Vol. 5, No. 3/March 1988/J. Opt. Soc. Am. B 585

Measurements of air-broadened and nitrogen-broadenedhalf-widths and shifts of ozone lines near 9 gm

M. A. H. Smith and C. P. Rinsland

Atmospheric Sciences Division, NASA Langley Research Center, Hampton, Virginia 23665-5225

V. Malathy Devi and D. Chris Benner

Department of Physics, College of William and Mary, Williamsburg, Virginia 23185

K. B. Thakur*

Department of Physics, The Ohio State University, Columbus, Ohio 43210

Received July 7, 1987; accepted October 12, 1987

Air- and nitrogen-broadened half-widths and line shifts at room temperature for more than 60 individual vibration-rotation transitions in the vi fundamental band of 1603 and several transitions in the 3 band were determined frominfrared absorption spectra. These spectra were recorded at 0.005-cm-1 resolution with a Fourier-transformspectrometer. A tunable-diode-laser spectrometer operating in the 1090-1150-cm'l region was also used to recorddata on oxygen-, nitrogen-, and air-broadened half-widths for selected individual transitions. The nitrogen- andair-broadened half-widths determined by these two different measurement techniques are consistent to within 4%.The results are in good agreement with other published measurements and calculations.

INTRODUCTION

Infrared remote sensing is a powerful method for accuratedetermination of the concentration and distribution ofozone in the terrestrial stratosphere. However, the accura-cy of both broadband and high-resolution ozone measure-ment techniques depends strongly on accurate knowledge ofthe basic spectroscopic parameters (position, intensity, as-signment, and air-broadened half-width) for each spectralline included in the measurement. Smith and Gordley'have shown that limb-viewing experiments are especiallysensitive to errors in knowledge of air-broadened half-widths. Unfortunately, most infrared spectroscopic studiesof ozone have emphasized the determination of line posi-tions, intensities, and assignments. Only a few papers re-porting infrared air- or nitrogen-broadened half-width mea-surements have appeared in the literature.2 -10 Together,these measurements cover only 168 transitions in the V3

band, 33 transitions in the band, 9 transitions in the + 3

band, and 6 rotational transitions. No measurements ofpressure-induced line shifts for ozone perturbed by N2 or byair have been published to our knowledge.

In this paper, we present high-resolution measurements ofair- and N2 -broadened linewidths and line shifts for 68 indi-vidual lines in the v, band and for 6 lines in the P3 band ofi603 . Detailed half-width measurements were made on 13well-resolved, isolated v lines at room temperature by usinga tunable-diode-laser (TDL) spectrometer. 0 2-broadenedhalf-widths were also determined for six of these transitions.N2- and air-broadened half-widths for a total of 74 lines,including the 13 measured with the TDL system, were alsoobtained from spectra recorded at 0.005-cm-' resolutionwith the McMath Fourier-transform spectrometer (FTS) at

the National Solar Observatory on Kitt Peak. In addition,pressure-induced line shifts were determined for 67 of theselines. The measurements were performed to assess the ac-curacy of half-widths derived from the two different mea-surement techniques (TDL and FTS) and to expand thedata base of measured 03 half-widths, particularly in the band. The half-width and line-shift values reported in thiswork are useful, not only for applications such as remotesensing and monitoring of 03 in the upper atmosphere butalso for verification of theoretical calculations such as thoseof Gamache and co-workers."",12

EXPERIMENTAL DETAILS AND DATAANALYSIS

Tunable-Diode-Laser SpectraThe TDL system that was used in this study is essentiallythe same as described in our work on CH4 half-widths.' 3 Wehave, however, added a new digital data system (HP 9000,200 series microcomputer). Detector outputs, after passingthrough two lock-in amplifiers, were sampled every 0.1 secand were stored digitally on floppy disks for subsequentanalysis. Programs to calculate spectral dispersion and linehalf-widths were developed and used in the analysis of thesedigital data. All the TDL spectra used in this study wereobtained by using a single Laser Analytics diode laser oper-ating between 1090 and 1150 cm-'.

The body of the 1.22-m path absorption cell used in theexperiments was constructed of Pyrex with Teflon valves.Wedged potassium chloride windows were cemented to theends of the absorption cell. The 03 samples were generatedusing the standard silent-discharge technique and were pu-

0740-3224/88/030585-08$02.00 ) 1988 Optical Society of America

Smith et al.

Smith et al.586 J. Opt. Soc. Am. B/Vol. 5, No. 3/March 1988

1.00 Torr 03

Torr 03, 56.25 Torr N2

1.15 TorY 03, 66.39 Torr N2

I

-J

z0

) Etalon FSR 0.0245 cm'

1122.4009 1122.5439

WAVE NUMBER (CM- 1)Fig. 1. Diode-laser spectra in the v band of ozone near 1122 cm-1,recorded using a 50-cm absorption cell at room temperature withpure ozone or ozone broadened by N2. Germanium 6talon fringesrecorded simultaneously with the lowest scan are also shown (fringespacing, 0.0245 cm-'). All scans have the same intensity scale butare vertically offset for clarity. FSR, free spectral range.

rified by repeated condensation in a liquid-N2 trap while

excess 02 was pumped out. The broadening gases wereresearch-grade N2, 02, and zero air purchased from AirProducts. A 0-100-Torr Barocel pressure head connectedto a Datametrics Model 1174 digital manometer was used tomonitor the total pressure in the cell. Sample temperaturesin the absorption cell were monitored by three thermocouplejunctions attached to the cell wall.

