Line positions, pressure broadening and shift coefficients for the second overtone transitions of carbon monoxide in argon

Journal of Quantitative Spectroscopy & Radiative Transfer 191 (2017) 46–54

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Line positions, pressure broadening and shift coefficients for the second overtone transitions of carbon monoxide in argon G. Kowzan n, K. Stec, M. Zaborowski, S. Wójtewicz, A. Cygan, D. Lisak, P. Masłowski, R.S. Trawiński Institute of Physics, Faculty of Physics, Astronomy and Informatics, Nicolaus Copernicus University in Toruń, ul. Grudziadzka 5, 87-100 Toruń, Poland

art ic l e i nf o

a b s t r a c t

Article history: Received 23 July 2016 Received in revised form 24 December 2016 Accepted 27 December 2016 Available online 2 February 2017

Absolute positions and spectral line-shape parameters of carbon monoxide 0 → 3 band, P branch transitions are reported. The speed-dependent effects and the influence of velocity-changing collisions were taken into account in the fitted line-shape models. For the first time the values of pressure shift coefficients of CO in argon for this band were determined. The measurements were made with the Pound– Drever–Hall-locked frequency-stabilized cavity ring-down spectrometer, with the frequency axis linked through an optical frequency comb to the UTC(AOS) frequency reference based on a hydrogen maser. Achieved uncertainties of line positions are between 70 kHz and 420 kHz. & 2017 Elsevier Ltd. All rights reserved.

Keywords: Carbon monoxide Spectral line shapes Absolute frequency measurements Cavity ring-down spectroscopy

1. Introduction Many applications depend on or benefit from accurate measurements of line shapes and frequencies of molecular transitions. One branch of applications is related to gas composition determination and includes ground- and satellite-based remote sensing techniques used for monitoring concentration of gases of atmospheric interest [1] and exoplanetary science [2]. In telecommunications, gas cells of samples with precisely known transition frequencies are used as frequency references in wavelengthdivision multiplexing (WDM) systems [3]. For basic research, precise knowledge of transition frequencies and pressure shift and broadening coefficients is crucial for validation of intramolecular potentials and enables testing of quantum chemical methods, determination of spectroscopic constants and investigation of molecular collisions [4,5]. Investigations of spectral line shapes of carbon monoxide have mostly concerned the fundamental band ( 0 → 1) around 4.7 μm [6–8] and the first overtone band ( 0 → 2) around 2.35 μm [9,10]. The spectral lines of the second overtone band ( 0 → 3) of carbon monoxide around 1.6 μm have been measured very rarely [3]. The reason for this being their very low intensities, which are lower by two and four orders of magnitude, as compared to 0 → 2 band and 0 → 1 band, respectively. Most recently, Mondelain et al. [11] have measured 184 lines of several isotopologues of CO in 0 → 3 and n

Corresponding author. E-mail address: gkowzan@fizyka.umk.pl (G. Kowzan).

http://dx.doi.org/10.1016/j.jqsrt.2016.12.035 0022-4073/& 2017 Elsevier Ltd. All rights reserved.

1 → 4 bands. The measurements were made with a comb-assisted cavity ring-down spectrometer with reported combined uncertainties of line positions equal to 300 kHz. Transition frequencies and pressure shifts of two CO lines from the 0 → 3 band were recently measured with combined standard uncertainties of line positions below 100 kHz [12] using three comb-assisted spectroscopic methods: frequency-stabilized cavity ring-down spectroscopy (FS-CRDS) [13], cavity mode-width spectroscopy (CMWS) [14] and one-dimensional cavity mode-dispersion spectroscopy (1D-CMDS) [15]. Accurate measurements of pressure shift and broadening coefficients of CO in argon can be useful in testing intermolecular potentials and for comparison of the experimental and theoretical line shape profiles [16–19], due to the relative simplicity of the system. The data for CO in argon is quite sparse for the overtone bands, mainly owing to difficulties in measuring the weak transitions of these bands. Line shift coefficients are available for the fundamental band [16,19,20] and the first overtone band [21], but so far no values were reported for the second overtone band. For line broadening, there is a single article reporting the values for the 0 → 2 band [22]. A very low intensity of molecular transitions in the near-infrared precludes the use of the most precise line position measurement techniques based on Doppler-free saturation spectroscopy [23]. Recently it is more common to use comb-assisted cavity ring-down spectrometers, which provide very accurate frequency axis and self-calibrated absorption measurements [11,24]. For proper line shape and line positions determination it is

