Development of optimized Raman Spectroscopy setup for species detection in flames

Transcription

1 Development of optimized Raman Spectroscopy setup for species detection in flames Henrik Johansson Thesis submitted for the degree of Bachelor of Science Project duration: 2 months Supervised by Christian Brackmann Department of Physics Division of Combustion Physics May 2016

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3 Abstract A multi-pass Raman spectroscopy setup, consisting of a measuring cell built as a cavity, using two concave circular mirrors, has been constructed and optimized. As the light reflects between the mirrors, the Stokes Raman signal is enhanced with every pass through the cavity. The setup is tested by measurements of species in ambient laboratory air, N 2 gas flowing through a transparent plastic tube, and a premixed propane/air flame. The signals are recorded using a grating spectrometer connected to a CCD camera. The spectra recorded with the multi-pass setup are then compared to spectra recorded using a single-pass setup to show the improvement in signal-to-noise ratio (SNR). The results show a significant improvement (by a factor of 5) for the multi-pass setup compared to measurements made using a single-pass setup. There are, however, several ways of improving the system further, to make it reach its full potential. i

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5 Acknowledgements Thank you, to my supervisor, Christian Brackmann, for giving me the chance to work with this project, and for the support he has given along the way. iii

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7 Acronyms and abbreviations CCD CW LASER Nd:YAG SNR Charge-Coupled Device Continuous Wave Light Amplification by Stimulated Emission of Radiation Neodymium-doped Yttrium Aluminum Garnet Signal-to-Noise Ratio v

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9 Contents Abstract i Acknowledgements iii Acronyms and abbreviations v 1 Introduction Theory Confinement condition for multi-pass mirror cavity The Raman scattering signal Experimental Laser safety Multi-pass system Detector Measurements Results & Discussion Characterization of multi-pass cavity Raman spectroscopy measurements Measurements in air Measurements in N 2 gas Measurements in C 3 H 8 /air flame Outlook References Appendix A Tables vii

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11 1 Introduction When light is scattered off a molecule, it can be scattered either elastically, known as Rayleigh scattering, or in-elastically, which is known as Raman scattering. Inelastic scattering means that an incoming photon with energy hν 0 - where h is Planck s constant and ν is the frequency - results in scattering of a photon of a different energy, hν 1. In a quantum-mechanical energy-level representation the photon excites the molecule into a virtual energy state, as can be seen in Figure 1. When the molecule then de-excites into a lower energy state other than the ground state, it will send out a photon with an energy hν 1. The scattered photons can have lower or higher energy than that of the incoming and are referred to as Stokes- and anti-stokes Raman scattering, respectively. In the anti-stokes Raman scattering process the photon thus gains energy from the molecule. However, most molecules are in their quantum mechanical ground state, without excess energy, resulting in few anti-stokes scattered photons. Instead Stokes Raman scattering, in which energy is transferred to the molecule, is the dominant component. This is known as the Stokes Raman signal, and most Raman-active species have a unique one, as the difference E = h(ν 0 ν 1 ) between two energy levels is also unique for a species [1]. Figure 1: Schematic energy-level representation of the Raman-scattering process. The incoming photon excites the molecule from the ground state into a virtual state. When the molecule de-excites into a lower state other than the ground state, it sends out a photon with a different frequency/wavelength. This is what is known as Stokes Raman scattering. For anti-stokes Raman scattering, the molecule is excited to a virtual state from a state other than the ground state, and de-excites to the ground state. The properties mentioned above make Raman spectroscopy a valuable method for species detection and concentration measurements in combustion processes, as it is a non-intrusive probing method where a laser of virtually any wavelength can be used to detect multiple species [2]. There are, in general, two forms of Raman spectroscopy commonly utilized: vibrational Raman spectroscopy and rotational Raman spectroscopy. This project utilizes vibrational Raman spectroscopy; focusing on vibrational transitions of molecules. While vibrational and rotational Raman are induced simultaneously, the rotational levels lie close to each other, which means that the peaks of the rotational 1