Unlike the v3 region of 03, the transitions in the P1 bandwere fairly well separated and were fully resolved in manywavelength regions. The lines were identified easily andwere selected for recording by a well-calibrated 1-mMcPherson monochromator attached to our optical system.A list of line positions obtained from low-pressure, high-resolution spectra, which we recorded using the 0.005-cm'1

resolution FTS at the National Solar Observatory on KittPeak, proved useful in selecting the desired wavelength re-

gions. Figure 1 shows sample TDL spectra recorded in this

work. Data were plotted on a Hewlett-Packard X-Y plot-ter, and the digitized data were stored simultaneously onfloppy disks. The data-acquisition process was controlledby the microcomputer described earlier in this section.

In determining the foreign-gas (02, N2, or air) -broadenedhalf-widths, an effective Doppler half-width bD' was deter-mined for each line from spectra recorded at two or more lowpressures of pure 03. After recording these low-pressurescans, each spectral line was recorded at a minimum of threedifferent pressures of (03 + 02), (03 + N2), or (03 + air), witha fixed 03 pressure. Under typical experimental conditions,the 03 pressures varied from 1.2 to 5 Torr, and the perturb-ing gas pressures varied from 30 to 70 Torr. From TDLspectra recorded with pure 03 at several pressures between15 and 25 Torr, we also determined a self-broadened half-width of 0.098 ± 0.002 cm'i atm-1 at 296 K for the (14, 5, 9)- (13, 4, 10) v transition at 1143.002 cm-'. We note that

this value is lower than the self-broadened half-widths mea-sured for two other l lines by Hoell et al.4 and values mea-sured for rotational lines by Lichtenstein et al.14 and Mon-nanteuil and Colmont.15 However, our measured value isclose to the values observed for lines with Ka' = 4 in the v +V3 and v1 + v2 + V3 bands.6"16 Therefore we have adopted anominal value of 0.100 cm-' atm'1 for the self-broadeningcoefficient of all lines included in the present study of for-eign-gas broadening.

A computer program was used to calculate the dispersionin each spectrum by using the simultaneously recorded 6ta-lon fringes with a free spectral range of 0.0245 cm-'. Theprogram also measured the half-width of each line at thehalf-maximum height corresponding to the square root ofthe minimum transmittance r(0). This half-width at half-maximum (HWHM) for each pressure-broadened line wasassumed to be the HWHM of a Voigt line, b,. From themeasured values of bD' and b,, the Lorentz half-width bL wascomputed by using the approximation of Whiting,' 7 as modi-fied by Olivero and Longbothum.'8 Corrections were ap-plied to the measured half-widths to take into account theinaccuracies introduced in locating the 100% transmittanceline as described by Smith et al.19 These corrections rangedfrom 2 to 8%, depending on the percentage absorptions andtotal pressures used. The Lorentz half-widths bL deter-mined for various pressures of the perturbing gas were fittedto a straight line passing through the origin (bL = 0, p = 0) todetermine the broadening coefficient bL0 for the line. Theresults are given in Table 1. The numbers in parenthesesare one standard deviation in units of the last digit quoted.

Fourier-Transform SpectraWe have also recorded N2- and air-broadened room-tem-perature spectra of 1603 at 0.005-cm-' resolution with theFTS at the National Solar Observatory on Kitt Peak. The50-cm-long absorption cell had a Pyrex body and wedgedpotassium chloride windows. The partial pressures of 03 forthese data ranged from 5 to 11 Torr; the (03 + N2) or (03 +

air) pressures varied from 107 to 316 Torr. A total of sixspectra were recorded, three each with N2 or air as thebroadening gas. The sample pressures were monitored con-tinuously during the 1-h time period required for recordingeach spectrum by using a Datametrics Model 1174 Barocel

electronic manometer with a 0-1000-Torr pressure head.Sample temperatures were also monitored by thermocou-

Vol. 5, No. 3/March 1988/J. Opt. Soc. Am. B 587

Table 1. Comparison of 03 vl Half-Widths Measured by TDL and FTS TechniquesWave Number bL (3:N2) (cm-' atm-1) bL (03:Air) (cm-' atm'1)