G. Kowzan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 191 (2017) 46–54

crucial to perform measurements in a scan range broad enough and with low noise to properly reconstruct the line shape of measured transition. We have measured spectral line shapes of a range of P branch, second overtone transitions of carbon monoxide in argon. The P2, P4, P6, P9 and P14 transitions were selected to be representative of the whole branch and to facilitate comparison with previous measurements of CO–Ar spectra in the fundamental band [17–19]. The spectra were obtained with an optical frequency comb-assisted Pound–Drever–Hall-locked frequency-stabilized cavity ringdown spectrometer (OFC-assisted PDH-locked FS-CRDS) [24]. The accuracy of the technique was recently analyzed in comparison with the CMDS technique [25]. The optical frequency comb [26] was referenced [12] to a UTC primary standard based on a hydrogen maser. The measurements were performed in pressure range from 10 to 700 Torr, which allowed us to obtain for these lines for the first time pressure-induced line shift coefficients of CO in argon. We also report significantly more accurate values of pressure broadening coefficients than before [22] and provide parameters for the empirical formula introduced by Sung and Varanasi [27]. The formula allows for estimation of pressure broadening parameters of P branch transitions not measured in this work. The pressure shift coefficients were also compared with values from the first overtone and fundamental bands and were found to follow the trend of increasing red shift with increasing difference between vibrational quantum numbers of upper and lower states, Δν . We compare line-shape parameters obtained from the speed-dependent Nelkin–Ghatak profile (SDNGP) [28,29] and the Voigt profile (VP) fits and present the results of investigation of pressure range and line profile influence on line center determination. The VP is found to show significant dependence on the fitted pressure range.

2. Experimental details An earlier version of the spectrometer [30,31] was successfully applied to a low pressure line shape study of self-broadened CO transitions around 1.61 μm [32]. Since then, it had undergone significant changes. Fig. 1 shows the OFC-assisted PDH-locked FSCRDS spectrometer used in this work. The HeNe laser previously used for cavity-length stabilization was exchanged for I2-stabilized [33] Nd:YAG laser (Innolight Prometheus P20) operating at 1.064 μm wavelength. The probe laser was left unchanged (ECDL,

47

New Focus, Model: TLB-6330), but instead of using a low-bandwidth feedback loop to increase the number of coincidences between the laser and the cavity mode, it is now tightly locked to the cavity with the Pound–Drever–Hall locking scheme [34,35] augmented with active offset correction [36]. The cavity length is about 74 cm, corresponding to free spectral range (FSR) of 204 MHz, and with cavity mirrors' reflection coefficient of 0.99975 at 1.58 μm wavelength its finesse is equal to 12 500; for the reference beam the reflection coefficient is equal to 0.96, which corresponds to finesse equal to 80. The frequency axis of acquired spectra is now determined by beating the probe laser beam with a stabilized optical frequency comb [37]. The PDH-locked probe beam is divided into two orthogonally polarized beams. The vertically polarized (V) beam goes through AOMP (see Fig. 1) and it is the actual probe beam, while the other one (H) is used for the PDH locking and absolute frequency measurement. The acoustooptic modulator serves twofold purpose, it acts as a fast light switch, initializing ring-down events, and couples the actual probe beam (V) into the cavity by shifting its frequency by the cavity FSR. The separation of the PDH-locking and the probe beam allows the laser to stay locked to the cavity during ring-down events and obviates the need for relocking after every ring-down measurement [15]. The absolute frequency measurement of the probe beam is realized by heterodyne beat technique with the OFC [26,38–40]. The frequency νLH of the locking beam is calculated from the following formula:

νLH = m × frep ± f0 ± fbeat .

(1)

The repetition rate of the OFC, frep ; the offset frequency, f0; and the beat note frequency of the locking beam with the OFC, fbeat , are measured with frequency counters referenced to a 10 MHz signal from the hydrogen maser. The OFC's frep is around 250 MHz, the f0 is stabilized at 20 MHz and the frequency of the locking beam is also independently measured with a wavelength meter, with accuracy better than frep /2. With these frequencies established the only thing left is to determine the integer comb mode number m from the following formula:

⎛ ν H, WM ∓ f ∓ f ⎞ L 0 beat ⎟ m = Round⎜⎜ ⎟, frep ⎝ ⎠

(2)

νLH , WM

where is the reading of the wavelength meter. This way the frequency of the locking beam (νLH) is measured and the frequency

Fig. 1. Experimental setup of the OFC-assisted PDH-locked FS-CRDS spectrometer. OFC, optical frequency comb; PBS, polarizing beam splitter; DetBN , beat note photodetector; AOMP and AOMR, acoustooptic modulator for probe and reference beam, respectively; λ/2, halfwave plate; ECDL, external cavity diode laser (probe laser); Nd:YAG, I2-stabilized Nd:YAG laser (reference laser); Pol, polarizer; EOM, electrooptic modulator; DetPDH, probe beam detector in the PDH technique; FR, Faraday rotator; DM, dichroic mirror; SM, spherical mirror; PZT, piezoelectric transducer; DetYAG , reference laser photodetector; CamYAG , reference laser camera; λ/4, quarterwave plate; DetRD , ring-down signal photodetector; CamRD , cavity modematching camera.

