termed multiplex CARS and offers single-pulse temperature/concentration measurements. The energy-level diagram shown in Fig. 1a corresponds to degenerate multiplex vibrational CARS of N2 and CO, where the fact that both molecules have closely spaced Raman resonances is used.

To increase the number of detectable species, a third narrowband beam (ω3) is added instead, using the first narrowband laser twice. For the generation of signals from two different molecules the frequency difference of each pump laser (ω1,ω3) and the broadband dye laser (ω2) has to coincide with a Raman transition. This is shown schematically in the energy diagram in Fig. 1b as the so-called dual-pump approach (DP-CARS) for H2 with a Raman shift of 4150cm1 and N2 with a Raman shift of 2330cm1. Note that also the freqency of ω2 had to be changed compared to 1a. For a more detailed description of this combination see Ref. [2].

Pure rotational transitions can be accessed by using two dye laser beams from the same broadband laser source as pump and Stokes beams, which is shown in Fig. 1c (DBB-CARS). The excitation profile is smeared out, and thus Stokes and anti-Stokes (CSRS and CARS) transitions are excited simultaneously [16, 17]. Commonly, only the anti-Stokes part is detected, because it is free from redshifted fluorescence. However, stray light from the narrowband pump laser can be problematic in technical systems. Moreover, a multiplicity of molecules have similar Raman resonances, which enables multispecies concentration measurements only if the respective signals can be modeled.

Consequently, to set up a DP-DBB-CARS system, at least two narrowband and one broadband laser are needed. In that case, degenerate CARS processes where the second pump laser beam is generated by the broadband dye laser are additionally executed. This process is termed smeared vibrational CARS (S-VCARS) and leads to a broadband ro-vibrational signature [Fig. 1c], which adds to the pure rotational signals. This has been exploited in the past for species measurements [21, 26] but may also be a drawback if the pure rotational signals need to be extracted [21, 26].

If a folded BOXCARS phase-matching geometry [27, 28] is employed, then CARS signals generated according to Figs. 1b, 1c, 1d emerge from the probe volume at nearly the same angle locally separated from the laser beams. This situation is demonstrated in Fig. 2 by a scheme of the folded BOXCARS arrangement. Hence, with nearly collinear travelling signals, detection with only one spectrometer and one CCD camera system is possible.

The DP-DBB-CARS system developed in this work is based on a DP-CARS setup that has been used in a previous study [2]. It consists of a frequency-doubled Nd:YAG laser (ω1, 532nm, 0.003cm1), a narrowband dye laser with intracavity etalon (ω3, 593.6nm, 0.03cm1), and a broadband dye laser (ω2, 680nm, 250cm1). One change to the previous setup was the splitting ratio of the pulse energy of the Nd:YAG laser to increase the output of the broadband dye laser, which now serves 50mJ/pulse. This pulse is split into two pulses (6040), where the weaker pulse is used for the VCARS process. This is done to adjust the dynamic range of the signals because a lower signal of RCARS compared to VCARS is expected at high temperatures. The phase- matching scheme was changed from a planar to a folded BOXCARS arrangement. This is necessary to generate both signals, RCARS and VCARS, at nearly the same position, as shown in Fig. 2. The top red and the green beam are used in both CARS processes. The remaining red beam is employed in the DBB-RCARS process, and the orange beam is used in the DP-VCARS process. Thus, with the latter two beams signal levels of both signals can be optimized independently. With the DP-VCARS part of this setup VCARS signals of N2, CO, and H2 are accessible and with the DBB-RCARS part rotational lines of N2, O2, CO, and CO2 can be detected. The complete experimental setup is shown in Fig. 3.

Additionally, a beam monitoring system similar to the one published in Ref. [29] was applied. For this purpose, a glass plate is placed after the focusing lens (f=450mm). The reflected parts of the laser beams are attenuated using neutral density filters. A standard consumer webcam with dismounted lens was mounted on a rail to scan along the focal volume. This system was used to fine-adjust the telescopes in the beams, to improve the beam overlap, and thus to maximize the signal level and to investigate coalignment of both probe volumes. During the course of the CARS measurements and for further optimizing CARS signal levels, the glass plate was taken out of the beam path.

Before the recollimating lens, a beam dump was placed in the path of the Nd:YAG beam to minimize scattered stray light. The remaining laser beams are also guided into a beam trap. The signals are locally separated from the laser beams, and therefore they can be easily guided to the spectrometer by two silver mirrors without the use of dichroic mirrors. Several apertures are placed in the signal path to minimize stray light. Finally, both signals are focused to the spectrometer (triaxial imaging, f=550mm, 2400grooves/mm) by the use of a spherical and cylindrical lens. This was done to disperse the signals along the height of the CCD chip (1600×1200pixels) to attain maximum dynamic range. A photograph of the spectrometer with the paths of the respective signals is shown in Fig. 4. An additional concave spherical mirror with focal length of f=500mm was placed inside the spectrometer to independently focus the RCARS signal onto the same CCD chip. With this modification only one detection system for both the DP-VCARS and the DBB-RCARS signals was necessary. A knife edge is placed on the camera window to inhibit stray light at low Raman shifts from saturating the chip.

By reducing the region of interest in the height of the chip to the part where the signals were placed, readout time could be reduced to be able to operate at the repetition rate of the Nd:YAG laser. A binning of two was applied in horizontal direction to minimize readout noise in the images. In the flame, maximum signal-to-noise ratio was above 10 for RCARS and above 30 for VCARS. A sample image from the CCD camera with spectra from a partially premixed flame is shown in Fig. 5a. The upper part of the images displays the DP-VCARS spectrum with lines of nitrogen and hydrogen. The lower part displays the DBB-RCARS spectrum. For evaluation the spectra are extracted from the respective signals [boxes in Fig. 5a]. These spectra are shown with their theoretical fits in Fig. 5b. The dispersion in these spectra is 0.38cm1/pixel (VCARS) and 0.28cm1/pixel (RCARS) with a resolution of 0.75cm1. The results of the single shot evaluations for RCARS are a mean value of 778K with O2/N2 ratio of 0,185mol/mol, and relative standard deviations of 6.8% and 8.3%. For VCARS the values are 819K with a H2/N2 ratio of 0.044mol/mol and relative standard deviations of 11.8% and 17.7%. In general, the values of standard deviations are rather high, which might be attributed to unstability in the single longitudinal mode operation of the Nd:YAG laser or the small cavity length in the broadband dye laser (100mm). A comparison with a new laser will in the future help to resolve this question.