(cm-') J' Ka' Kc JI Ka" Kca" FTS TDL FTS + TDL FTS TDL FTS + TDL

1103.8413 35 4 32 34 5 29 0.0695 (12) 0.0730 (9) 0.0697 (8) 0.0660 (1) 0.0705 (9) 0.0662 (5)1103.8966 42 5 37 41 6 36 0.0765 0.0698 (21) 0.0738 (22) 0.0767 0.0706 (29) 0.0741 (23)1103.9475 18 2 16 17 3 15 0.0759 (14) 0.0787 (9) 0.0761 (9) 0.0760 (8) 0.0747 (12) 0.0758 (5)1104.0237 34 4 30 33 5 29 0.0747 (21) 0.0716 (11) 0.0745 (14) 0.0716 (5) 0.0693 (27) 0.0715 (6)1104.0767 26 3 23 25 4 22 0.0740 (18) 0.0753 (5) 0.0740 (11) 0.0712 (10) 0.0681 (7) 0.0710 (7)1122.4009 23 1 23 22 0 22 0.0751 (1) 0.0742 (2) 0.0750 (1) 0.0721 (2) 0.0717 (10) 0.0720 (2)1122.5439 24 0 24 23 1 23 0.0744 (3) 0.0733 (7) 0.0743 (2) 0.0733 (3) 0.0717 (7) 0.0732 (3)1128.7515 31 1 31 30 0 30 0.0710 (1) 0.0714 (5) 0.0710 (1) 0.0692 (1) 0.0688 (5) 0.0692 (1)1129.0095 29 2 28 28 1 27 0.0746 (5) 0.0705 (11) 0.0743 (6) 0.0699 (13) 0.0735 (11) 0.0702 (9)1135.1837 25 3 23 24 2 22 0.0770 (6) 0.0788 (11) 0.0771 (4) 0.0750 (3) 0.0780 (12) 0.0752 (4)1135.3184 39 1 39 38 0 38 0.0687 (5) 0.0704 (6) 0.0689 (3) 0.0667 (1) 0.0681 (11) 0.0667 (2)1135.4004 40 1 39 39 2 38 0.0752 (11) 0.0721 (10) 0.0748 (7) 0.0713 (11) 0.0682 (6) 0.0710 (6)1135.4587 39 2 38 38 1 37 0.0738 (3) 0.0704 (11) 0.0729 (7) 0.0717 (3) 0.0689 (11) 0.0714 (4)

ples attached to the cell wall and were read by a digitalvoltmeter.

The broadening coefficients were derived from the FTSspectra by an iterative least-squares technique. Details ofthe analysis method are described in Ref. 20. Line positionsobtained from the Kitt Peak spectra recorded with pure 03samples2 ' were used, and the initial values for intensities andhalf-widths were taken from the atmospheric trace moleculespectroscopy line list.22 For each fit of a narrow spectralregion, the free parameters included the positions, intensi-ties, and half-widths of the one to four strong lines of interestas well as two parameters describing the height and slope ofthe background. The positions, intensities, and half-widthsof weak lines remained fixed to their initial values. Thespectra recorded for determining N2- or air-broadened half-widths by using the FTS covered the 900-1300-cm-1 spec-tral interval, including both the vP and 3 bands. However,at the pressures used for the absorbing and broadening gas-es, most 3 lines could not be analyzed accurately because ofstrongly overlapping line wings. Therefore most of our re-ported results are for the P, band. Figure 2 shows a portionof an FTS laboratory spectrum along with the residuals(calculated spectrum - observed spectrum) resulting from aleast-squares fit. The N2- and air-broadening coefficients(in inverse centimeters per atmosphere) were determined byleast-squares fitting the measured Lorentz half-widths ob-tained from all these spectra with the corresponding broad-ening gas pressures. The self-broadening effect due to 03was also taken into account in computing each Lorentz half-width; we assumed a nominal self-broadening coefficient of0.100 cm-' atm-' for all lines. The results are given inTables 1 and 2. The uncertainties quoted in parenthesesare one standard deviation in units of the last digit quoted.

The least-squares fitting procedure also determined thepositions of the stronger spectral lines in each scan. Aftercalibration using residual H2O lines in the 1300-cm-1 re-gion,23 the retrieved positions of all the 03 lines were com-pared with those from the low-pressure scans21 to determinethe magnitude of pressure-induced line shifts. For eachbroadening gas, shifts determined in the individual spectraat three different pressures were then fitted by using linearregression to obtain the line-shift coefficients in inverse cen-timeters per atmosphere [Fig. 3(b)]. In all, pressure-in-duced line shifts were determined for 63 of the 68 tq lines and

LLJ

U-

U-

H

0

2.0 -

1.0_

0.0 . __ x,,

-1.0_

-2.0_ -I

1.0_

0

nI

H

0.8_

(a)

W A V E N U M B E R

1072.75

[CM13

(b)Fig. 2. Comparison between a FTS laboratory spectrum of 03 anda least-squares best fit to the data. The laboratory spectrum in (b)was obtained with 10.08 Torr of 03 in 218.5 Torr of N in a 50-cmabsorption path at 270C. The differences (observed - calculated)are shown in (a) and are expressed as a percentage of this peakintensity in the plotted region. The standard deviation of the fit is0.08%.

Smith et al.