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of the actual probe beam (νPV) is determined by adding the ΔAOMP frequency shift, νPV = νPH + ΔAOMP . The measurement procedure we followed was very similar to the one described in [41]. Once the probe beam is locked to the cavity with the PDH method, the frep is changed so that fbeat is in the range of (30 75) MHz, which is the bandwidth of our frequency counter. During this step the derivative of fbeat with respect to frep is also observed to determine the sign of fbeat . After each

change of νPH, the frep is adjusted to keep the beat note frequency centered on 30 MHz and the beat note sign is established. The accuracy and stability of our frequency axis was estimated by taking into account different statistical and systematic effects. It should be noted that the optical frequency comb, the frequency counters and the AOM RF signal used for frequency determination are linked to the UTC(AOS) frequency reference installed at the Astro-Geodynamic Observatory in Borowiec [42,43], via the OPTIME network [44,45]. Its short term stability is in the range of 2 × 10−13 for averaging time of 1 s and goes down to 7.1 × 10−16 for one day. The statistical uncertainty of the frequency of the hydrogen maser and the stability of the OPTIME frequency distribution network was verified with a strontium optical lattice clock in KL FAMO in Toru [46]. A thorough analysis of the frequency accuracy of the described CRDS system has been done recently by Cygan et al. [12] and will not be repeated here. The most significant uncertainty in the frequency axis is the stability of the cavity resonances, which are locked to the I2-stabilized Nd:YAG laser. Fig. 2(b) shows the beat note between the probe laser locked to the cavity and the optical frequency comb. Since the PDH lock of the probe laser to the cavity causes the laser frequency to tightly follow the cavity resonance frequency, the frequency fluctuations visible on the graph correspond to changes in the cavity length and allow us to estimate the stability of cavity resonances. Each spectral point is a result of averaging 2000 ringdown events, which took from 15 s to 75 s, so the cavity resonance frequency uncertainty in this time span has to be taken into account. Fig. 2(a) shows the Allan deviation of the beat note signal, where the shaded region corresponds to the acquisition time of a single spectral point. The maximum frequency uncertainty corresponding to this span is equal to 5 kHz and represents the largest

contribution to line center position uncertainty from the frequency axis.

3. Line-shape fitting and line centers We have performed measurements of five P branch transitions of carbon monoxide 0 → 3 band perturbed by argon. Each line was scanned three times in five different pressures—10, 50, 100, 300 and 700 Torr—and each spectral point was calculated from 2000 averaged ring-down events. Depending on the number of recorded spectral points and their spacing, each scan took from 30 to 150 min. The measurements of each line in a specific pressure were divided into three scans to head off eventual negative effects of long-term drifts of the measurement system. For lower pressures, from 10 to 100 Torr, a spectral point was acquired every quarter of the cavity FSR, i.e. about every 51 MHz; for higher pressures the spectral points were separated by the cavity FSR, i.e. about 204 MHz. Pressures were measured using an MKS Baratron gauge with relative uncertainty of 0.05% and temperature was measured using a calibrated thermistor with absolute uncertainty of 100 mK. The average temperatures are given in Table 1. The measured sample was a CO–Ar gas mixture with certified carbon monoxide concentration of 1003 720 ppm. Because the CO concentration is very low, it is safe to neglect its partial pressure when converting the pressure gauge readings to the argon atom concentrations. Therefore, all the concentration-dependent quantities are given as functions of the total gas concentration. By the same token, any influence of CO–CO collisions on the line shapes was also considered negligible and ignored. The line-shape analysis was performed using the Voigt profile (VP), the Galatry profile (GP) [47] and the Nelkin–Ghatak profile (NGP) [48,49], of which the last two take into account collisional narrowing [50], with the NGP being based on hard-collision approximation and the GP profile—on soft-collision approximation [51]. From our previous low-pressure measurements of pure CO [32], it was apparent that the speed-dependent effects [52] cannot be neglected, therefore the speed-dependent variants of these profiles were also fitted. The speed dependence in the speed-dependent Voigt profile (SDVP) [52], the speed-dependent Nelkin– Ghatak profile (SDNGP) [29,28] and the speed-dependent Galatry profile (SDGP) [53] was introduced using the quadratic approximation given by Priem et al. [54]. The reduced speed-dependent collisional width, BW(x), and collisional shift, BS(x), functions were approximated by:

BW (x) = 1 + aW (x2 − 3/2), BS (x)

= 1 + aS (x2 − 3/2),

(3)

where x is the reduced absorber speed, equal to the ratio of absorber speed to the most probable absorber speed, and aW, aS are fitted parameters. For P4 and P6 lines which showed a clear asymmetry in the residuals for measurements at 50 Torr and 100 Torr, we have also used the confluent hypergeometric function as a model of the speed dependence [55]:

BW (x; m) = BS (x; n) = Fig. 2. The stability of the cavity length locking to the I2-stabilized Nd:YAG laser. Panel (a): Allan deviation of the beat note between the probe laser PDH-locked to the cavity and the optical frequency comb. The shaded region corresponds to an acquisition of a single spectral element, i.e. recording of 2000 ring-down events. Panel (b): beat note of the laser PDH-locked to the cavity with the optical frequency comb.

μ=

mp ma

,

1 m /2

(1 + μ) 1

(1 + μ)n /2 m=

⎡ m 3 ⎤ M ⎢− , , −μx2⎥, ⎣ 2 2 ⎦

⎡ n 3 ⎤ M ⎢− , , −μx2⎥, ⎣ 2 2 ⎦

q−3 , q−1

n=−

3 , q−1

(4)

where mp, ma are perturber and absorber masses, respectively, M (a, b , z ) is the confluent hypergeometric function, and q is the exponent of the molecular interaction potential function, which is

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Table 1 Line-shape parameters determined by the multispectrum fit of the qSDNGP and the pCqSDNGP. The coefficients Δ/N , γL/N , νopt/N are in units of 10−19GHz/(molecule/cm3) , the line positions are in MHz, temperatures are in K and aW, QF parameters are dimensionless. The total combined uncertainties given in the parentheses were calculated from the rule of uncertainty propagation with systematic uncertainty components given in Table 3 and statistical components from the least-squares multispectrum fits. Line

P2 P4 P6 P9 P14

ν0

190 147 688.56(16) 189 901 444.51(9) 189 642 678.79(7) 189 231 129.57(7) 188 483 102.44(42)

γL/N

Δ/N

1.588(7) 1.403(6) 1.2568(52) 1.148(5) 1.103(5)


0.06008(31)
0.0882(4)
0.10167(42)
0.10639(44)
0.1083(5)

Reνopt/N

Reνopt / N

Imνopt/N

aW

QF

Temp.

– 0.0219(15) 0.016(1) 0.0115(9) –

0.1075(23) 0.1369(16) 0.1372(12) 0.115(2) 0.149(2)

854 1474 2202 1998 942

295.6 295.7 296.1 295.7 295.7

νdiff / N

0.0563(43) 0.053(3) 0.046(2) 0.0640(24) 0.0359(26)

assumed to take an inverse power form—V (r ) ∝ 1/r q . Additionally, following the IUPAC recommendation [56] we have also fitted the partially correlated quadratic-speed-dependent Nelkin–Ghatak profile (pCqSDNGP) [29], for which a simple analytical form, called the Hartmann–Tran profile [56], in terms of the complex error function can be given [57]. The spectra were analyzed with single-spectrum fits and the multispectrum fitting technique [58]. The multispectrum fitting procedure reduces the correlations between fitted parameters [59,60] and provides more accurate line-shape parameters [37]. In multispectrum fitting procedure, the Doppler width of each line was calculated based on the measured temperature, the line intensity was fitted independently for each scan, and the rest of the parameters were fitted simultaneously for all the pressures for a given line. The FWHM (full width at half maximum) collisional width, γL, the collisional shift, Δ, the frequency of optical collisions, νopt , were assumed to be linear functions of molecule concentration, N, while the speed-dependent parameters aW, aS, were fitted without pressure dependence. The hypergeometric speed dependence was treated phenomenologically and the m and n parameters were fitted independently, without forcing consistency in the corresponding q values. In single-spectrum fits, the Doppler width of each line was calculated based on the measured temperature. The rest of the line-shape parameters were fitted, with the exception of the collisional shifts, Δ, which were fixed to the values obtained from the multispectrum fits. This allowed us to compare the positions obtained from the multispectrum fits with the positions from single-spectrum fits and to fit the dimensionless speed-dependent shift parameters, aS and n. Therefore, with the exception of the pCqSDNGP, all the speed-dependent profiles included speed-dependent asymmetry. In both single-spectrum and multispectrum fits, we also fitted background, slope and at most two etalons, independently for each line scan. To quantify the quality of fitted line shapes, the quality-of-the-fit (QF) values were calculated for each single-spectrum and multispectrum fit, with QF being defined as the ratio of the peak absorption to the standard deviation of fit residuals [61,62]. For multispectrum fits the QFmulti is calculated differently: the peak absorption is equal to the absorption of the most intense scan, and the sum of squared residuals goes over all the residuals of all the lines. Fig. 3 presents the results of our measurements and singlespectrum line-shape fitting of the P6 line at 100 Torr. The commonly used Voigt profile does not include speed-dependent effects or collisional narrowing, so it was not able to properly model the obtained spectra. Inclusion of collisional narrowing in the form of the NGP or GP significantly reduces the residuals, but a slight asymmetry remains. Similarly, the addition of speed-dependent effects also significantly improves the fit. From comparison of the four profiles which are based on the NGP and include some form of asymmetry, it is clear that the hard-collision approximation is the most appropriate one for this system. This is not surprising,