In order to investigate the performance of the technique and to investigate the influence of S-VCARS onto rotational CARS signals measurements were taken in a gas cell and a Bunsen-type burner. The gas cell [30] and burner [2] were already used and described in detail in earlier works.

3. Results and Discussion

3A. Cell Measurements

For characterization of the technique measurements were taken in a cell at ambient pressure and temperature using mixtures of different gases. In order to demonstrate the potential of this DP-DBB-CARS technique for multispecies detection, first a mixture of Biogon (N2CO2=8020) and pure gases of O2, CO, and H2 was investigated. The mixture was generated by evacuating the cell and then adding up partial pressures. Spectra from the two signals are shown in Fig. 6. The RCARS spectrum [Fig. 6a] consists of transitions of all molecules but H2, because the Raman shift of the first H2 line (S(0)) is located at 354cm1. In contrast, CO2 transitions are closely spaced and located at low Raman shifts up to 60cm1. The stronger lines above 65cm1 originate from O2 and N2 with a concentration ratio that was adjusted to the ratio of air (0.25). CO is barely visible in the DBB-RCARS spectrum at a concentration of about 10%. In contrast, the DP-VCARS signature of CO is easily identified. Also H2 is visible in the DP-VCARS spectrum even with a concentration below 0.5%. Furthermore, it has to be noted that for the DP-CARS spectrum the signal frequency is plotted because two Raman shift scales would be needed, one for N2 and CO (2100cm12350cm1) and one for H2 (4060cm14310cm1).

A common problem for such combined CARS techniques is that the pump beams in Fig. 1c can be exchanged, which leads to a S-VCARS signal [see Fig. 1d] as a background in the RCARS spectrum. The signal occurs due to scattering of a broadband pump beam by the H2 polarization driven by Nd:YAG pump and broadband Stokes beam. To investigate the effect of the additional S-VCARS signal on the evaluation of the DBB-RCARS spectra different mixtures of hydrogen in nitrogen (0%, 10%, 16%, and 26%) were investigated. A typical approach to correct this disturbance is to model the S-VCARS signal as a Gaussian function with a certain width and to fit the amplitude to the experimental spectrum and subtract it [23]. This approach is possible for S-VCARS signals, e.g., from N2 or CO with closely spaced rotational lines in the vibrational Q-branch. Then the spectral shape of the S-VCARS signal is mainly dominated by the dye laser profile. For the H2 Q-branch lines the situation is different as can be seen in Fig. 5b. Due to the convolution of the broadband laser profile with this lines the S-VCARS-signal will have a certain structure that cannot be approximated with a Gaussian function. However, one advantage that lies within the DP-DBB CARS setup presented in this work is that it is possible to record a “pure” S-VCARS spectrum if only hydrogen is present in the measurement volume. This is possible because hydrogen does not show rotational lines in the observed spectral RCARS-range. Consequently, this spectrum can be scaled and subtracted to realize a flat background (method 1). Figure 7 shows a RCARS spectrum from the mixture with 16% H2 and the scaled “pure” S-VCARS spectrum. At the range of 40cm1 the aforementioned structure resulting from the convolution of the dye laser profile with the line spectrum of hydrogen is visible. Furthermore, the shape of this S-VCARS background will change with temperature, which involves the necessity to record a set of pure S-VCARS spectra at varying temperatrures. However, at low temperatures the structure is not very pronounced.

A second option is to use a theoretical spectrum to find the unknown background function (method 2). This however involves ab initio knowledge of temperature and concentrations, and therefore an iterative process would be needed for flame evaluations. Since this approach would be very time consuming it is in most cases not appropriate. However, to investigate the validity of this method and also for comparison it was used in the current investigations.

Figure 8 shows the applied scaling factor for the background function of each method as a variation of hydrogen concentration. Both scaling factors were normalized to the 26% hydrogen value. Both methods show the same trend with increasing scaling factor for increasing hydrogen concentrations. At approximately 9% hydrogen concentration the scaling factor tends to zero. Consequently, this value is the lower limit, where the S-VCARS signal has to be taken into account. The results of temperature evaluations without correction and with correction using methods 1 and 2 are summarized in Table 1.

Without correction very high temperatures are fitted. If a correction is applied, the temperature is recovered with an inaccuracy of less than 4%. This value seems rather high but it may even increase if single-pulse evaluations are conducted or the signal-to-noise ratio decreases due to measurements in a flame. Hence, it is important to know at which level the effect needs to be taken into account in flame measurements. This will be answered in the next section.

3B. Burner Measurements

Since all measurements so far were taken at ambient pressure and temperature conditions, experiments were also conducted in a partially premixed flame, where the concentration of hydrogen generated as an intermediate species is at the level of about 10%. Partially premixed flames are numerous in practice, from the very simple domestic gas burners to highly complex phenomena in automotive direct-injection engines. In such flames, intermediate species like CO and H2 play an important role in the ongoing chemistry. The local concentration of these intermediate species is strongly dependent on the O2 concentration. Therefore, additionally the knowledge of the local O2 concentration is important for the understanding of such processes.

Measurements were performed in a partially premixed propane flame established on a Bunsen-type burner at an equivalence ratio of Φ=1.9. Soot is not a problem in these conditions using propane as a fuel. However, it should be mentioned that in sooting flames problems arise due to interference effects from the C2 radical, which is quantified by Malarski [31] and was recently investigated in heavily sooting flames using DP-CARS [32] with a shifted signal wavelength. Since in our setup the signal wavelength is in the problematic region of 473nm, the option is to use the RCARS spectra under heavy sooting conditions [33, 34].

