Total Absorptance by Nitrous Oxide Bands in the Infrared

Darrell E. Burch and Dudley Williams

Instrumentation and experimental techniques employed for the determination of the total absorptancef A(v)dv of the bands of various atmospheric gases are described. The total absorptances of the 2563,2461, 2224, 1285, 1167, 692, and 589 cm-' bands of pure N20 and N20 mixed with N2 have been deter-mined as a function of absorber concentration w and equivalent pressure P,, which involves the partialpressures of the two gases. The results are given in graphical form. In general, it is found that in situa-tions in which existing theory predicts absorptance proportional to the square roots of pressure andabsorber concentration, the total absorptance is indeed nearly proportional to the square root of absorberconcentration but not to the square root of the pressure; for the 2224 cm-' band, f A(v)dv P37.In addition to graphical presentation of results, it is possible to expressf A(v)dv in terms of w and P bymeans of empirical equations applicable to certain definite ranges of the variables; the validity and thelimitations of such empirical equations are discussed. For samples for which the product of the absorp-tion coefficient k( v) and the absorber concentration is much less than unity for all frequencies in an absorp-tion band, it is possible to measure the band intensity or band strength fk(v)dv. Values of band intensityfor the 2563, 2461, 2224, 1167, and 589 cm-' N20 bands are listed and compared with values previouslyreported by others.

A detailed knowledge of the infrared transmission ofplanetary atmospheres is of importance to spacephysics in connection with studies of planetary heatbalances and with the possible development of infraredprobing and signaling systems. Laboratory studies of"synthetic atmospheres" are desirable, even in connec-tion with telluric studies, and provide a basis for inter-pretation of observed absorption in the atmospheres ofother planets. The major purpose of the present workis the determination of the total absorptance fA (v)dvof various absorption bands as a function of absorberconcentration w and equivalent pressure Pe.1 Thepresent paper on nitrous oxide N20 is the first in a seriesdealing with absorption by various telluric gases. Al-though N20 is a relatively minor atmospheric con-stituent, a knowledge of the absorptance of N20 bandsis important in the calculation of the transmission of

The authors are of the Laboratory of Molecular Spectroscopyand Infrared Studies, Department of Physics and Astronomy,The Ohio State University. The present address of D. E. Burchis Aeronutronic, A Division of the Ford Motor Company, New-port Beach, California. D. Williams is presently a National Sci-ence Foundation Senior Postdoctoral Fellow at the University ofLiige.

Received 6 December 1961.

Supported in part by Geophysics Research Directorate, AirForce Cambridge Research Laboratories.

the "atmospheric windows" between the carbon dioxideand water vapor bands in the infrared.

Instrumentation

A double-beam single-pass Perkin-Elmer Model 21spectrometer with an NaCl prism and thermocouple wasemployed for frequencies between 4000 cm-' and 670cm-1 and was equipped with a drive mechanism thatprovided a direct plot of A (v) versus v on the recorderchart. The spectrograph is equipped with two multi-ple-traversal cells, each of which has a base path of 1meter and can be set for 40 traversals or any smallernumber divisible by 4. Although the cells are equippedwith heating coils capable of maintaining sample tem-peratures as high as 1000 C, all data included in thepresent study were obtained at approximately 30'C.These long cells can easily be replaced by short con-ventional absorption cells when short absorption pathsare desired.

The gas-handling manifold was equipped withpackless miniature stainless steel valves, which can beconnected to the sample cell, the reference cell, variouspressure gauges, and various gas cylinders. Gas pres-sures between 1 and 50 mm Hg were measured by aWallace and Tiernan absolute pressure gauge givingan accuracy of 1 part in 300 when properly adjusted.Pressures lower than 1 mm Hg were measured by meansof a McLeod gauge, which was also used to check the

July 1962 / Vol. 1, No. 4 / APPLIED OPTICS 473

Wallace-Tiernan gauge at low pressures. A simplemercury manometer was employed for pressures be-tween 50 mm Hg and 1 atm. An Ashcroft Duragaugeof the Bourdon type was used to measure pressuresgreater than 1 atm.