0.20 0.19 0.16 0.22 0.12

Fig. 3. Experimental (green circles) and fitted (solid blue line) line shape of P6 line at 100 Torr. The Doppler FWHM was fixed at 442 MHz. In the lower part in red, residuals and quality factors (QFs) of single-spectrum fits of the indicated lineshape models. The bottom two panels (in blue) show residuals of the same scan, but obtained from the multispectrum fits of the qSDNGP (without speed-dependent asymmetry) and of the pCqSDNGP. The lower QF values of multispectrum fits are caused by forcing an imperfect model to fit over the whole pressure range. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

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G. Kowzan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 191 (2017) 46–54

since with the perturber-to-emitter mass ratio around 1.43 the physical situation is closer to the hard-collision model, which assumes that the perturber is much heavier than the emitter, than to the soft collision model, which assumes that the emitter is much heavier than the perturber. It is also clear that based on a singlespectrum fit it is not possible to establish the physical mechanism responsible for the line asymmetry. Following the reports of Brault et al. [9] and Malathy Devi et al. [10] on the self- and air-broadened first overtone spectra of carbon monoxide, we expected to observe line-mixing asymmetry in the measured spectra. This effect should be most clearly visible in the high-pressure scans, therefore we have fitted the quadratic-speeddependent asymmetric Nelkin–Ghatak profile (qSDANGP) to the 700 Torr scans of each of the lines. The profile includes dispersive line asymmetry, which is suitable for modeling asymmetry caused by finite-time duration of collisions [63–65] or line-mixing asymmetry [66,67], hence it should reduce the fit residuals if any of these two effects affects our spectra. The fits were performed with the aS parameter fixed to zero, i.e. with only line mixing contributing to the asymmetry of the line shape. The residuals of one of such fits are shown in Fig. 3 labeled as qSDANGP. We did not find any consistent improvement in QF values for the measured lines, pointing to the conclusion that the amplitude of this effect is below our detection limits. We would like to note that direct examination of the qSDNGP residuals of the high pressure scans does not show any systematic effects unaccounted for, therefore the lack of improvement in QF values is expected. The multispectrum qSDNGP line-shape fits of P2 and P14 without the speed-dependent asymmetry reproduced the measured spectra within the experimental noise limits. The good fit of the qSDNGP was further verified by comparing the positions obtained from the single-line fits with the multispectrum fit positions, as calculated from the fitted values of the transition frequency and the pressure shift. To account for the asymmetry visible in Fig. 3, we have performed multispectrum fits of the SDNGP, the SDANGP and the pCqSDNGP. The SDNGP was fitted in three variants: without any speed-dependent pressure shift (qSDNGP), serving as a baseline for all the other fits; with the shift modeled by the quadratic approximation ( qSDNGP aS ); and with the broadening and the shift modeled by the confluent hypergeometric function (hgSDNGP). The pCqSDNGP was fitted with the aS parameter fixed to zero to check if the line asymmetry was better described by including the correlation between different kinds of collisions. The obtained QFmulti for the multispectrum fit of the P6 line were as follows: qSDNGP—2098, SDANGP—2129, hgSDNGP—2156, qSDNGP aS —2162, pCqSDNGP—2202. Similarly, for the P4 line we obtained following QFmulti: qSDNGP—1420, pCqSDNGP—1474; and for the P9 line: qSDNGP—1971, pCqSDNGP —1998. The bottom two panels of Fig. 3 show the reduction of the residuals from qSDNGP to pCqSDNGP for one of the 100 Torr scans of the P6 line. The QFmulti values are higher than the single-line QFs shown in Fig. 3, because the peak absorption is taken from the most intense scan at the highest pressure. The multispectrum fit is in general somewhat worse than single-line fits. This can be seen by comparing the QF values of a single line for the same profile, obtained from a single-line fit and multispectrum fit (see Fig. 3). The difference in QFs between different lines is predominantly caused by different strengths of the transitions and correspondingly different peak absorption spans. Table 1 presents the results of the fits. For all of the lines we report the SDNGP parameters without the aS parameter, which was fixed to zero, with the addition of the imaginary part of frequency of optical collisions for P4, P6 and P9 lines (i.e. the pCqSDNGP parameters), which describes the correlation between velocity- and phase-changing collisions, and is the cause of asymmetry in the profile [29]. Aside from higher QFs for the pCqSDNGP fits of P6 and P9 lines, another