All spectra were recorded at a constant height of 12mm above the burner exit and a varying radial position 250 single-pulse spectra were recorded at each measurement point. In contrast to the cell measurements, now single-pulse spectra are evaluated. For each position in the flame a library of varying temperature and H2N2 concentration (VCARS) or O2N2 concentrations (RCARS) was generated. Due to a low concentration and therefore low spectral signature, the CO concentration was fitted to an accumulated spectrum and set constant in the VCARS library. This was also done for the nonresonant background. No signatures from CO and CO2 were visible in the RCARS spectra for the investigated locations in the flame. The result of the evaluation is shown in Fig. 9. Also standard deviations were calculated, and representative values are shown by error bars for both low and high temperatures and concentrations. Measurements were only performed for one half of the burner, and the position zero indicates the axis of the burner. Solid symbols represent temperature results, and nonsolid symbols represent concentration results. Triangles and rectangles are used for the information inferred from DP-CARS, i.e., temperature and relative hydrogen and carbon monoxide concentrations, and circles are used for results from DBB-CARS, i.e., temperature and relative oxygen concentration. In the evaluations of the DP-CARS spectra, the temperature was fitted by using only the nitrogen part of the spectrum due to the uncertainties in the hydrogen linewidth modeling [2].

These measurements can be used to compare the temperature evaluated from the rotational and the vibrational spectrum and therefore estimate the S-VCARS influence at positions with increased hydrogen concentration. In comparison the trends of both evaluated temperatures are similar with differences at high temperatures. Since these differences can also be observed at positions where no hydrogen is present, it can be concluded that this is mainly due to noise in the RCARS spectra. In general, the influence of S-VCARS at higher temperatures is comparable to the effect at ambient temperature. The temperature evaluated from VCARS shows the double plateau that is characteristic for a partially premixed flame. Also, as expected for this type of flame, H2 and CO as intermediate species are generated in the inner flame zone, with both having their maximum value at the same position. From the inner to the outer flame zone the CO and H2 concentration decreases until it is fully consumed to the final products CO2 and H2O. The relative O2 concentration is at a constant level at the unburnt zone and decreases towards the inner flame front. In this fuel rich flame (Φ=1.9) the N2 concentration in the inner flame zone is much lower than that in the outer diffusion zone. This limits the detection of O2 relative concentration close to the inner flame front. Therefore, O2 concentration values at these positions (4mm6mm) are not correctly represented, whereas a more accurate O2 profile is determined in the outer diffusion zone. In general, this investigation in a partially premixed flame shows the applicability of DP-DBB-CARS for temperature and multispecies concentrations.

4. Conclusions

Simultaneous measurements of temperature and multiple-species concentrations using the dual-pump dual-broadband CARS technique were presented in this work. The experimental complexity was reduced significantly by achieving detection of both signals, pure rotational and vibrational CARS, with one detection system. Cell measurements of the obtainable molecular species are shown, and disturbances inherent to the technique due to an interfering S-VCARS signal are discussed in detail. Solutions were pointed out to correct for this effect and tested for cell spectra. A first test of this DP-DBB-CARS system for temperature and multispecies measurements was performed in a partially premixed propane flame. In general it was found that the S-VCARS-effect is negligible not only at ambient temperature but also in the flame if the hydrogen concentration is below 10%. Above this level the S-VCARS signal should be taken into account. The relative concentrations of O2, H2, and CO were determined in a partially premixed flame. Because of the noises in the RCARS spectra, above 1200K the VCARS spectra were more suitable to fit the flame temperature. Hence, for future investigations a better signal-to-noise ratio is desirable for RCARS. However, the number and type of detectable species and the simultaneous temperature determination make the technique interesting for the investigation of a reforming process, where lower temperatures are also expected.

The authors acknowledge financial support by the German National Science Foundation (DFG) and funding of the Erlangen Graduate School in Advanced Optical Technologies (SAOT) by the German National Science Foundation (DFG) in the framework of the excellence initiative.

Tables Icon

Table 1. Evaluated CARS Temperatures Without Correction (Two) and With Correction Using Method 1 (TM1) and Method 2 (TM2)

 

Fig. 1 Energy-level diagrams of possible CARS processes: (a) degenerate vibrational CARS of N2 and CO, (b) dual-pump-CARS of N2 and H2, (c) dual-broadband pure rotational CARS, (d) smeared vibrational CARS.

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Fig. 2 Schematic representation of folded BOXCARS phase matching. The four beams are entering from the left side and focused to the interaction volume. Two CARS signals (light green and blue) are generated and emitted at nearly the same angle locally separated from the four laser beams.

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Fig. 3 Schematic of the experimental DP-DBB- setup with one detection system: T, telescope; GP, Glan-polarizing prisms; BS, beam splitter; DC, dichroic mirror; BVS, beam view system; BD, beam dump; SM, silver mirror; L, lens.

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Fig. 4 Schematic signal traces in the spectrometer: dashed, DP-CARS; dotted, DBB-CARS.

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Fig. 5 (a) Averaged CCD image from the spectrometer with the region of interest for vibrational (top) and rotational CARS signals (bottom). (b) CARS spectra extracted from the image with theoretical fits and difference spectrum. The difference spectrum is set off by 0.2 for better visibility.

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Fig. 6 (a) Pure rotational CARS spectrum from a gas mixture with signatures from N2, O2, CO2 and CO. (b) Dual-pump CARS spectrum of N2, H2 and CO.

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Fig. 7 Spectrum from a mixture of 16% hydrogen in nitrogen showing RCARS and S-VCARS spectral signatures. Additionally shown is the scaled “pure” S-VCARS spectrum (black line).

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Fig. 8 Effect of S-VCARS onto the rotational CARS spectrum presented in the form of the normalized scaling factor that is applied to correct the RCARS spectrum.

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Fig. 9 DP-DBB results from a partially premixed propane flame. The dots represent information from DBB-RCARS, and the triangles are information inferred from DP-VCARS.