Before introduction of gases into the sample cell, theentire system was first evacuated and then the referencecell was closed off. The absorbing gas was then ad-mitted to the manifold and the sample cell at the desiredpressure and then the sample cell was closed off. Themanifold was then first re-evacuated and filled with

nitrogen* to some selected pressure greater than that inthe sample cell. Nitrogen was added to the sample cellby briefly opening the valve until the desired total pres-sure was obtained. By following this procedure it was

possible to minimize or eliminate backward flow of theabsorbing gas from the sample cell to the manifold.No data were accepted until thorough mixing of the

absorbing and broadening gases had occurred in thesample cell; reproducibility of measured absorptancewas the criterion for thorough mixing. At low totalpressure, thorough mixing by diffusion wvas accom-plished within a few seconds, or at most a few minutes,depending on the sample cell being used. At higherpressures it was necessary to use a fan mounted in themultiple-traversal absorption cell to ensure thoroughmixing within a reasonably brief time. In order tominimize mixing time the valve was located adjacent tothe cell so that nitrogen in the tubing leading to themanifold would not diffuse into the sample.

Studies of absorption at frequencies higher than 4000

cm-' were made with a Perkin-Elmer Model 99 spec-trometer equipped with an LiF prism and an thermo-

couple. A multiple traversal cell giving paths as

long as 48 meters was used with this instrument;

pressures employed with this cell were atmospheric or

less. This spectrometer, which was mounted inside a

vacuum tank, was also used with shorter absorption

cells to investigate the absorption by small samples of

H20 and CO2 in the regions of the strong absorption

bands. This was found to be necessary in order to

eliminate error due to absorption by the air in the opti-

cal path of the spectrometer. The larger Model 21

spectrometer could not be evacuated and could not be

flushed sufficiently well that error was negligible forsmall samples.

The total absorptance fA (v)dv could be determinedby planimetering the records obtained with the Model21 spectrometer, since the abscissa is linear in frequencyand the ordinate is linear in absorptance A (v). In

some cases slight corrections were needed to take

* Although nitrogen was employed as a "broadening gas"

throughout the present work, the effects of other gases can easilybe computed oni the basis of the relative broadening abilities given

in ref. 1.

account of scattered light, unequal attenuation in thesample and reference cells, and atmospheric absorptionwithin the spectrograph; these effects were easilyrecognized and corrected so that they caused negligibleerrors in measured values of f A (v)dv. In the case ofdata obtained with the Model 99, an "envelope spec-trum" taken with the absorption cell evacuated wassuperposed on each sample spectrum. The envelopespectrum served as the zero absorption curve. Curvesrepresenting spectral absorptance as a function offrequency were then replotted and planimetered toobtain f A (v)dv as in earlier studies.2

Three major types of experimental error in thepresent work are: (1) Sampling errors, which includeuncertainties in the amounts of absorbing gas andbroadening gas in the sample cell, (2) errors in recordingby the spectrograph due to noise, drift, and possiblenonlinearity in the detection-amplification-recordingsystem, and (3) errors in planimetering the recordedspectra. With the set of pressure gauges employed,pressures greater than 10 mm Hg could be measuredto i 41%, with somewhat greater uncertainty forsmaller samples. Possible error due to incompletemixing of gases in the sample cells was largely elim-inated by use of the fan mentioned earlier. A carefulstudy of the possible effects of adsorption of gasesshowed that errors due to adsorption could be mini-mized by certain procedures used in filling the cells;it is estimated that errors due to adsorption amount to±42% to i3% for larger samples and not more thani5% for the smallest samples. The recording errorsare estimated as ±+5% for values of total absorptanceless than 10 cm-' and ±2%o for values of total absorp-tance greater than 10 cm-'. Repeated tests byexperienced operators show that planimetering errorsamount to less than ±i 1%. It is estimated that theover-all error does not exceed i 10% for values of totalabsorptance less than 10 cm-' and is less than ±t5% ifthe total absorptance is greater than 10 cm-'.

Treatment of Data

When the study of a given absorption band or regionwas started, a definite slit program for the spectrometerwas selected and used to take all data. Although totalabsorptance is independent of slit width, there areoccasions when it is desirable to compare spectralabsorptance A (v) at some definite frequency for dif-ferent samples; such a comparison is impossible unlessall data are taken with the same slit program. How-ever, since the datum of primary interest is f A (v)dv, itis not necessary to use narrow slits. It is desirable towork with slits sufficiently wide to give large signal-to-noise ratios even for the largest values of fA (v)dv;wide slits are convenient from the practical standpointof planimetering the spectral records. For nearly

every band studied it would have been possible to ob-

474 APPLIED OPTICS / Vol. 1, No. 4 / July 1962

tain more detailed information concerning band shapehad this been of importance to the investigation.