Fig. 4. Differences between positions from the multispectrum and single-line fits of the worst case—P6 line (bottom panel), and the typical case—P14 line (top panel). The shaded region encompasses the 3s position uncertainty, calculated based on the uncertainties of the transition frequency, the pressure shift and their covariance; the error bars are the 3s uncertainties of single-line fits.

reason to assume that the asymmetry in the profile is caused by correlations between collisions is given by the hgSDNGP fit. The hgSDNGP multispectrum fit converged with values of m and n parameters pointing to significantly different forms of the interaction potential, with q ¼6 for the pressure broadening and q¼ 23.2 for the pressure shift. The total combined uncertainties are given in parentheses and were calculated from the rule of uncertainty propagation with systematic uncertainty components given in Table 3 and statistical components taken from the leastsquares fits of the lines. The relative stability of both pressure and temperature was significantly better than the systematic uncertainties, with the highest relative statistical uncertainty of 4.2 × 10−5 for temperature and 1.6 × 10−4 for pressure, therefore their effect was negligible and did not increase the reported final uncertainties. For P2 and P14 lines, differences between positions obtained with the qSDNGP and the pCqSDNGP were used to estimate additional line-asymmetry systematic uncertainty components. For P2 line position and shift the relative uncertainties caused by line asymmetry were 8.9 × 10−10 and 1.6 × 10−3, respectively. For P14 line positions and shifts they were 3.7 × 10−9 and 3.7 × 10−3, respectively. The pressure shifts and line centers determined from multispectrum fits were compared with positions from single-line fits and in all cases they agree with each other within the 3s combined uncertainties of the fits. The typical and the worst-case values are shown in Fig. 4. As an additional verification of the fitting procedure, we checked the linearity of the line intensity with pressure. We performed linear least-squares fits of the dependence of the line profile integrals on pressure and calculated the fractional uncertainties (1σ ) of the fitted slope values. The ratios between the standard deviations of the fit to the slope parameter values were as follows: P2— 3.4 × 10−4 , P4— 1.9 × 10−4 , P6— 2.8 × 10−4 , P9 — 1.2 × 10−4 , P14— 5.3 × 10−4 . We also report the ratios of the fitted frequencies of optical collisions ( νopt ) to the dynamic friction coefficients ( νdiff ) calculated from the mass diffusion constant, D. The D constant values needed to determine νdiff were calculated using the model of Bzowski et al.

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Table 2 Comparison of line positions obtained in this work, by Mondelain et al. [11], by Picqué and Guelachvili [68] and by Farrenq et al. [68]. Columns marked as “Diff.” contain the differences between our transition frequencies and the ones in the columns immediately to the left. All line positions are in MHz. Line

This work

Mondelain et al.

Diff.

Picqué et al.

Diff.

Farrenq et al.

Diff.

P2 P4 P6 P9 P14

190 147 688.56(16) 189 901 444.51(9) 189 642 678.79(7) 189 231 129.57(7) 188 483 102.44(42)

190 147 687.09(30) 189 901 444.22(30) 189 642 678.81(30) 189 231 128.90(30) 188 483 102.03(30)

1.47 0.29
0.02 0.67 0.41

190 147 686.7(9) 189 901 443.4(9) 189 642 677.8(9) 189 231 128.2(9) 188 483 101.7(9)

1.9 1.1 1.0 1.3 0.7

190 147 686.9(1.5) 189 901 443.5(1.5) 189 642 678.2(1.5) 189 231 128.6(1.5) 188 483 102.0(1.5)