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29. D. Bivolaru and G. C. Herring, “Focal-plane imaging of crossed beams in nonlinear optics experiments,” Rev. Sci. Instrum. 78, 056102 (2007). [CrossRef]   [PubMed]  

30. M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous temperature and relative O2-N2 concentration measurements by single-shot pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5MPa,” Appl. Opt. 39, 6918–6925 (2000). [CrossRef]  

31. A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102–108 (2005). [CrossRef]  

32. S. P. Kearney and M. N. Jackson, “Dual-pump coherent anti-Stokes Raman scattering thermometry in heavily sooting flames,” AIAA J. 45, 2947–2956 (2007). [CrossRef]  

33. P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129–140 (1992). [CrossRef]  

34. T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150–1156 (2004). [CrossRef]  

References

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  1. K. Aron, L. E. Harris, and J. Fendell, “N2 and CO vibrational CARS and H2 rotational CARS spectroscopy of CH4/N2O flames,” Appl. Opt. 22, 3604-3611 (1983).
    [Crossref] [PubMed]
  2. M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
    [Crossref]
  3. K. W. Boyack and P. O. Hedman, “Dual-Stokes CARS system for simultaneous measurement of temperature and multiple species in turbulent flames,” in Proceedings of the 23rd Symposium (International) on Combustion (Combustion Institute, 1990), pp. 1893-1899.
  4. F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
    [Crossref]
  5. S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
    [Crossref]
  6. J. P. Singh and F. Y. Yueh, “Multiplex CARS for simultaneous measurement of temperature and CO2 and H2 concentrations in a combustion environment,” Appl. Opt. 30, 1967-1975(1991).
    [Crossref] [PubMed]
  7. A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Combustion Science & Technology Book Series (Gordon & Breach, 1996).
  8. R. P. Lucht, “Three-laser coherent anti-Stokes Raman scattering measurements of two species,” Opt. Lett. 12, 78-80(1987).
    [Crossref] [PubMed]
  9. S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
    [Crossref]
  10. L. Martinsson, P.-E. Bengtsson, and M. Aldén, “Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent Anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29-37 (1996).
    [Crossref]
  11. M. Afzelius, C. Brackmann, F. Vestin, and P.-E. Bengtsson, “Pure rotational coherent anti-Stokes Raman spectroscopy in mixtures of CO and N2,” Appl. Opt. 43, 6664-6672 (2004).
    [Crossref]
  12. J. Bood, P.-E. Bengtsson, and M. Aldén, “Temperature and concentration measurements in acetylene-nitrogen mixtures in the range 300-600 K using dual-broadband rotational CARS,” Appl. Phys. B 70, 607-620 (2000).
    [Crossref]
  13. J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
    [Crossref]
  14. M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous and time-resolved temperature and relative CO2-N2 and O2-CO2-N2 concentration measurements with pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 44, 5582-5593 (2005).
    [Crossref] [PubMed]
  15. M. Schenk, T. Seeger, and A. Leipertz, “Time-resolved CO2 thermometry for pressures as great as 5 MPa by use of pure rotational coherent anti-Stokes Raman scattering,” Appl. Opt. 44, 6526-6536 (2005).
    [Crossref] [PubMed]
  16. M. Aldén, P.-E. Bengtsson, and H. Edner, “Rotational CARS generation through a multiple four-color interaction,” Appl. Opt. 25, 4493-4499 (1986).
    [Crossref] [PubMed]
  17. A. C. Eckbreth and T. J. Anderson, “Simultaneous rotational coherent anti-Stokes Raman spectroscopy and coherent Stokes Raman spectroscopy with arbitrary pump-Stokes spectral separation,” Opt. Lett. 11, 496-498 (1986).
    [Crossref] [PubMed]
  18. S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
    [Crossref]
  19. T. Seeger and A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665-2671 (1996).
    [Crossref] [PubMed]
  20. P.-E. Bengtsson, L. Martinsson, and M. Aldén, “Combined vibrational and rotational CARS for simultaneous measurements of temperature and concentrations of fuel, oxygen, and nitrogen,” Appl. Spectrosc. 48, 188-192 (1994).
  21. T. Seeger, J. Jonuscheit, M. Schenk, and A. Leipertz, “Simultaneous temperature and relative oxygen and methane concentration measurements in a partially premixed sooting flame using a novel CARS-technique,” J. Mol. Struct. 661-662, 515-524 (2003).
    [Crossref]
  22. R. P. Lucht, R. E. Palmer, and M. A. Maris, “Simultaneous acquisition of pure rotational and vibrational nitrogen spectra using three-laser coherent anti-Stokes Raman spectroscopy,” Opt. Lett. 12, 386-388 (1987).
    [Crossref] [PubMed]
  23. S. Roy, T. R. Meyer, R. P. Lucht, M. Afzelius, P.-E. Bengtsson, and J. R. Gord, “Dual-pump dual-broadband coherent anti-Stokes Raman scattering in reacting flows,” Opt. Lett. 29, 1843-1845 (2004).
    [Crossref] [PubMed]
  24. M. C. Weikl, F. Beyrau, J. Kiefer, T. Seeger, and A. Leipertz, “Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements,” Opt. Lett. 31, 1908-1910(2006).
    [Crossref] [PubMed]
  25. T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
    [Crossref]
  26. C. Brackmann, J. Bood, P.-E. Bengtsson, T. Seeger, M. Schenk, and A. Leipertz, “Simultaneous vibrational and pure rotational coherent Anti-Stokes Raman spectroscopy for temperature and multispecies concentration measurements demonstrated in sooting flames,” Appl. Opt. 41, 564-572(2002).
    [Crossref] [PubMed]
  27. Y. Prior, “Three-dimensional phase matching in four-wave mixing,” Appl. Opt. 19, 1741-1743 (1980).
    [Crossref]
  28. J. A. Shirley, R. J. Hall, and A. C. Eckbreth, “Folded BOXCARS for rotational Raman studies,” Opt. Lett. 5, 380-382 (1980).
    [Crossref] [PubMed]
  29. D. Bivolaru and G. C. Herring, “Focal-plane imaging of crossed beams in nonlinear optics experiments,” Rev. Sci. Instrum. 78, 056102 (2007).
    [Crossref] [PubMed]
  30. M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous temperature and relative O2-N2 concentration measurements by single-shot pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 39, 6918-6925 (2000).
    [Crossref]
  31. A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102-108 (2005).
    [Crossref]
  32. S. P. Kearney and M. N. Jackson, “Dual-pump coherent anti-Stokes Raman scattering thermometry in heavily sooting flames,” AIAA J. 45, 2947-2956 (2007).
    [Crossref]
  33. P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
    [Crossref]
  34. T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
    [Crossref]

2007 (4)

M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
[Crossref]

S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
[Crossref]