Once a slit program had been selected, large numbersof spectral records were made. These records provideddata on fA (v)dv for wide ranges of absorber concentra-tion w, * partial pressure p of the absorbing gas, and totalpressure P-including of course pure samples of theabsorbing gas for which p = P. The value of f A (v)dvfor various cell lengths, absorber concentrations, andequivalent pressures Pe were then organized into plotsto develop relationships between f A ()dv and thevariables w and P and to provide tests of theoreticalpredictions. t

One type of relationship important to nearly all cur-rent theories is the relationship between absorptanceand pressure. In order to establish this relationship,a set of logarithmic plots of total absorptance as afunction of equivalent pressure Pe was made for variousvalues of absorber concentration w. From the slopes ofthe curves, the relation between f A (v)dv and P, can beobtained. In general, it is found that over certainranges of Pe and w, fA (v)dv Pe", where n < 0.5 evenin situations where existing theories predict a square-root relationship.

Another set of logarithmic plots was then preparedgiving f A ()dv as a function of w for various values ofequivalent pressure P. From the slopes of thesecurves, it is usually found that fA (v)dv w', wherem ; 0.5 in situations for which theory predicts asquare-root dependence on absorber concentration.

The next step in attempting to establish experimentalrelationships between f A ()dv and sample parameterswas to make logarithmic plots of f A ()dv as a functionof WP,". From the resulting plots it is frequently pos-sible to obtain empirical equations of the form

f A(v)dv = c(wPa)b, (1)

where a, b, and c are empirical constants with b 0.5.Such equations are valid for intermediate values off A ()dv and P, for which strong but not seriously over-lapping rotational lines are present throughout mostof the band.

* In the present series of articles, values of absorber concen-

tration w are expressed in atm cm and are found by w = P X760

273273 + TX where p is partial pressure of the absorbing gas in mm

Hg, 1 is the absorption path length in cm, and is the sampletemperature in C. The factor including T reduces values of wto normal temperature, and a given value of w corresponds tothe same number of molecules per unit area regardless of temper-ature.

f The term equivalent pressure is applied to the quantity PeP + (B - 1) p, where B is a self-broad6ning coefficient giving theratio of the "self-broadening ability" of an absorbing gas to the linebroadening ability of nitrogen. Values of B for N20 and otherabsorbing gases are given in ref. 1.

For large values of fA (v)dv, the central portion of aband is a spectral region of nearly complete absorption.Further increase in w or P merely causes increasedspectral absorptance in the wings of the band. Forsuch a band, the total absorptance can be expressed inthe form

f A(v)dv = C + D Log (wPe"), (2)

where C, D, and a are empirical constants.It is usually rather difficult to derive empirical equa-

tions for extremely small values of f A (v)dv and Pe.Under certain circumstances fA (v)dv is nearly inde-pendent of Pe, a result indicating that Doppler broaden-ing is the dominant factor in determining line width;under other conditions f A (v)dv is found to vary lin-early with absorber concentration, as predicted bythe theory for weak lines.

It should be emphasized that, although empiricalequations of the forms (1) and (2) can be useful inpractical work provided they are properly applied,they are not based on any valid theory. Although theycan be used to test predictions of theory, it is usuallymore desirable to employ interpolations between curvesshown in logarithmic plots. Limitations of empiricalequations will become evident in the detailed discussionof results obtained for the 2224 cm-' band of N20.