12 Raman scattered signals on the recorded spectra will be located close to the peak representing the laser light, thus making suppression of the laser light more challenging and the spectra harder to interpret. The main problem with Raman spectroscopy vibrational and rotational is that the obtained signal is very weak, and therefore often hard to separate from the surrounding background and noise. Trying to solve this by sending in high energy pulses with a low repetition frequency ( 10 Hz) laser, normally employed for combustion diagnostics, leads to electric breakdowns and ionization, resulting in an unreadable spectrum [3]. To avoid these breakdowns, it is advantageous to instead send in low energy pulses at high repetition frequency ( 1 khz). Once the problems of ionization and electric breakdowns are solved, another way to further improve the method is to utilize a multi-pass arrangement of the laser beam. The concept of a multi-pass arrangement is, as the name suggests, to let an incoming laser pulse pass multiple times through the sample volume, thus enhancing the signal-to-noise ratio (SNR) and detection sensitivity [4]. This is achieved by placing one mirror at each side of the volume, resulting in a setup similar to that of a laser cavity. Different types of mirrors can be applied, but this project will utilize two circular concave mirrors, as it provides good stability and is fairly easy to align [5]. The next aspect to take into consideration is whether the incoming laser pulse should enter the cavity from the side of one of the mirrors or through a small hole, placed near the edge, in the mirror itself. Previous experiments have concluded that the hole-option is superior, as it allows for more round-trips of the pulse inside the cavity [5, 6], before it exits through the hole in the first mirror. To maximize the possible number of passes is essential, as it decides the intensity of the output signal, which is what makes the signal easy to distinguish from background and noise. Afterwards, the spectrum provided by the Raman spectroscopy system can be compared to spectra obtained from simulations of the process at different temperatures, so that the molecule concentrations and temperatures of the sample can be determined. Succeeding in implementing and optimizing the setup presented in this paper will result in a Raman spectroscopy system that trumps the best systems available in the field today, due to the high average power of the laser and the multi-pass configuration system providing a signal enhancement that is potentially two to three orders of magnitude stronger than the older versions, while also supplying an improved detection sensitivity. In addition, higher spectral resolution of the measurements will be attainable. This will improve the detection specificity, while also allowing temperature measurements by analysis of temperature-dependent spectral signatures. 2

13 2 Theory 2.1 Confinement condition for multi-pass mirror cavity A stable cavity consisting of two mirrors requires that the confinement condition 0 g 1 g 2 1 (1) should be fulfilled [7]. Here, g 1 = 1 + d/r 1 and g 2 = 1 + d/r 2, where d is the length of the cavity, and R 1 and R 2 represents the radius of curvature for the two mirrors. For this setup, two identical mirrors are used, meaning the radius of curvature R 1 = R 2 = R and, therefore, g 1 = g 2 = g, giving that g 2 1, or d R 1. (2) This implies that the confinement condition could be written as [7] 0 d ( R) 2 (3) For a concave mirror, the focal length, f, can be expressed by [7] f = ( R) 2 Substituting Eq. (4) into Eq. (3) then gives that (4) 0 d 4f (5) which states the longest cavity length for which the cavity is stable. 2.2 The Raman scattering signal To be able to evaluate species concentration and estimate the SNR, it is necessary to know the relation between species concentration and the power of the Raman scattered signal, P r, which can be expressed as ( ) σ P r = P i n Ωlɛ (6) Ω where P i is the incident laser power, n is the number density of scattering species, ( σ/ Ω) is the differential Raman cross section, Ω is the solid angle, l is the sampling extent, and ɛ is the collection efficiency [2]. The locations of the spectral lines from Raman scattering are determined by the conservation of energy. For transitions in the Stokes Q-branch ( J = 0), where the transition between two vibrational states, v = +1, and rotational states, J 0 = J, an equation for spectral lines positions can be written as ν v+1,j:v,j = ν 0 [ω e 2ω e x e (v + 1) α e J(J + 1)] (7) where ν 0 is the incident light frequency, ω e = ν/c - the vibration frequency in [cm 1 ] - and ω e x e ω e are correction factors, and α e is the vibration-rotation interaction constant [2]. 3