Smith et al.588 J. Opt. Soc. Am. B/Vol. 5, No. 3/March 1988

Table 2. Measured Half-Widths and Shifts of 1603 in the 9-Am Region

WaveNumber Half-Width (cm-' atm-') Shift (cm-' atm-')

(cm-1)a J' Ka' Kc' J" Ka' K" bL0 (03:N 2) bL0 (03:Air) 60 (O3:N2) 60 (03:Air)

56 6 5147 4 4351 3 4856 5 5249 4 4551 4 4741 10 3227 8 2032 8 2432 0 3225 7 1927 7 2142 9 3320 6 1435 8 2829 1 2928 7 2143 9 3535 4 3242 5 3718 2 1634 4 3026 3 2316 0 1613 1 1324 1 2319 1 1926 1 2523 1 2315 2 1424 0 2417 2 1628 1 2725 1 2534 2 3227 1 2730 1 2928 0 2823 2 2225 2 2429 1 2910 3 730 0 3011 3 932 1 3127 2 2631 1 3112 3 929 2 2832 0 3234 1 3331 2 3033 1 3340 2 3817 3 1536 1 3535 1 3535 2 3436 0 3638 1 3737 1 3721 3 1912 4 8

55465055485040263133242641193430274234411733251512231825221423162724332629272224289

291031263011283133303239163534343537362011

6 504 423 475 514 444 46

11 299 179 231 338 168 18

10 327 139 250 308 20

10 325 296 363 155 294 221 150 122 220 182 240 221 131 231 152 260 243 310 262 281 271 211 230 282 81 292 82 301 250 302 101 271 312 321 290 323 372 142 340 341 331 352 360 362 183 9

0.0551 (10)0.0722 (2)0.0707 (9)0.0698 (32)0.0729 (2)0.0703 (1)0.0731 (9)0.0786 (11)0.0698 (29)0.0722 (35)0.0727 (34)0.0672 (16)0.0665 (15)0.0786 (10)0.0774 (12)0.0740 (40)0.0763 (4)0.0755 (28)0.0697 (8)0.0738 (22)0.0761 (9)0.0745 (14)0.0740 (11)0.0799 (4)0.0799 (6)0.0764 (2)0.0735 (9)0.0747 (6)0.0750 (1)0.0862 (10)0.0743 (2)0.0790 (7)0.0701 (12)0.0717 (2)0.0712 (15)0.0718 (4)0.0755 (3)

Q_0728 (2)0.0769 (5)0.0753 (5)0.0720 (3)0.0907 (2)0.0709 (1)0.0842 (17)0.0733 (9)0.0760 (4)0.0710 (1)0.0757 (9)0.0743 (6)0.0712 (8)0.0736 (6)0.0730 (9)0.0699 (6)0.0690 (10)0.0726 (9)0.0723 (6)0.0703 (2)0.0723 (24)0.0717 (5)0.0695 (13)

0.0713 (16)0.0767 (16)0.0830 (25)

0.0539 (32)0.0698 (1)0.0690 (7)0.0595 (39)0.0725 (3)0.0687 (3)0.0729 (32)0.0806 (25)0.0688 (11)0.0651 (10)0.0753 (11)0.0654 (14)0.0627 (25)0.0786 (7)0.0724 (10)0.0716 (1)0.0714 (13)0.0640 (30)0.0662 (5)0.0741 (23)0.0758 (5)0.0715 (6)0.0710 (7)0.0761 (11)0.0789 (5)0.0736 (5)0.0723 (6)0.0745 (0)0.0720 (2)0.0782 (11)0.0732 (3)0.0771 (1)0.0699 (12)0.0696 (3)0.0687 (18)0.0688 (14)0.0732 (3)0.0700 (7)0.0757 (7)0.0721 (8)0.0690 (5)0.0929 (38)0.0674 (6)0.0850 (21)0.0702 (9)0.0742 (7)0.0692 (1)0.0732 (6)0.0702 (9)0.0685 (1)0.0723 (3)0.0705 (7)0.0673 (7)0.0677 (3)0.0732 (19)0.0697 (8)0.0675 (0)0.0695 (20)0.0671 (9)0.0661 (8)

0.0666 (5)0.0767 (5)0.0818 (10)

-0.0032 (3)-0.0024 (6)

-0.0028 (3)-0.0036 (3)

-0.0017 (2)0.0004 (5)

-0.0020 (3)

0.0004 (13)0.0003 (3)0.0003 (11)

-0.0016 (6)

-0.0018 (8)

-0.0021 (1)0.0001 (7)

-0.0018 (10)0.0014 (5)

-0.0026 (4)-0.0006 (2)-0.0006 (2)-0.0016 (5)-0.0009 (1)

0.0005 (5)-0.0021 (1)-0.0015 (2)-0.0043 (5)-0.0012 (2)-0.0018 (9)-0.0021 (3)-0.0012 (3)-0.0021 (12)-0.0017 (4)-0.0018 (1)-0.0011 (1)

0.0001 (6)-0.0012 (2)

-0.0023 (12)-0.0021 (1)

0.0030 (8)-0.0023 (1)-0.0017 (1)-0.0021 (2)-0.0013 (5)-0.0014 (6)

0.0010 (10)-0.0080 (11)-0.0018 (1)-0.0013 (1)-0.0004 (2)-0.0022 (0)-0.0011 (10)-0.0025 (4)

0.0000 (9)0.0027 (11)

-0.0034 (1)-0.0021 (5)

-0.0031 (1)-0.0038 (6)

-0.0011 (1)0.0020 (4)

-0.0028 (7)0.0008 (7)