D. Bivolaru and G. C. Herring, “Focal-plane imaging of crossed beams in nonlinear optics experiments,” Rev. Sci. Instrum. 78, 056102 (2007).
[Crossref] [PubMed]

S. P. Kearney and M. N. Jackson, “Dual-pump coherent anti-Stokes Raman scattering thermometry in heavily sooting flames,” AIAA J. 45, 2947-2956 (2007).
[Crossref]

2006 (2)

M. C. Weikl, F. Beyrau, J. Kiefer, T. Seeger, and A. Leipertz, “Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements,” Opt. Lett. 31, 1908-1910(2006).
[Crossref] [PubMed]

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

2005 (4)

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous and time-resolved temperature and relative CO2-N2 and O2-CO2-N2 concentration measurements with pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 44, 5582-5593 (2005).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Time-resolved CO2 thermometry for pressures as great as 5 MPa by use of pure rotational coherent anti-Stokes Raman scattering,” Appl. Opt. 44, 6526-6536 (2005).
[Crossref] [PubMed]

T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
[Crossref]

A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102-108 (2005).
[Crossref]

2004 (3)

2003 (3)

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
[Crossref]

T. Seeger, J. Jonuscheit, M. Schenk, and A. Leipertz, “Simultaneous temperature and relative oxygen and methane concentration measurements in a partially premixed sooting flame using a novel CARS-technique,” J. Mol. Struct. 661-662, 515-524 (2003).
[Crossref]

2002 (1)

2000 (2)

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous temperature and relative O2-N2 concentration measurements by single-shot pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 39, 6918-6925 (2000).
[Crossref]

J. Bood, P.-E. Bengtsson, and M. Aldén, “Temperature and concentration measurements in acetylene-nitrogen mixtures in the range 300-600 K using dual-broadband rotational CARS,” Appl. Phys. B 70, 607-620 (2000).
[Crossref]

1996 (2)

L. Martinsson, P.-E. Bengtsson, and M. Aldén, “Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent Anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29-37 (1996).
[Crossref]

T. Seeger and A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665-2671 (1996).
[Crossref] [PubMed]

1994 (1)

P.-E. Bengtsson, L. Martinsson, and M. Aldén, “Combined vibrational and rotational CARS for simultaneous measurements of temperature and concentrations of fuel, oxygen, and nitrogen,” Appl. Spectrosc. 48, 188-192 (1994).

1992 (1)

P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
[Crossref]

1991 (1)

1990 (1)

S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
[Crossref]

1987 (2)

1986 (2)

1983 (1)

1980 (2)

Afzelius, M.

Aldén, M.

J. Bood, P.-E. Bengtsson, and M. Aldén, “Temperature and concentration measurements in acetylene-nitrogen mixtures in the range 300-600 K using dual-broadband rotational CARS,” Appl. Phys. B 70, 607-620 (2000).
[Crossref]

L. Martinsson, P.-E. Bengtsson, and M. Aldén, “Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent Anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29-37 (1996).
[Crossref]

P.-E. Bengtsson, L. Martinsson, and M. Aldén, “Combined vibrational and rotational CARS for simultaneous measurements of temperature and concentrations of fuel, oxygen, and nitrogen,” Appl. Spectrosc. 48, 188-192 (1994).

P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
[Crossref]

S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
[Crossref]

M. Aldén, P.-E. Bengtsson, and H. Edner, “Rotational CARS generation through a multiple four-color interaction,” Appl. Opt. 25, 4493-4499 (1986).
[Crossref] [PubMed]

Anderson, T. J.

Aron, K.

Bengtsson, P. E.

S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
[Crossref]

Bengtsson, P.-E.

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

M. Afzelius, C. Brackmann, F. Vestin, and P.-E. Bengtsson, “Pure rotational coherent anti-Stokes Raman spectroscopy in mixtures of CO and N2,” Appl. Opt. 43, 6664-6672 (2004).
[Crossref]

S. Roy, T. R. Meyer, R. P. Lucht, M. Afzelius, P.-E. Bengtsson, and J. R. Gord, “Dual-pump dual-broadband coherent anti-Stokes Raman scattering in reacting flows,” Opt. Lett. 29, 1843-1845 (2004).
[Crossref] [PubMed]

C. Brackmann, J. Bood, P.-E. Bengtsson, T. Seeger, M. Schenk, and A. Leipertz, “Simultaneous vibrational and pure rotational coherent Anti-Stokes Raman spectroscopy for temperature and multispecies concentration measurements demonstrated in sooting flames,” Appl. Opt. 41, 564-572(2002).
[Crossref] [PubMed]

J. Bood, P.-E. Bengtsson, and M. Aldén, “Temperature and concentration measurements in acetylene-nitrogen mixtures in the range 300-600 K using dual-broadband rotational CARS,” Appl. Phys. B 70, 607-620 (2000).
[Crossref]

L. Martinsson, P.-E. Bengtsson, and M. Aldén, “Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent Anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29-37 (1996).
[Crossref]

P.-E. Bengtsson, L. Martinsson, and M. Aldén, “Combined vibrational and rotational CARS for simultaneous measurements of temperature and concentrations of fuel, oxygen, and nitrogen,” Appl. Spectrosc. 48, 188-192 (1994).

P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
[Crossref]

M. Aldén, P.-E. Bengtsson, and H. Edner, “Rotational CARS generation through a multiple four-color interaction,” Appl. Opt. 25, 4493-4499 (1986).
[Crossref] [PubMed]

Beyrau, F.

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

M. C. Weikl, F. Beyrau, J. Kiefer, T. Seeger, and A. Leipertz, “Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements,” Opt. Lett. 31, 1908-1910(2006).
[Crossref] [PubMed]

A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102-108 (2005).
[Crossref]

T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
[Crossref]

F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
[Crossref]

Bivolaru, D.

D. Bivolaru and G. C. Herring, “Focal-plane imaging of crossed beams in nonlinear optics experiments,” Rev. Sci. Instrum. 78, 056102 (2007).
[Crossref] [PubMed]

Bonamy, J.

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

Bood, J.