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15 3 Experimental Optimization of the multi-pass setup consists of finding the correct angle of the incoming laser beam, so that, when the two mirrors are properly aligned, the beams form a circular dot pattern on the mirror surfaces. It also involves finding a distance between the mirrors where their focal points almost coincide in the middle of the cavity. The reason for not wanting the two focal points in exactly the same point is that the beams should not overlap inside the measurement volume, but instead form a tight circular pattern, so as to keep the local peak power density low [5]. Completing the optimization leaves the matter of collecting and detecting the Raman signal. The signal is usually detected at an angle perpendicular to that of the beam inside the aforementioned cavity. The Raman signal is, however, not collimated, which means that an arrangement of lenses is needed for collecting it in the detector. The detection system will then register the signal and present a readable spectrum, displaying intensity versus frequency/wavelength. 3.1 Laser safety Before any work on the experimental setup started, a risk evaluation of the experiment was performed. This section will state the conclusions of that evaluation. Details regarding the setup will be presented in the next section. Before any alignment starts, the optical table containing the setup must be screened off, using metal screens. A laser setup providing a beam at eye safe intensity level was arranged for initial setup and alignment of the cavity. To achieve this, the beam of a class 3B, 532 nm, cw, Thorlabs DJ diode laser, with an output power of 40 mw at I = 330 ma and T = 22.5 C, is reflected into the cavity using two glass plates, thus reducing the output power to 0.1 mw. The major part of the beam was thus transmitted through the plates and captured in beam dumps. During alignment of the glass plate system, and a lens system focusing the beam inside the cavity, laser safety eye-wear marked at least D L3 for the wavelength in question - according to the EN 207:2009 standard - must be employed. When this alignment is completed, the part of the table containing the diode laser and glass plates must be encapsulated using metal screens and black paper on all sides, as to ensure that only the eye-safe beam is exposed. During the actual Raman experiments, the full power of a frequency doubled, class 4 Nd:YAG laser will be used without attenuation. In addition to careful screening of the beam, laser safety eye-wear marked at least DR L8 for the wavelength in question (EN 207:2009) must be utilized when operating this laser. 3.2 Multi-pass system A schematic view of the multi-pass setup arranged with the alignment diode laser is shown in Figure 2. The setup employs a focusing lens, with focal length f L = 100 mm, positioned in the beam path, just before the hole in the first cavity mirror (M 1 ), so that the beam is focused at the center of the cavity (d 2f M ). The mirrors used are circular concave mirrors, with diameter mm and focal length f M = 100 mm. The second mirror (M 2 ) is positioned on a translation stage, at a distance close to 4f M from the first mirror. Adjustments of the horizontal and vertical position of the lens, as well as the tilting of and distance between the mirrors, are made, until a near-circular dot pattern can be clearly seen on each of the mirrors - see Figure 3. 5

16 When this setup is aligned and optimized, the diode laser is exchanged for a pulsed Edgewave HD40I-OE Nd:YAG laser, frequency doubled from 1064 nm to 532 nm. This laser has an average output power of 100 W and a pulse energy of 10 mj. Initially, the laser will be operated at lasing threshold, and the power will then be increased gradually as the optimization progresses. During measurements, the laser will be controlled by a BNC Model 575 external pulse generator, operating at a frequency of 1 khz. A set of dichroic mirrors (M A -M C ), with high reflectance at 532nm, and lenses - with focal lengths f L1 = 500 mm, f L2 = 150 mm and f L3 = 250 mm - will be used to guide the laser beam, reduce its diameter, and focus it in the center of the cavity, as can be seen in Figures 4 and 5. To collect the Raman-scattered signal, a set of two lenses with focal lengths f L4 = 100 mm and f L5 = 250 mm will be placed close to the cavity center, perpendicular to the length of the cavity. These lenses will focus an image of the beam envelope onto the entrance slit of the spectrometer. At the entrance slit, a filter, F, will be placed to block out the laser light at wavelength 532 nm, so that the Raman-scattered signal will be easier to distinguish. Figure 2: Schematic view of the initial alignment setup. M A and M B are glass plates used to reduce the power of the diode laser. M 1 and M 2 are the circular concave cavity mirrors, and L is the focusing lens. 6

17 Figure 3: Spot pattern acquired on mirror M 2 during alignment. The 41 laser spots visible on the mirror are generated as the beam completes 82 passages back and forth between the cavity mirrors. Figure 4: Schematic view of the setup for Raman spectroscopy. M 1 and M 2 are the circular concave cavity mirrors, M A, M B and M C are dichroic mirrors directing the laser beam to the cavity. L 1 -L 5 are lenses, and F is a filter. 7