-0.0037 (5)

0.0003 (4)-0.0001 (7)

0.0009 (5)-0.0004 (11)

-0.0010 (10)

-0.0018 (13)

0.0004 (4)-0.0031 (2)

0.0002 (1)-0.0013 (2)-0.0006 (3)-0.0003 (3)

0.0013 (4)-0.0019 (1)-0.0012 (1)-0.0010 (2)-0.0008 (3)-0.0009 (3)-0.0022 (4)-0.0011 (4)-0.0011 (2)-0.0021 (8)-0.0019 (2)-0.0011 (1)

0.0001 (7)-0.0015 (1)

-0.0038 (12)

-0.0022 (1)0.0006 (9)

-0.0017 (2)-0.0014 (2)-0.0011 (9)-0.0010 (2)-0.0028 (6)-0.0009 (3)-0.0081 (8)-0.0013 (2)-0.0014 (2)-0.0006 (3)-0.0016 (1)-0.0010 (4)-0.0018 (3)-0.0004 (6)

0.0039 (10)

1070.9898*1071.0834*1071.1231*1071.2198*1071.9168*1072.6477*1072.92481073.13741077.18181077.40621077.45691079.08771079.21981079.40901079.57041079.79071079.89981079.97761103.84131103.89661103.94751104.02371104.07671115.17731115.39891119.28681119.44631121.56171122.40091122.47001122.54391123.42341123.77221123.94571124.08211125.52431125.90451126.02181126.08991127.00081127.12851127.23481127.73081127.78961127.95271127.96721128.75151128.96681129.00951129.42601129.91821130.13861130.34751131.64361131.75911131.80791132.02431132.65701132.78601133.6317

1133.67121133.72451135.0833

Vol. 5, No. 3/March 1988/J. Opt. Soc. Am. B 589

Table 2. Continued

WaveNumber Half-Width (cm-' atm-') Shift (cm-' atm'1)(cm-l)a J K0' Kc' J" K0

1' Kr" bL0 (03:N2) bL0 (03:Air) 50 (03:N2) 6° (03:Air)1135.1837 25 3 23 24 2 22 0.0771 (4) 0.0752 (4) -0.0026 (2) -0.0031 (3)1135.3184 39 1 39 38 0 38 0.0689 (3) 0.0667 (2) -0.0007 (2) -0.0006 (1)1135.4004 40 1 39 39 2 38 0.0748 (7) 0.0710 (6) -0.0003 (7) -0.0012 (3)1135.4587 39 2 38 38 1 37 0.0729 (7) 0.0714 (4) -0.0049 (11) -0.0027 (3)1138.2530 37 3 35 36 2 34 0.0704 (3) 0.0689 (13) 0.0001 (11) -0.0009 (4)1138.3033 46 2 44 45 3 43 0.0765 (15) 0.0684 (3) -0.0025 (6) -0.0044 (7)1138.3599 16 4 12 15 3 13 0.0728 (15) 0.0697 (33) 0.0032 (6) -0.0006 (6)1138.4414 43 2 42 42 1 41 0.0661 (1) 0.0653 (1) -0.0010 (4) -0.0012 (3)1138.6062 43 1 43 42 0 42 0.0697 (9) 0.0662 (15) -0.0014 (4) -0.0013 (5)1138.8119 44 1 43 43 2 42 0.0721 (17) 0.0706 (17) -0.0019 (8) -0.0025 (5)1139.0500 17 4 14 16 3 13 0.0792 (11) 0.0781 (8) 0.0003 (3) 0.0012 (2)

a An asterisk indicates a transition in the P3 fundamental band. All unmarked transitions belong to the Pv band.

4 of the 6 3 lines studied, for both N2 and air broadening.The values are reported in Table 2.

RESULTS AND DISCUSSION

The results obtained for the half-width measurements arepresented in Tables 1-3. In Table 1, the results from theTDL data are given in the columns labeled TDL and arecompared with the results for the same lines from the FTSdata. With the exception of the second line, whose FTShalf-widths are based on single spectra, the FTS and TDLvalues differ in the table for each line by 1-7%, with appar-ently no systematic effects for either air or N2 broadening.Where possible, we have combined the results obtained bythe TDL and FTS techniques to cover a wider range ofbroadening pressures (30-316 Torr) and to enhance the ac-curacy of the final results. The broadening coefficients list-ed in the columns FTS + TDL were obtained from linearleast-squares fits to all the measurements for each line. Anexample of one of these fits is shown in Fig. 3(a), along withthe corresponding individual measurements.

In addition to the air- and N2 -broadening measurements,02-broadened half-widths were measured for six of the ,ozone lines near 1122 cm-' and 1135 cm-'. In Table 3, theseresults are given along with the FTS + TDL N2- and air-broadened half-widths measured for the same lines fromTable 1. As shown in the table, the directly measured air-broadened half-widths are in excellent agreement (2% orbetter) with the values calculated from separate N2- and 02-broadening measurements.