Results for the 2224 cm-, Band

The 3 fundamental of the N 4016 molecule has itscenter at 2224 cm-'. However, in the same spectralregion there is absorption due to the V3 fundamental ofless abundant isotopic molecules of N20, and at leastone weak band (V3 + 2 - P2) reported by Thompsonand Williams.3 For the purposes of the present paper,all these bands will be referred to as the 2224 cm-' N20band. More than 200 spectral records of this regionwere obtained. Cell lengths of 1.55, 6.35, 400, 800,and 1600 cm were employed. Different combinationsof N20 and N2 were used to provide absorber concentra-tions from 0.00016 to 76.4 atm cm and total pressuresfrom 1 to 3000 mm Hg. All spectra were obtained withslit widths corresponding to approximately 25 cm-' andwith the cell temperature near 301C. The values ofequivalent pressure were calculated from the total pres-sure P and the partial pressure p of N20 by the relation

P = P + 0.12 p

on the basis of earlier studies of self-broadening.Tracings of spectra of two samples having the largest

absorber concentrations are shown in the left panel ofFig. 1. A slight growth of the band with increasingpressure is to be noted. The "band limits," beyondwhich there is negligible spectral absorptance, areindicated by the band wings in these records; theselimits were used as limits of integration for total ab-sorptance for all samples studied. The right panel

July 1962 / Vol. 1, No. 4 / APPLIED OPTICS 475

2300 2200 2100 2300 2200 2100

WAVENUMBER in cm-,

Fig. 1. Spectral absorptance, expressed as "Percent Absorp-

tion," for the 2224 cm-' band. Values of P, and w are listed forsuccessive curves in the figure.

of Fig. 1 shows the spectra of two samples having dif-

ferent values of w and P0 but having approximatelyequal total absorptance. It will be noted that theshapes of the two bands are quite different even thoughthe spectrometer slit widths are the same. Thus, itis apparent that different portions of the band growdifferently with increasing w and P0.

Other typical spectral records are shown in Fig. 2.Those in the upper left panel show the relatively smalleffects of increasing P, when the absorber concentrationis large. The curves in the upper right panel representresults obtained with pure N2O samples; these curvesillustrate the influence of simultaneous increase of w

and I,. The curves in the middle and lower panelsshow the effect of increasing PO for smaller values ofw. The curves in the lower left panel were obtainedwith the ordinate scale expanded approximately fivetimes. It will be noted that the P- and R-branchesbecome more clearly defined as P.. increases.

Many of the results obtained are plotted on a log-

arithmic scale in Fig. 3, which gives f A (v)de as a func-

tion of P,. Each curve corresponds to a given absorberconcentration and shows the effect of increasing P0

by the addition of N2. Path lengths indicated in thefigure give the lengths of the absorption cells used for

each curve. The points marked x at the lower ends

of curves A through P were obtained with pure samplesof N.2 0; the points at the lower ends of curves Q, R,and S represent results obtained with previously mixed

samples of N20 and N2. Parts of curves D and E areomitted from the figure for purposes of clarity; how-ever, the upper portions actually occupy positions thatcan be accurately estimated by comparison with F, G,and H.

There is a general decrease in the slopes of the curves

with increasing pressure, indicating a decrease in thedependence of total absorptance on equivalent pressure.This "saturation phenomenon" can be explained on thebasis of the change of line shape with pressure. As thepressure increases, the half-width of a spectral line

increases; the absorption coefficient k(v) increases in

the wings of the line and decreases at the line center.For pressures sufficiently high that the line half-widthis equal to the spacing between the lines, the rotationalfine structure diminishes, and further increases in pres-sure have but little effect on total absorptance. Goodyand Wormell4 have shown that the line half-width be-comes essentially equal to line spacing in N20 at a pres-sure of approximately 4100 mm Hg. The onset of thiseffect probably accounts for the saturation phenomenonin Fig. 3 at high values of P,.

It will be noted from Fig. 3 that the value of P0 atwhich saturation begins is greater for large values ofabsorber concentration than for smaller values. Inthe case of large w, the decrease of A(v) near the linecenters accompanying increased P0 does not appreciablychange spectral absorptance at these frequencies sincek(v)w is still sufficiently great that spectral absorptanceremains essentially complete at the line centers. How-ever, in the case of small w, a relatively small value ofP0 is sufficient to reduce k(v)w at the line centers to avalue such that the decrease in spectral absorptancenear the line centers is approximately the same as theincrease in spectral absorptance in the wings of thelines. Therefore there is little or no increase inf A (v)dv with increasing P0.