18 Figure 5: Photography of the cavity taken during flame measurements, showing the two mirrors, the laser beam focused in the flame, and the first of the two lenses focusing the Raman-scattered signal into the spectrometer. 3.3 Detector The spectrometer used in the experiment is a Princeton Instruments Acton SP2500 grating spectrometer with a rotating grating selector - employing one grating of density 150 g/mm, blazed at 300 nm; one of density 1200 g/mm, blazed at 300 nm; and one of density 1200 g/mm, blazed at 500 nm - and an entrance slit, which are both controlled using the computer software LightField. At the exit of the spectrometer a Princeton Instruments PI-MAX 3 CCD camera with chip size 1024x1024 pixels is mounted. The camera intensifier is triggered by the laser pulse generator and the gate width is set to 100 ns in order to suppress continuous background light. 3.4 Measurements Initial measurements were made in ambient laboratory air. Moreover, measurements were made in an open-ended flow cell made of transparent plastic, through which a controlled gas flow of N2 was directed. Measurements were also made in a standard laboratory Bunsen flame, burning a premixed propane/air mixture. 8

19 4 Results & Discussion Here the acquired results are presented and discussed. The first section displays results from measurements made using the alignment laser to characterize the multi-pass arrangement. In the second section the results from Raman spectroscopy measurements performed with the high-power laser are presented. 4.1 Characterization of multi-pass cavity The first measurements performed concerned the effect of the cavity length on the number of round-trips and the diameter of the beam envelope in the center of the cavity. Figure 6 shows the dependence of the number of round-trips on the cavity length. Here, it can be seen that the number of round-trips increases with the cavity length, and more rapidly so as it approaches the critical cavity length given by d = 4f M, according to Eq. 5. Up to 72 round-trips were achieved using the diode laser. Using a similar configuration, Utsav et al. [5] achieved >150 round-trips. Thus, an even higher number of round trips is feasible, but requires more precise methods for focusing of the beam and adjustments of cavity length. Figure 6: The number of round-trips versus the cavity length for the alignment laser. A strong increase in the number of passages is observed as the cavity length approaches the distance d = 4f M, setting the limit for a stable cavity. In Figure 7, the diameter of the beam envelope in the center of the cavity versus the cavity length can be seen. It is clear that the envelope diameter decreases rapidly as the cavity length approaches d = 4f M. This is in compliance with results presented in [5], which showed that the envelope diameter is inversely proportional to the cavity length. They, however, managed to reach an envelope diameter of 1 mm. 9

20 Figure 7: The diameter of the beam envelope in the center of the cavity versus the cavity length for the alignment laser. The diameter of the beam envelope decreases rapidly as the cavity length approaches the distance d = 4f M From these two measurements, it can be concluded that to minimize the diameter of the beam envelope in the cavity center it is crucial to be able to tune the cavity length with high accuracy and precision. Another factor to take in to consideration is the importance of the incident laser beam to be in focus in the center of the cavity, so that the spots do not start to overlap on the mirrors and the spot pattern becomes smudged. The data plotted in Figure 6 and 7 are presented in Appendix A, Table Raman spectroscopy measurements As a way to test the setup, and optimize it further, the first measurements were performed in air. The next step was to measure species in a controlled gas flow of N 2, and, finally, to measure the species in a propane/air flame. All these measurements were made with d = cm and 56 round-trips. For air and N 2, the measurements were made with 300 on-ccd accumulations and 100 exposures per frame, resulting in an average over laser pulses. During the flame measurements the same number of on-ccd accumulations were used, but with 500 exposures per frame, resulting in an average over laser pulses Measurements in air The spectrum displayed in Figure 8 was recorded in air, using the multi-pass setup. The small peak to the left ( 580 nm) represents O 2 and the large peak to the right ( 607 nm) represents N 2. By using Eq. 7, and assuming that ω e x e and α e are small enough to be rejected, the theoretical frequencies/wavelengths of the two peaks are calculated. 10

21 The result shows that λ O2 = nm and λ N2 = nm, which fit in well with the observed locations of the peaks. Figure 8: The spectral profile of air, recorded using the multi-pass setup. The leftmost peak at 580 nm represents O 2, the large peak at 607 nm represents N 2 and the small, rightmost peak at 620 nm supposedly represents stray light from the laser, entering the detector at a large angle. In Figure 9, the recorded spectrum for air, using a single-pass setup, is displayed. It can be clearly seen that the peaks are amplified about two times in the multi-pass arrangement, compared to the single-pass setup. Thus, the noise in multi-pass recording is much less prominent. By applying Eq. (6) on N 2 and O 2 it is possible to establish the Raman power ratio, P rn2 /P ro2, between the two gases. This can then be compared to ratio between the two peaks in Figure 8. The ratio between the two peaks in the spectral profile is 3400/1250 = 2.72 and the theoretical value is P rn2 /P ro2 = 3.15, which proves to be roughly the same. However, the amplification differs from the expected theoretical value of a factor of 56 times. To achieve this kind of amplification, the diameter of the beam envelope in the measuring sample needs to be decreased further while also optimizing the collection system of the signal, so that more of it reaches the slit of the spectrometer. Also, in Figure 8, there can be seen a small peak to right of the N 2 peak, at 620 nm. Although not so prominent in this case, in later measurements it becomes more dominant. It would appear that this peak could represent emissions from photo-dissociated O 2 [8]. That is, O 2 molecules separated into its atoms. This is, however, not so plausible, as the peak at 620 nm does not seem to follow the strength of the O 2 peak, which is what would be expected if the two were associated in any kind. Instead, this peak most likely represents stray light at wavelength 532 nm from the laser, entering the spectrometer at a large angle and therefore ending up in the wrong location in the recorded spectrum. 11