The complete set of air- and N2 -broadened 03 half-widthsdetermined in this study is given in Table 2. These resultscover a wide range of rotational quantum numbers (9 J" <45, 0 < K,, < 11) in theiv, band but only a narrow range (46 <J" 55, 3 K,, < 6) in the 3 band. Our average value ofthe air-to-N2 broadening efficiency for all 74 lines is 0.967 0.032, which is close to the theoretical value of 0.95 given byGamache and Rothman.12 Taking into account all sourcesof error, including uncertainties in pressure, temperature,ozone amount, self-broadening, and calculation of weakoverlapping lines, we estimate the root-sum-of-squares un-certainty of our half-widths to be about 2% for the best (i.e.,strong, well-isolated) lines and about 6% for the worst lines.

In Fig. 4(a) we compare our N2-broadened halfwidths for

the v band with the measured values of Margolis7 and thecalculated values of Gamache and Rothman.12 For the ninevl lines measured both by us and by Margolis,7 our values aregenerally about 4% smaller, but the Margolis values scatterconsiderably (14%) relative to our measurements and tothe calculations. Our measured N2-broadened half-widthsare consistently about 7% larger than the calculated half-widths for most, of the J" values, and for J" < 15, where thehalf-widths also vary greatly with K,,", the differences aresomewhat greater (10-20%). These discrepancies are not

0.04

E0.03

E

0.02 -

0.01 0 TDL

,0 I 0 FTS

0 0.1 0.2 0.3 0.4 0.5Pressure (atm)

(a)

0.004 l

E 0.002

o, 0

- -0.002

-0.004

, _

0 FTSl I I I

0 0.1 0.2 0.3 0.4Pressure (atm)

(b)

0.5

Fig. 3. Least-squares fits of individual (a) half-width and (b) shiftmeasurements for the 03 line at 1135.4587 cm-' broadened by air.In each plot the symbols represent individual measurements, andthe slope of the straight line corresponds to (a) the pressure-broad-ening coefficient bL0 = 0.0714 cm-1 atm-1 or (b) the shift coefficient60 = -0.0027 cm-' atm'1. The standard deviations of the fits are0.6% for the broadening and 11% for the shift.

Smith et al.

590 J. Opt. Soc. Am. B/Vol. 5, No. 3/March 1988

Table 3. Comparison of Air-, N2 -, and 0 2-Broadened Half-Widths

Wave Number bN2 bO2 bAir (Calc.) bAir (Obs.) Obs. - Calc. (%)(cm'1) (cm-' atm-') (cm-' atm-') (cm' atm-l)a (cm-' atm'1) Calc.

1122.4009 0.0750 (2) 0.0631 (6) 0.0725 0.0720 (2) -0.71122.5439 0.0743 (2) 0.0633 (5) 0.0720 0.0732 (3) +1.71135.1837 0.0771 (4) 0.0647 (14) 0.0745 0.0752 (4) +0.91135.3184 0.0689 (3) 0.0583 (3) 0.0667 0.0667 (2) 0.0

1135.4004 0.0748 (7) 0.0586 (5) 0.0714 0.0710 (6) -0.61135.4587 0.0729 (7) 0.0578 (8) 0.0697 0.0714 (4) +2.4