The small variation in total absorptance with w andP0 for large values of these parameters results in thecrowding of the curves in the upper right-hand cornerof Fig. 3. The observed effects are to be expected for

w= 23.7at mOs m

20

40-- P ,I m'm Hg 1

60 - 10362103

80-

100

01 \\ - - 1

z0

0

0r

LX

L

20i

40,

60

80

100 I

9'nmm Hg

11.2

51.2

I0I200 -400_

1 ~~740w~ 00°74 3075atmos cm

. ~~I0. Ad w 003 ?/ 1 [ Xw- 0037/ ein' 047V =10 03m /s mm Hg

ol os m m 98.1 20in mmHg 182 4

8 ---- / / 5.6 414 -408.1 -7 35

12 \\ /, 11 8 L. 3070 H6020.5

16 t 32 6 2300 2200498 1

2300 2200 2100

WAVENUMBER In cm'

Fig. 2. Spectral absorptance of various samples in the vicinityof the 2224 cm - band.

476 APPLIED OPTICS / Vol. 1, No. 4 / July 1962

I I . I % ~ I-

III I

-"\A ' in Pe i-

,'QmOS IM -cm Hg- - -3.7 9 -

-0.074 3075 -

N20, . , I I , I

-' A

_ E

140 - G

IH

I

K

L

M

'V~T --.-- '--- -a - -_Jem____ ----- - ----- __

stmos cn n cm N,0 .A 76,4 1611 A 224 m| i=...*F G-;11 6 400 oo - ~_ _ _ __ _ _5.8 4002.8 400 -- - *1.4 400 D. . .3.02 6.35 *

0.74 6.350.37 6.35 /0.148 6.35(.074 6.350.037 635 --.---. * 0.46135 / ._

10~ - " .0101 .55. 0 o 0.0054 1.55

P 0.0032 1,55 -. 0 0.0020 1 .55 /- ----7 R 0.0011 1.55

S (.0007? 155 /-. - .P

i ~ ~~~~~~~~~~~~~~~~~~~~~~~~~~~~ i- ... ...... I

III 50~~~1( Jn '300 .000 4000

Fig. 3. Total absorptance of the 2224 crn- band versus equivalent pressure for samples having constant values of absorber concen-tration w, which are listed for the successive curves.

situations in which k()w is large for nearly all frequen-cies within the band. Inspection of the spectral recordscorresponding to the points in the upper right-handcorner of Fig. 3 reveals that spectral absorptance is in-deed complete near the band center; any band growthaccompanying further increase in w or P is slight andoccurs in the wings of the band.

Curves J through 0 in Fig. 3 have approximately thesame slopes for pressures lower than 200 mm Hg. Theaverage value of the slopes of these curves is 0.37.Thus, it is possible to express the total absorptance assome function of absorber concentration times Peo 37 forthe values of w and Pe represented by these curves.

In Fig. 4 are five curves giving f A ()dv as a functionof P for samples in which w is directly proportional toP0 . Curves A, B, and C are for pure N 20 samples;the ratios of w to P for these three curves are dif-ferent because of the difference in path lengths. CurveD corresponds to a mixture of one part of N20 to nineparts of N2 by volume; curve E gives results for a mix-ture of one part of N20 to 49 parts of N2 by volume.Therefore, for curves D and E, w is proportional toP0 as for curves A, B, and C; however, in curves D andE the ratios of w to Pe are different as a result of dif-ferent dilutions with N2. The curves in Fig. 4 are basedon some data previously plotted in Fig. 3 and some addi-tional data not previously presented. The slopes ofcurves A, B, and C decrease for large values of w andP,, as in the case of the curves in Fig. 3; this saturationoccurs for smaller values of Pe for long path lengths be-cause w is greater. The maximum values of w were notsufficiently great to produce saturation in curves D andE.