22 Figure 9: The spectral profile of air, recorded using a single-pass setup. The leftmost peak at 580 nm represents O 2 and the rightmost peak at 607 nm represents N Measurements in N 2 gas The spectrum displayed in Figure 10 was recorded with a single-pass setup from a transparent tube, in which N 2 gas flows at 15 l/min. The N 2 is mixed with ambient laboratory air in the tube and suppresses the oxygen peak, compared with the spectra of Figures 8 and 9. Figure 11 shows the corresponding spectrum, but recorded using the multi-pass setup. The general slope of the profile for the multi-pass setup is due to scattered light from the laser at wavelength 532 nm entering the detector. The multi-pass setup is able to detect the O 2, which was not possible to do using the single-pass setup. However, there seems to be no significant amplification of the Raman scattered signal for the N 2 when using the multi-pass setup, compared to using the single-pass setup. Similar to the measurements made in ambient air, shown in Figures 8 and 9, an amplification is expected for both signals. This discrepancy could be an effect of the higher background accidentally giving additional signal at the position of the O 2 peak. In addition, the collection of the signals to the spectrometer slit might be more critical for measurements in the tube, where the signals pass through the curved transparent surface, possibly introducing lens effects. As can be seen in both Figures 10 and 11, the peak that was observed during the measurements in air is clearly visible, but is now shifted towards 630 nm. For the multipass measurement, the peak is much larger than the peaks representing O 2 ( 580 nm) and N 2 ( 607 nm). This is one of the reasons that the peak at 630 nm is considered to originate from stray laser light, as the tube used scatters the high intensity light in multiple directions, which can be seen in Figure

23 Figure 10: The spectral profile measured in a tube in which N 2 flows with 15 l/min, recorded using a single-pass setup. The small O 2 peak to the left at 580 nm is almost indistinguishable, the large peak at 607 nm represents N 2 and the small rightmost peak at 630 nm supposedly represents stray light from the laser, entering the detector at a large angle. Figure 11: The spectral profile from a tube in which N 2 flows with 15 l/min, recorded using the multi-pass setup. The O 2 peak at 580 nm can be distinguished to the left, the peak at 607 nm represents N 2 and the large rightmost peak at 630 nm supposedly represents stray light from the laser, entering the detector at a large angle. The general slope of the spectrum is due to light from the laser entering the detector. 13

24 Figure 12: Photography showing the multi-pass setup during measurements of N2 gas inside of a transparent tube. As can be seen, there is a considerable amount of scattered laser light from the tube Measurements in C3 H8 /air flame These measurements were taken for a premixed propane (C3 H8 )/air flame, positioned in the center of the cavity (see photo in Figure 5). In Figure 13, the spectral profile of the flame for a single-pass measurement is displayed. Figure 14 shows the same spectral profile for a multi-pass measurement and Figure 15 shows a high resolution spectral profile for the multi-pass setup. Comparing Figures 13 and 14, clearly shows an improvement in SNR by approximately 4-5 times, for the multi-pass system. Even in these measurements, a distinct peak can be observed at 630 nm, which might originate from stray laser light. However, C3 H8 is known to have peaks from C-H vibrations (ωe 3000 cm 1 ) in the hydrocarbon [2], resulting in wavelengths of nm, which might also add in. In the spectral profile presented in Figure 15, it is possible to observe the first hot band of the N2 vibrational transitions, just to the left of the large peak. The first hot band corresponds to transitions between the vibrational levels v = 1 and v = 2, compared to the transitions between v = 0 and v = 1 that are represented by the large peak at 607 nm. A hot band is so called, because it occurs at high temperatures, when more levels are populated, enabling more transitions. The reason for the hot band peak being so small, and also the reason for the large peak being rather narrow, is probably due to the temperature in the measured volume being quite low. This is highly plausible, since the measured volume was mostly part of the preheat zone of the flame, due to limitations in height adjustments of the burner when placed in the cavity. This is partly visible in Figure 5. 14