a bAir = O.79bN2 + 0.21bo 2

3.10

00.09

0

0.07 ' A

- ~~~~~~A0.06

0.05 10 I 20 3 40---.L 0 1 0 20 30 40 bu

J

(a)

both about 15% smaller than the calculated value. We notethat the calculated values in Ref. 12 beyond J' = 35 areextrapolations.

For air broadening, shown in Fig. 4(b), there is some over-lap in coverage between our measurements and those ofHoell et al.

4 and Lundqvist et al.5 For the 3 line at1072.6477 cm-1 our air-broadened half-width is within 2% ofthe value measured previously by Hoell et al.,4 and for 5 linesin the v, band the differences between our values and thoseof Hoell et al.4 are at most 14%. For the first four lines listedin Table 1, our measurements agree well with those of

0.1

0.10

T0.09

X 08

E Act i ,

0.07 -

M0.06 Aco

0.05 . . . . E I I l0 10 20 30 40 50

J

(b)

Fig. 4. Comparison of half-widths in the vl band of 1603 (a) N2broadening: filled circles indicate measurements from the presentwork, open squares indicate previous measurements of Margolis,7

and open triangles represent calculated values of Gamache andRothman.2 (b) Air broadening: filled circles indicate measure-ments from the present work and open squares and open diamondsindicate previous measurements of Hoell et al.

4 and Lundqvist etal.,5 respectively. Open triangles represent calculated values ofGamache and Rothman.2

unexpected because the calculations of Gamache and Roth-man'2 were done only for ground-state to ground-state B-type transitions, and the resulting half-widths were alsoadopted for the v band. When measured and calculatedN2-broadened half-widths are compared for the six V3 lineslisted in Table 2, our values are all about 5% smaller than theMargolis measurements and, except for one transition, 7-8%larger than the calculated values. For the (56, 5, 51) - (55,6, 50) transition, our measurement and that of Margolis7 are

EC)

0.09

0.08

0.07

0.06

0 5 10 15 20 25 30J

(a)

0.1

I

E.C)

0.09

0.08

0.07

0.06

0.05

35 40 45 50 55

0 5 10 15 20 25 30 35 40 45 50J

(b)

Fig. 5. Comparison of average 03 half-width as a function of J indifferent bands: (a) N2 broadening, (b) air broadening. In bothpanels, triangles represent measurements for rotational lines (Refs.9 and 10), the light solid line represents measurements in the vl band(present work and Refs. 4, 5, and 7), the dashed line representsmeasurements in the P3 band (Refs. 4, 5, 7, and the present work),the circles represent measurements in the vU + P3 band (Ref. 6), andthe heavy solid line indicates the calculations of Gamache and Roth-man.12

E

._EC,~

.,

A I,

A A -"'I" 1 1

A- . - 1 1. . - 1 - . .I. . . .I. . ' l

55

u~~~~~~~~~~~~~~~~uz~~~~~~~~~~~~~~ --

Smith et al.

.I . ... I .., . I . . .. I . . .-n no:

Vol. 5, No. 3/March 1988/J. Opt. Soc. Am. B 591

compared directly with our own measurements because ofthe strong vibrational dependence of the line shifts.

0 _ z CONCLUSIONS__ 0 0 We have used two different techniques (TDL and FTS) to

0- ° ° Ct oh % 8 °.-s2 accurately measure N2- and air-broadened half-widths for74 03 absorption lines in the 9-,um region. This data set

~ 9 8 O m< a aincludes 50 lines in the P1 band for which half-widths had not- o been measured previously. Our measured values agree with

previous measurements 45 7 within stated experimental er-rors. Our results also verify the half-width calculations ofGamache and Rothman12 within their stated accuracy (7-

0 10 20 30 40 50 10%), although the calculated N2-broadened half-widths ap-J pear to be systematically about 7% smaller than our mea-

ressure-induced line shifts in the v band of 1603 perturbed sured values in the v, band. We have also verified experi-rcles) and by air (squares). mentally that the average ratio of air- to N2-broadened half-

widths for 03 lines is approximately 0.95.For most of the lines studied, we have determined pres-

st et al.,5 differing by 4-8%. For both N2 and air sure-induced line shifts in addition to half-widths. Theseng, the differences among our measurements, pre- measurements of pressure-induced line shifts for vibration-

.asurements, and the calculated values are all well rotation transitions of ozone perturbed by N2 or by air are, tose absolute uncertainties stated for each data set. our knowledge, the first published.

riowever, ere appear to e small systematic drtaerencesbetween our measurements and the calculated values.These differences may be related to the lack of explicitconsideration of the vibrational dependence in the calcula-tion and need to be explored further.

It is also interesting to compare 03-broadening measure-ments for transitions in different vibration-rotation bands.However, because of the scarcity of measurements, transi-tions having identical rotational quantum numbers cannotusually be compared. Therefore, in Fig. 5(a) for N2 broad-ening and in Fig. 5(b) for air broadening, we have averagedall available measurements for each J value in a given bandand compared the results with the calculated average half-widths given by Gamache and Rothman.12 In both figuresnearly all the measured values appear to be larger than thecalculated values. However, some of this discrepancy maybe artificial because the measured half-widths cover mostlylow K0

1' values (Katz < 5), where the half-widths are larger;the calculated average half-widths include all possible K'values. Nevertheless, the half-width measurements for N2broadening and air broadening in the various bands areconsistent with each other and exhibit an overall J-depen-dent trend that corresponds to that of the calculations. For02 broadening, too few measurements are available to enableus to make direct comparisons, but our results appear to beconsistent with those of Refs. 6, 9, and 10.