1.7 1.0 0.6 1.0 0.4

[69] and should be accurate to within 2.5%. Significant differences between the νopt and νdiff were observed previously for soft-collision, hard-collision and billiard ball models for the CO–Ar system [7,18,70] and the fivefold difference between these values in our case is not surprising. There are several reasons for this discrepancy. For one, only when the perturber is much heavier than the absorber does the (pC)qSDNGP accurately describe the velocity changes caused by the collisions, but the CO–Ar system represents an intermediate case between the soft- and hard-collision models and cannot be fully described be either. The speed dependence in this work is not determined from quantum mechanical scattering calculations based on an accurate interaction potential, but it is fitted to a phenomenological model. The speed dependence of the pressure broadening and the velocity-changing collisions both reduce the width of the lines and are highly correlated, so a proper description of both of these effects is required to retrieve physically meaningful values from the fit. Finally, the fitted collision rate includes only the velocity-changing collisions, while νdiff also includes collisions which change both phase and velocity. In principle, the pCqSDNGP accounts for existence of such collisions, but, as has been established, it is based on the description of the effect of the collisions on the absorber's motion, which is known to be incorrect for this system. In Table 2 we compare our line positions with the experimental results of Mondelain et al. [11] and Guelachvili [68], and the theoretical results of Farrenq et al. [71]. The results of Farrenq are actually the improved calculations reported in [68] and represent the most accurate calculated transition frequencies for these lines. We also observe good agreement with HITRAN [72] line positions, which is to be expected since their uncertainties are two orders of magnitude higher than in the current work. We observe good agreement with Refs. [11,68,71] for P4, P6 and P14 lines, and for the P9 line with Ref. [71]. The positions of P2 and P9 lines differ by 1.47 MHz and 0.67 MHz between our measurements and those of Mondelain et al. [11], respectively, which is about three and two times higher than the combined uncertainties of 460 kHz and 370 kHz for these lines, respectively. Mondelain et al. [11] have also provided a comprehensive comparison of the line center positions with theoretical results of Farrenq et al. [71], Velichko et al. [73], Coxon and Hajigeorgiou [74] and Li et al. [75] and the reader

Fig. 5. Collision-induced line shift coefficients for P branch lines of CO in Ar for different absorption bands as a function of the rotational quantum number of the lower state J.

is referred there for details.

4. Line shift and broadening coefficients The line shift coefficients of carbon monoxide in argon have been previously measured only for the fundamental and the first overtone bands, therefore the values presented here are the first reported ones. Fig. 5 shows a comparison between values for the fundamental band [16,19,20], the first overtone band [21] and the second overtone band measured in this paper. As expected we observe an increase of line shift with increasing value of the rotational quantum number of the lower state J, and increasing value of the vibrational quantum number of the higher transition state. Similar to the line shift coefficients, the reported line broadening coefficients were mostly acquired for other perturbers. The only values of argon-induced broadening in the second overtone come from Bouanich and Haeusler [22] (shown in Fig. 6). Sung and Varanasi [27] proposed an empirical formula to account for pressure broadening in carbon monoxide:

Table 3 Relative systematic uncertainties (type B) common to all the measured lines. The ∂f /∂T symbol signifies the influence of the temperature dependence of the specified line-shape parameters on their uncertainties and the symbols ϵP and ϵT signify the systematic uncertainties of pressure and temperature measurements, respectively. Source of error

Rel. uncertainty

Affected quantities

ϵP /P

7.0 × 10−3

γL/N , Δ/N , νopt/N

ϵT /T

3.3 × 10−4

γL/N , Δ/N , νopt/N

∂f /∂T

2.3 × 10−4

γL/N , Δ/N , νopt/N

Cavity stability

2.7 × 10−11

ν0

Nd:YAG stability

3.3 × 10−12

ν0

UTC(AOS) accuracy

5.3 × 10−12

ν0

Fig. 6. Comparison of P branch, second overtone collision-induced line broadening coefficients measured in this work with the results of Bouanich and Haeusler [22] and an empirical formula [27] fitted to the current data (details in the text).