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

C. Brackmann, J. Bood, P.-E. Bengtsson, T. Seeger, M. Schenk, and A. Leipertz, “Simultaneous vibrational and pure rotational coherent Anti-Stokes Raman spectroscopy for temperature and multispecies concentration measurements demonstrated in sooting flames,” Appl. Opt. 41, 564-572(2002).
[Crossref] [PubMed]

J. Bood, P.-E. Bengtsson, and M. Aldén, “Temperature and concentration measurements in acetylene-nitrogen mixtures in the range 300-600 K using dual-broadband rotational CARS,” Appl. Phys. B 70, 607-620 (2000).
[Crossref]

Boyack, K. W.

K. W. Boyack and P. O. Hedman, “Dual-Stokes CARS system for simultaneous measurement of temperature and multiple species in turbulent flames,” in Proceedings of the 23rd Symposium (International) on Combustion (Combustion Institute, 1990), pp. 1893-1899.

Brackmann, C.

Brown, M. S.

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

Buldyreva, J.

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

Cutler, A. D.

S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
[Crossref]

Danehy, P. M.

S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
[Crossref]

Dankers, S.

T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
[Crossref]

Eckbreth, A. C.

Edner, H.

Egermann, J.

T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
[Crossref]

Fendell, J.

Gord, J. R.

T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
[Crossref]

S. Roy, T. R. Meyer, R. P. Lucht, M. Afzelius, P.-E. Bengtsson, and J. R. Gord, “Dual-pump dual-broadband coherent anti-Stokes Raman scattering in reacting flows,” Opt. Lett. 29, 1843-1845 (2004).
[Crossref] [PubMed]

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

Hall, R. J.

Harris, L. E.

Hedman, P. O.

K. W. Boyack and P. O. Hedman, “Dual-Stokes CARS system for simultaneous measurement of temperature and multiple species in turbulent flames,” in Proceedings of the 23rd Symposium (International) on Combustion (Combustion Institute, 1990), pp. 1893-1899.

Herring, G. C.

D. Bivolaru and G. C. Herring, “Focal-plane imaging of crossed beams in nonlinear optics experiments,” Rev. Sci. Instrum. 78, 056102 (2007).
[Crossref] [PubMed]

Hierold, R.

M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
[Crossref]

Jackson, M. N.

S. P. Kearney and M. N. Jackson, “Dual-pump coherent anti-Stokes Raman scattering thermometry in heavily sooting flames,” AIAA J. 45, 2947-2956 (2007).
[Crossref]

Jonuscheit, J.

T. Seeger, J. Jonuscheit, M. Schenk, and A. Leipertz, “Simultaneous temperature and relative oxygen and methane concentration measurements in a partially premixed sooting flame using a novel CARS-technique,” J. Mol. Struct. 661-662, 515-524 (2003).
[Crossref]

Kearney, S. P.

S. P. Kearney and M. N. Jackson, “Dual-pump coherent anti-Stokes Raman scattering thermometry in heavily sooting flames,” AIAA J. 45, 2947-2956 (2007).
[Crossref]

Kiefer, J.

Kröll, S.

P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
[Crossref]

S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
[Crossref]

Leipertz, A.

M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
[Crossref]

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

M. C. Weikl, F. Beyrau, J. Kiefer, T. Seeger, and A. Leipertz, “Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements,” Opt. Lett. 31, 1908-1910(2006).
[Crossref] [PubMed]

A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102-108 (2005).
[Crossref]

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous and time-resolved temperature and relative CO2-N2 and O2-CO2-N2 concentration measurements with pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 44, 5582-5593 (2005).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Time-resolved CO2 thermometry for pressures as great as 5 MPa by use of pure rotational coherent anti-Stokes Raman scattering,” Appl. Opt. 44, 6526-6536 (2005).
[Crossref] [PubMed]

T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
[Crossref]

T. Seeger, J. Jonuscheit, M. Schenk, and A. Leipertz, “Simultaneous temperature and relative oxygen and methane concentration measurements in a partially premixed sooting flame using a novel CARS-technique,” J. Mol. Struct. 661-662, 515-524 (2003).
[Crossref]

F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
[Crossref]

C. Brackmann, J. Bood, P.-E. Bengtsson, T. Seeger, M. Schenk, and A. Leipertz, “Simultaneous vibrational and pure rotational coherent Anti-Stokes Raman spectroscopy for temperature and multispecies concentration measurements demonstrated in sooting flames,” Appl. Opt. 41, 564-572(2002).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous temperature and relative O2-N2 concentration measurements by single-shot pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 39, 6918-6925 (2000).
[Crossref]

T. Seeger and A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665-2671 (1996).
[Crossref] [PubMed]

Lucht, R. P.

T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
[Crossref]

S. Roy, T. R. Meyer, R. P. Lucht, M. Afzelius, P.-E. Bengtsson, and J. R. Gord, “Dual-pump dual-broadband coherent anti-Stokes Raman scattering in reacting flows,” Opt. Lett. 29, 1843-1845 (2004).
[Crossref] [PubMed]

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

R. P. Lucht, “Three-laser coherent anti-Stokes Raman scattering measurements of two species,” Opt. Lett. 12, 78-80(1987).
[Crossref] [PubMed]

R. P. Lucht, R. E. Palmer, and M. A. Maris, “Simultaneous acquisition of pure rotational and vibrational nitrogen spectra using three-laser coherent anti-Stokes Raman spectroscopy,” Opt. Lett. 12, 386-388 (1987).
[Crossref] [PubMed]

Malarski, A.

A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102-108 (2005).
[Crossref]

F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
[Crossref]

Maris, M. A.

Martinsson, L.

L. Martinsson, P.-E. Bengtsson, and M. Aldén, “Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent Anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29-37 (1996).
[Crossref]

P.-E. Bengtsson, L. Martinsson, and M. Aldén, “Combined vibrational and rotational CARS for simultaneous measurements of temperature and concentrations of fuel, oxygen, and nitrogen,” Appl. Spectrosc. 48, 188-192 (1994).

P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
[Crossref]

Meyer, T. R.

T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
[Crossref]

S. Roy, T. R. Meyer, R. P. Lucht, M. Afzelius, P.-E. Bengtsson, and J. R. Gord, “Dual-pump dual-broadband coherent anti-Stokes Raman scattering in reacting flows,” Opt. Lett. 29, 1843-1845 (2004).
[Crossref] [PubMed]

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

Nilsson, D.

S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
[Crossref]

O'Byrne, S.