Results for pressure-induced line shifts are listed in Table2 and are presented graphically in Fig. 6. Within experi-mental uncertainty (15-25% at best) the shifts by N2 and byair for a given line are nearly the same. For low values of J"($20), the shifts appear to be highly dependent on J andKatz and have values ranging from approximately +0.004cm' atm-1 to-0.008 cm' atm-1. For J" >20 the shifts arenearly constant or slowly varying with J and have a meanvalue of about -0.002 cm-' atm-1. No previous measure-ments of 03 line shifts by N2 or air are available for compari-son. Gamache and Rothman12 calculated line shifts by N2for rotational transitions with J" 35, but the values for theshifts were not published. These calculated shifts cannot be

ACKNOWLEDGMENTSWe thank Rob Hubbard and Jeremy Wagner of the NationalSolar Observatory for their assistance with the FTS mea-surements. The help rendered by Lewis G. Burney ofNASA Langley Research Center and Frank H. Farmer ofKentron International Inc. with the diode-laser experimentsis gratefully acknowledged. We also thank R. R. Gamacheof the University of Lowell for helpful discussions in thecourse of this work. Research at the College of William andMary is supported by cooperative agreement NCCl-80 fromNASA. This research was also partially supported underU.S. Air Force agreement RES D5-674 with the U.S. AirForce Geophysics Laboratory.

*Present address, Bhabha Atomic Research Centre,Trombay, Bombay 400085, India.

REFERENCES1. M. A. H. Smith and L. L. Gordley, "Sensitivity of ozone retriev-

als in limb-viewing experiments to errors in line-width parame-ters," J. Quant. Spectrosc. Radiat. Transfer 29, 413 (1983).

2. D. Walshaw, "Line widths in the 9.6 band of ozone," Proc.Phys. Soc. A 68, 530 (1955).

3. R. T. Menzies, "Ozone spectroscopy with a CO2 waveguide la-ser," Appl. Opt. 15, 2597 (1976).

4. J. M. Hoell, C. N. Harward, C. H. Bair, and B. S. Williams,"Ozone air-broadening coefficients in the 9 m region," Opt.Eng. 21, 548 (1982).

5. S. Lundqvist, J. Margolis, and J. Reid, "Measurements of pres-sure-broadening coefficients of NO and 03 using a computer-ized tunable diode laser spectrometer," Appl. Opt. 21, 3109(1982).

6. C. Meunier, P. March6, and A. Barbe, "Intensities and air-broadening coefficients of 03 in the 5- and 3-jum regions," J.Mol. Spectrosc. 95, 271 (1982).

7. J. S. Margolis, "N2 broadening parameters of ozone at 9.6 m,"J. Quant. Spectrosc. Radiat. Transfer 29, 539 (1983).

8. A. Barbe, P. March6, C. Meunier, and P. Jouve, "Variation avecla temperature des coefficients d'elargissement des raies de

0.01 CO.O1 C0.006

0.006

E 0.0041J 0.002

70IE C

0

-0.004

- 0.006

-0.01c

-0.01

Fig. 6. Pby N2 (cir

Lundqvibroadenivious mewithin ti

Smith et al.

592 J. Opt. Soc. Am. B/Vol. 5, No. 3/March 1988

l'ozone et l'air pour la Bande P, + P3," J. Phys. (Paris) 44, 1015(1983).

9. J. M. Colmont and N. Monnanteuil, "Measurements of N2-, 02-,and air-broadened linewidths of ozone in the millimeter region:temperature dependence of the linewidths," J. Mol. Spectrosc.104, 122 (1984).

10. B. J. Connor and H. E. Radford, "Pressure broadening of milli-meter-wave ozone lines by atmospheric gases," J. Mol. Spec-trosc. 117, 15 (1986).

11. R. R. Gamache and R. W. Davies, "Theoretical N2-, 02-, and air-broadened halfwidths of 1603 calculated by quantum Fouriertransform theory with realistic collision dynamics," J. Mol.Spectrosc. 109, 283 (1985).

12. R. R. Gamache and L. S. Rothman, "Theoretical N2 -broadenedhalfwidths of 1603," Appl. Opt. 24, 1651 (1985).

13. V. Malathy Devi, C. P. Rinsland, M. A. H. Smith, and D. C.Benner, "Measurements of 12CH 4 4 band halfwidths using atunable diode laser system and a Fourier transform spectrome-ter," Appl. Opt. 24, 2788 (1985).

14. M. Lichtenstein, J. J. Gallagher, and S. A. Clough, "Millimeterwave spectrum of ozone," J. Mol. Spectrosc. 40, 10 (1971).

15. N. Monnanteuil and J. M. Colmont, "Self-broadening in themillimeter-wave spectrum of ozone," J. Quant. Spectrosc. Ra-diat. Transfer 29, 131 (1983).

16. M. A. H. Smith, V. Malathy Devi, C. P. Rinsland, and D. C.Benner, "Intensities and self-broadening of ozone near 5 ,um,"

presented at Forty-First Symposium on Molecular Spectrosco-py, The Ohio State University, Columbus, Ohio.

17. E. E. Whiting, "An empirical approximation to the Voigt pro-file," J. Quant. Spectrosc. Radiat. Transfer 8, 1379 (1968).

18. J. J. Olivero and R. L. Longbothum, "Empirical fits to the Voigtline width: a brief review," J. Quant. Spectrosc. Radiat. Trans-fer 17, 233 (1977).

19. M. A. H. Smith, C. P. Rinsland, B. Fridovich, and K. NarahariRao, "Intensities and collison broadening parameters from in-frared spectra," in Molecular Spectroscopy: Modern Re-search, K. Narahari Rao, ed. (Academic, Orlando, Fla., 1985),Vol. 3, p. 111.

20. C. P. Rinsland, D. C. Benner, D. J. Richardson, and R. A. Toth,"Absolute intensity measurements of the (1110),, - 0000 bandof 12C'602 at 5.2 Am," Appl. Opt. 22, 3805 (1983).

21. J.-M. Flaud, C. Camy-Peyret, V. Malathy Devi, C. P. Rinsland,and M. A. H. Smith, "The vl and V3 bands of 1603: line positionsand intensities," J. Mol. Spectrosc. 124, 209 (1987).

22. L. R. Brown, C. B. Farmer, C. P. Rinsland, and R. A. Toth,"Molecular line parameters for the atmospheric trace moleculespectroscopy (ATMOS) experiment," Appl. Opt. 26, 5154(1987).

23. L. R. Brown and R. A. Toth, "Comparison of the frequencies ofNH3, C02, H20, N20, CO, and CH 4 as infrared calibration stan-dards," J. Opt. Soc. Am. B 2, 842 (1985).

Smith et al.