52

G. Kowzan et al. / Journal of Quantitative Spectroscopy & Radiative Transfer 191 (2017) 46–54

pressure shift coefficient is 3.4% bigger and has nominally four times higher statistical uncertainty than the pCqSDNGP one. The value of the obtained pressure broadening coefficient shows a significant disagreement with the pCqSDNGP fit (solid line in Fig. 7 (b)), with the VP multispectrum pressure broadening coefficient being 12% lower than the pCqSDNGP one. When fitting in the full pressure range, the VP line position is 820 kHz lower than the pCqSDNGP one and the pressure broadening coefficient (dashed line in Fig. 7(b)) is 6% lower than the pCqSDNGP one. The pressure shift agrees to within 0.09% with the pCqSDNGP one. Table 4 summarizes the comparison between profiles. The results on line center fitting with the VP in the low pressure range agree to within 120 kHz with the pCqSDNGP fit, which suggests that the VP may be used for accurate measurements of such kind.

Fig. 7. Comparison of pressure shift (a) and pressure broadening values (b) obtained for the P6 line. Both panels show differences between values calculated by multiplying the coefficients from Table 1 by CO concentration and other fits. Violet circles correspond to single spectrum VP fits; blue squares—single spectrum pCqSDNGP fits; solid line—multispectrum VP fit in 10–100 Torr range, dashed line—multispectrum VP fit in 10–700 Torr range. The error bars of single spectrum fits represent the statistical uncertainties of the fits. (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this paper.)

Table 4 Comparison between values obtained from pCqSDNGP and VP fits of the P6 line. Pressure shift ( γL/N ) and pressure broadening coefficients ( Δ/N ) are expressed in

10
19 GHz/(molecule/cm3); line positions are in MHz. The statistical uncertainties of the fits are given in the parentheses. Profile

ν0

Δ/N

γL/N

pCqSDNGP VP 10–100 Torr VP 10–700 Torr

189 642 679.22(13)


0.1024(6)

1.253(6)

189 642 679.1(6)


0.1052(22)

1.11912(24)

189 642 678.4(4)


0.10176(6)

1.181(2)

γL N

=

c0 + c1 J , J+M

(5)

where c0 and c1 are fitted parameters and M is an adjusted integer parameter. This empirical formula was shown to better extrapolate for higher values of J in CO [27] and N2O [76] than a polynomial fit. We have obtained the best agreement with fixed M¼ 2 and fitted parameter values of c0 = 4.5 ± 0.1 and c1 = 0.925 ± 0.026, with c0 and c1 expressed in units of 10−19GHz/(molecule/cm3). Fig. 6 shows a comparison between our measurements, the empirical formula fit and those of Bouanich and Haeusler [22].

6. Conclusion This work provides the most accurate so far line positions of the 12C16O 0 → 3 band, P branch transitions. The frequency axis is directly referenced to UTC(AOS) and provides negligible contribution to the uncertainty budget, which is dominated by the quality of the cavity stabilization. The obtained results agree with data from the HITRAN database and partially agree with the measurements of Mondelain et al. [11]. These measurements allow for comparison between two comb-assisted CRDS systems representing one of the most accurate Doppler-limited spectrometers, with different operating principle and working in different measurement conditions. We report the first collision-induced shift coefficients of CO in argon for this rovibrational band and broadening coefficients with significantly improved uncertainties. Despite measuring only five lines of the rovibrational branch, the good agreement of the fit of Sung and Varanasi's [27] empirical formula will allow to extend the applicability of these measurements to other lines. These accurate measurements of strong pressure shift and broadening caused by CO–Ar collisions will allow for additional tests of intermolecular potentials and may lead to better theoretical understanding of such interactions. The investigations on line shape parameter's determination dependence on line-shape profile further delimit the applicability of the Voigt profile and point to the urgent need for improved spectroscopic databases. The Voigt profile offers significantly different performance depending on chosen data reduction scheme, with errors in obtained pressure broadening coefficients reaching as high as 12%. It also shows the robustness of line-shape parameters retrieval, assuming that the proper theoretical line-shape model is used.

Acknowledgments 5. Influence of line profile on the accuracy of line-shape parameters The commonly used Voigt profile is insufficient for analysis of molecular spectra and may lead to significant errors in determination of line-shape parameters (see [56,77] and references therein). Here we present the errors introduced by this profile in determining collision-induced broadening and shift in wide pressure range. We have performed VP multispectrum fits in two pressure ranges: between 10 and 100 Torr and in the full pressure range. For the first case, the transition frequency of P6 line obtained from the VP fit agrees within statistical uncertainty with the value obtained from the pCqSDNGP fit. On the other hand, the

We would like to thank Prof. Roman Ciuryło for careful reading of the manuscript and helpful discussions on the data analysis. The research is part of the program of the National Laboratory FAMO in Toruń, Poland, and is supported by the National Science Centre, Poland, Project Nos. DEC-2013/11/D/ST2/02663, 2015/17/B/ST2/ 02115, DEC-2012/05/D/ST2/01914.

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