S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
[Crossref]

Palmer, R. E.

Prior, Y.

Roy, S.

T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
[Crossref]

S. Roy, T. R. Meyer, R. P. Lucht, M. Afzelius, P.-E. Bengtsson, and J. R. Gord, “Dual-pump dual-broadband coherent anti-Stokes Raman scattering in reacting flows,” Opt. Lett. 29, 1843-1845 (2004).
[Crossref] [PubMed]

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

Schenk, M.

Seeger, T.

M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
[Crossref]

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

M. C. Weikl, F. Beyrau, J. Kiefer, T. Seeger, and A. Leipertz, “Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements,” Opt. Lett. 31, 1908-1910(2006).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous and time-resolved temperature and relative CO2-N2 and O2-CO2-N2 concentration measurements with pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 44, 5582-5593 (2005).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Time-resolved CO2 thermometry for pressures as great as 5 MPa by use of pure rotational coherent anti-Stokes Raman scattering,” Appl. Opt. 44, 6526-6536 (2005).
[Crossref] [PubMed]

T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
[Crossref]

T. Seeger, J. Jonuscheit, M. Schenk, and A. Leipertz, “Simultaneous temperature and relative oxygen and methane concentration measurements in a partially premixed sooting flame using a novel CARS-technique,” J. Mol. Struct. 661-662, 515-524 (2003).
[Crossref]

F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
[Crossref]

C. Brackmann, J. Bood, P.-E. Bengtsson, T. Seeger, M. Schenk, and A. Leipertz, “Simultaneous vibrational and pure rotational coherent Anti-Stokes Raman spectroscopy for temperature and multispecies concentration measurements demonstrated in sooting flames,” Appl. Opt. 41, 564-572(2002).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous temperature and relative O2-N2 concentration measurements by single-shot pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 39, 6918-6925 (2000).
[Crossref]

T. Seeger and A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665-2671 (1996).
[Crossref] [PubMed]

Shirley, J. A.

Singh, J. P.

Tedder, S. A.

S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
[Crossref]

Velur, V. N.

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

Vestin, F.

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

M. Afzelius, C. Brackmann, F. Vestin, and P.-E. Bengtsson, “Pure rotational coherent anti-Stokes Raman spectroscopy in mixtures of CO and N2,” Appl. Opt. 43, 6664-6672 (2004).
[Crossref]

Weikl, M. C.

M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
[Crossref]

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

M. C. Weikl, F. Beyrau, J. Kiefer, T. Seeger, and A. Leipertz, “Combined coherent anti-Stokes Raman spectroscopy and linear Raman spectroscopy for simultaneous temperature and multiple species measurements,” Opt. Lett. 31, 1908-1910(2006).
[Crossref] [PubMed]

Yueh, F. Y.

AIAA J. (2)

S. O'Byrne, P. M. Danehy, A. D. Cutler, and S. A. Tedder, “Dual-pump coherent anti-Stokes Raman scattering measurements in a supersonic combustor,” AIAA J. 45, 922-933 (2007).
[Crossref]

S. P. Kearney and M. N. Jackson, “Dual-pump coherent anti-Stokes Raman scattering thermometry in heavily sooting flames,” AIAA J. 45, 2947-2956 (2007).
[Crossref]

Appl. Opt. (10)

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous temperature and relative O2-N2 concentration measurements by single-shot pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 39, 6918-6925 (2000).
[Crossref]

M. Afzelius, C. Brackmann, F. Vestin, and P.-E. Bengtsson, “Pure rotational coherent anti-Stokes Raman spectroscopy in mixtures of CO and N2,” Appl. Opt. 43, 6664-6672 (2004).
[Crossref]

C. Brackmann, J. Bood, P.-E. Bengtsson, T. Seeger, M. Schenk, and A. Leipertz, “Simultaneous vibrational and pure rotational coherent Anti-Stokes Raman spectroscopy for temperature and multispecies concentration measurements demonstrated in sooting flames,” Appl. Opt. 41, 564-572(2002).
[Crossref] [PubMed]

Y. Prior, “Three-dimensional phase matching in four-wave mixing,” Appl. Opt. 19, 1741-1743 (1980).
[Crossref]

J. P. Singh and F. Y. Yueh, “Multiplex CARS for simultaneous measurement of temperature and CO2 and H2 concentrations in a combustion environment,” Appl. Opt. 30, 1967-1975(1991).
[Crossref] [PubMed]

K. Aron, L. E. Harris, and J. Fendell, “N2 and CO vibrational CARS and H2 rotational CARS spectroscopy of CH4/N2O flames,” Appl. Opt. 22, 3604-3611 (1983).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Simultaneous and time-resolved temperature and relative CO2-N2 and O2-CO2-N2 concentration measurements with pure rotational coherent anti-Stokes Raman scattering for pressures as great as 5 MPa,” Appl. Opt. 44, 5582-5593 (2005).
[Crossref] [PubMed]

M. Schenk, T. Seeger, and A. Leipertz, “Time-resolved CO2 thermometry for pressures as great as 5 MPa by use of pure rotational coherent anti-Stokes Raman scattering,” Appl. Opt. 44, 6526-6536 (2005).
[Crossref] [PubMed]

M. Aldén, P.-E. Bengtsson, and H. Edner, “Rotational CARS generation through a multiple four-color interaction,” Appl. Opt. 25, 4493-4499 (1986).
[Crossref] [PubMed]

T. Seeger and A. Leipertz, “Experimental comparison of single-shot broadband vibrational and dual-broadband pure rotational coherent anti-Stokes Raman scattering in hot air,” Appl. Opt. 35, 2665-2671 (1996).
[Crossref] [PubMed]

Appl. Phys. B (3)

L. Martinsson, P.-E. Bengtsson, and M. Aldén, “Oxygen concentration and temperature measurements in N2-O2 mixtures using rotational coherent Anti-Stokes Raman spectroscopy,” Appl. Phys. B 62, 29-37 (1996).
[Crossref]

J. Bood, P.-E. Bengtsson, and M. Aldén, “Temperature and concentration measurements in acetylene-nitrogen mixtures in the range 300-600 K using dual-broadband rotational CARS,” Appl. Phys. B 70, 607-620 (2000).
[Crossref]

S. Kröll, P. E. Bengtsson, M. Aldén, and D. Nilsson, “Is rotational CARS an alternative to vibrational CARS for thermometry?” Appl. Phys. B 51, 25-30 (1990).
[Crossref]

Appl. Spectrosc. (1)

P.-E. Bengtsson, L. Martinsson, and M. Aldén, “Combined vibrational and rotational CARS for simultaneous measurements of temperature and concentrations of fuel, oxygen, and nitrogen,” Appl. Spectrosc. 48, 188-192 (1994).