25 Figure 13: The spectral profile of a C 3 H 8 flame, recorded using a single-pass setup. The leftmost peak at 580 nm represents O 2, the large peak at 607 nm represents N 2 and the small, rightmost peak at 630 nm supposedly represents stray light from the laser, entering the detector at a large angle. The origin of the large dip in the N 2 peak and the narrow peak at 670 nm are due to electronic noise, which causes discrepancies when subtracting the background. Figure 14: The spectral profile of a C 3 H 8 flame, recorded using the multi-pass setup. The leftmost peak at 580 nm represents O 2, the large peak at 607 nm represents N 2 and the small, rightmost peak at 630 nm supposedly represents stray light from the laser, entering the detector at a large angle. Possibly, a contribution from the C 3 H 8 fuel can also be seen at 620 nm. 15

26 Figure 15: A high resolution spectral profile of a C 3 H 8 flame, recorded using the multi-pass setup. The peak seen at 607 nm represents N 2. To the left of the large peak, a small peak can be discerned at nm, which represents the first hot band. 16

27 5 Outlook The Raman multi-pass setup constructed in this project proved to be successful in enhancing the signal from the species measured. However, some problems arose along the course of the project, which need to be solved in order to maximize the efficiency of the setup. First of all, the high-power laser intended for the project turned out to have a rectangular beam profile. To be able to successfully focus the beam, both at the cavity entrance hole and the center of the cavity, a Gaussian beam profile is preferable, as it has the same dimensions in all directions. Another way to improve the setup is to have the ability to adjust lenses and mirrors, both horizontally and vertically, as well as having a method of measuring the cavity length accurately, in units of µm. This would enable more accurate tuning of the beam to achieve maximum number of passages and a narrower envelope. The latter improves the spatial resolution of the measurements and also makes it easier to collect the signal from the beam envelope through the spectrometer slit. It is also important to find a method to screen off the cavity as much as possible, and to have a collection system that is able to separate laser light from the signal, e.g. by using dichroic mirrors. This to avoid stray light entering the spectrometer, which causes spectra that are difficult to interpret. Also, a focusing mirror could be placed on the opposite side of the measuring volume from the first collection lens, to reflect back parts of the Stokes signal scattered in other directions. Succeeding to improve the system in the areas mentioned above will surely lead to an improvement in detection sensitivity and the strong signal enhancement predicted at the start of the project. The multi-pass setup will then be ready to be applied for species concentration measurements, as well as temperature measurements, in combustion processes, as originally intended. 17

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29 References [1] W. Demtröder. Atoms, molecules and photons: an introduction to atomic-, molecular-, and quantum-physics. 2nd ed. Heidelberg: Springer; [2] A. C. Eckbreth. Laser diagnostics for combustion temperature and species. 2nd ed. Amsterdam: Gordon & Breach; [3] K. C. Utsav and P. L. Varghese. Accurate temperature measurements in flames with high spatial resolution using Stokes Raman scattering from nitrogen in a multiple-pass cell. Applied Optics, July 2013; 52(20): [4] G. A. Waldherr and H. Lin. Gain analysis of an optical multipass cell for spectroscopic measurements in luminous environments. Applied Optics, March 2008; 47(7): [5] K. C. Utsav, J. A. Silver, D. C. Hovde, and P. L. Varghese. Improved multiple-pass Raman spectrometer. Applied Optics, August 2011; 50(24): [6] R. A. Hill and D. L. Hartley. Focused, Multiple-Pass Cell for Raman Scattering. Applied Optics, January 1974; 13(1): [7] B. E. A. Saleh and M. C. Teich. Fundamentals of photonics. 2nd ed. Hoboken, N. J.: Wiley, cop.; [8] L. C. Lee and T. G. Slanger. Observations on O( 1 D 3 P) and O 2 (b 1 Σ + g X 3 Σ g ) following O 2 photodissociation. The Journal of Chemical Physics, 1978; 69(4053): /

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31 Appendix A Tables Table 1: Number of round-trips inside the cell and the diameter of the beam envelope in the cell center as a function of the cell length. Cavity length [mm] Number of round-trips Diameter of beam envelope [mm] > > > >