Chem. Eng. Technol. (1)

T. Seeger, J. Egermann, S. Dankers, F. Beyrau, and A. Leipertz, “Comprehensive characterization of a sooting laminar methane-diffusion flame using different laser techniques,” Chem. Eng. Technol. 27, 1150-1156 (2004).
[Crossref]

Combust. Flame (1)

T. R. Meyer, S. Roy, R. P. Lucht, and J. R. Gord, “Dual-pump dual-broadband CARS for exhaust-gas temperature and CO2-O2-N2 mole-fraction measurements in model gas-turbine combustors,” Combust. Flame 142, 52-61 (2005).
[Crossref]

Combust. Sci. Tech. (1)

P.-E. Bengtsson, L. Martinsson, M. Aldén, and S. Kröll, “Rotational CARS thermometry in sooting flames,” Combust. Sci. Tech. 81, 129-140 (1992).
[Crossref]

J. Mol. Struct. (1)

T. Seeger, J. Jonuscheit, M. Schenk, and A. Leipertz, “Simultaneous temperature and relative oxygen and methane concentration measurements in a partially premixed sooting flame using a novel CARS-technique,” J. Mol. Struct. 661-662, 515-524 (2003).
[Crossref]

J. Raman Spectrosc. (4)

F. Beyrau, T. Seeger, A. Malarski, and A. Leipertz, “Determination of temperature and fuel/air ratios in an ethene-air flame by dual-pump CARS,” J. Raman Spectrosc. 34, 946-951 (2003).
[Crossref]

M. C. Weikl, T. Seeger, R. Hierold, and A. Leipertz, “Dual-pump CARS measurements of N2, H2 and CO in a partially premixed flame,” J. Raman Spectrosc. 38, 983-988 (2007).
[Crossref]

A. Malarski, F. Beyrau, and A. Leipertz, “Interference effects of C2-radical in nitrogen vibrational CARS thermometry using a frequency-doubled Nd:YAG laser,” J. Raman Spectrosc. 36, 102-108 (2005).
[Crossref]

J. Buldyreva, J. Bonamy, M. C. Weikl, F. Beyrau, T. Seeger, A. Leipertz, F. Vestin, M. Afzelius, J. Bood, and P.-E. Bengtsson, “Linewidth modelling of C2H2-N2 mixtures tested by rotational CARS measurements,” J. Raman Spectrosc. 37, 647-654 (2006).
[Crossref]

Opt. Commun. (1)

S. Roy, T. R. Meyer, M. S. Brown, V. N. Velur, R. P. Lucht, and J. R. Gord, “Triple-pump coherent anti-Stokes Raman scattering (CARS): temperature and multiple-species concentration measurements in reacting flows,” Opt. Commun. 224, 131-137 (2003).
[Crossref]

Opt. Lett. (6)

Rev. Sci. Instrum. (1)

D. Bivolaru and G. C. Herring, “Focal-plane imaging of crossed beams in nonlinear optics experiments,” Rev. Sci. Instrum. 78, 056102 (2007).
[Crossref] [PubMed]

Other (2)

K. W. Boyack and P. O. Hedman, “Dual-Stokes CARS system for simultaneous measurement of temperature and multiple species in turbulent flames,” in Proceedings of the 23rd Symposium (International) on Combustion (Combustion Institute, 1990), pp. 1893-1899.

A. C. Eckbreth, Laser Diagnostics for Combustion Temperature and Species, Combustion Science & Technology Book Series (Gordon & Breach, 1996).

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Figures (9)

Fig. 1
Fig. 1 Energy-level diagrams of possible CARS processes: (a) degenerate vibrational CARS of N 2 and CO, (b) dual-pump-CARS of N 2 and H 2 , (c) dual-broadband pure rotational CARS, (d) smeared vibrational CARS.
Fig. 2
Fig. 2 Schematic representation of folded BOXCARS phase matching. The four beams are entering from the left side and focused to the interaction volume. Two CARS signals (light green and blue) are generated and emitted at nearly the same angle locally separated from the four laser beams.
Fig. 3
Fig. 3 Schematic of the experimental DP-DBB- setup with one detection system: T, telescope; GP, Glan-polarizing prisms; BS, beam splitter; DC, dichroic mirror; BVS, beam view system; BD, beam dump; SM, silver mirror; L, lens.
Fig. 4
Fig. 4 Schematic signal traces in the spectrometer: dashed, DP-CARS; dotted, DBB-CARS.
Fig. 5
Fig. 5 (a) Averaged CCD image from the spectrometer with the region of interest for vibrational (top) and rotational CARS signals (bottom). (b) CARS spectra extracted from the image with theoretical fits and difference spectrum. The difference spectrum is set off by 0.2 for better visibility.
Fig. 6
Fig. 6 (a) Pure rotational CARS spectrum from a gas mixture with signatures from N 2 , O 2 , CO 2 and CO. (b) Dual-pump CARS spectrum of N 2 , H 2 and CO.
Fig. 7
Fig. 7 Spectrum from a mixture of 16% hydrogen in nitrogen showing RCARS and S-VCARS spectral signatures. Additionally shown is the scaled “pure” S-VCARS spectrum (black line).
Fig. 8
Fig. 8 Effect of S-VCARS onto the rotational CARS spectrum presented in the form of the normalized scaling factor that is applied to correct the RCARS spectrum.
Fig. 9
Fig. 9 DP-DBB results from a partially premixed propane flame. The dots represent information from DBB-RCARS, and the triangles are information inferred from DP-VCARS.

Tables (1)

Tables Icon

Table 1 Evaluated CARS Temperatures Without Correction ( T wo ) and With Correction Using Method 1 ( T M 1 ) and Method 2 ( T M 2 )

Metrics