It is to be noted that the curves B, C, D, and E inFig. 4 have regions that are nearly linear over wideranges of P greater than 10 mm Hg. The linearportions have slopes of 0.91, which is considerablygreater than the slopes of the linear portions of thecurves in Fig. 3. The greater slope of the curves inFig. 4 is due to the fact that w increases with increasing

100

40

E

.A

10

2202224 cm'

A ,/

B '

/C X/

/ xI/ 0

,/-1 / /

I - E // --

4

AI-

0.4

/ //A

.1z ~~~~~B/C

/ ~~~~DE

l-- - - -| I" I I , l , , I I I I I I I4 10 40

Pe in mm Hg

~1

PATH SAMPLE

400 N20 alon6.35 N20 aon

1.55 N20 lone1.55 1/50 NO -

100 400 O00

Fig. 4. Total absorptance of the 2224 cm-' band versusequivalent pressure for samples in which absorber concentrationis directly proportional to equivalent pressure'

July 1962 / Vol. 1, No. 4 /'APPLIED OPTICS 477

r , . . ......r If , , It | go | | , . . . ......I

. .... _ . , Is , , . ,

7

I- iI

. I-,

A/

1

- - 7T -- ; - T - I T7'- -

100 - -N20

F 2224 cm-'

- 10 <

Pe in mm Hg

3000760250100402010

-4

ji

0.4/ . L I LA | LL - ..l l.l l 0.0002 0.001 0.01 0.1 I 10 80

w in atmos cm

Fig. 5. Total absorptance of the 2224 cm -lband versus absorber concentration for samples having the equivalent pressures listed.

P0 in Fig. 4, but w is constant for each curve in Fig.

3. The slope of 0.91 in Fig. 4 indicates that for the

linear portion of the curves

f A(v)dv = cw-P m'z, (3)

where m + n = 0.91 and c is a constant for each curve.

Since it was shown in Fig. 3 that fA (v)dv is propor-

tional to P.0- 7 over considerable ranges of w and P0,

it would appear that n = 0.37 and m = 0.54 in (3).It will be noted that the slopes of curves B and C in

Fig. 4 decrease for values of P0 less than 10 mm Hg;

this decrease is general and cannot be explained on the

basis of pressure-broadened lines of Lorentz shape. It

is attributed to the increasing influence of Doppler

broadening at low pressures; similar effects at low pres-

sures have been reported by Goody and Wormell4 andby Benedict et al.5

In order to show more clearly the variation of

f A (v)dv with w, data from the curves of Figs. 3 and 4were replotted in Fig. 5, in which each curve corre-

sponds to a different value of P0 as indicated in the

figure. Although the curves in Fig. 5 converge at the

lowest and highest values of w, it will be noted that over

considerable ranges of w the five lower curves have

linear portions having slopes of 0.53 in close agreement

with the value of 0.54 proposed for m in (3). The

curves in Fig. 5 are quite useful in making estimates of

total absorptance f A (P)dp for any value of w and P0

covered in the investigation, since interpolations forP0 between the curves shown can easily be made.

Since there is coincidence of the ranges of w and P0 for

which the curves of Figs. 3 and 5 are linear, it is possibleto express fA (v)dv for these ranges by

fA(v)dv = cwO-53PO-37 c(wPo0.7)0 53. (4)

In order to check the range of validity of (4) and to

point out some of the dangers involved in the use of

empirical equations, all the data represented in Figs.3, 4, and 5 have been replotted in Fig. 6, which showsJA(v)dv as a function of (wP,0-7); each curve corre-sponds to a given value of P0 as indicated. If JA (v)dvwere indeed a function only of (Pe 0

0 7), all curves inFig. 6 would coincide. It is not surprising that thecurve corresponding to P0 = 3000 mm Hg falls wellto the right of the other curves, since the rotationalstructure is nearly smoothed out at this high pressure,and the effects of increasing pressure are small. It isto be noted that the other curves diverge for low valuesof (WPe0-7); this divergence shows the extreme dangerof extrapolating empirical equations like (4) to lowpressures. Since some of the curves in Fig. 6 cross, onemay conclude that the exponent 0.7 is too small forsome values of w and P0 and too large for others.

However, it is possible from the curves of Fig. 6to determine useful empirical relations and their rangesof validity. Thus, the nearly linear middle portionsof the curve can be represented by the equation

fA(v)dv = 18 (wP. 7)0.53 (5)

for the ranges 10 cm-' < f A ()dv<45 cm-' and 10 mmHg <P,<250 mm Hg. For larger values of f A(v)dv,

the following equation can be applied:

f A(v)dv = 15 + 40 Log (wPO0 7) (6)

for the ranges 45 cm-' < f A (v)dv< 120 cm-' and 10 mmHg <P0 <760 mm Hg. In (5) and (6) the absorber con-centration w is expressed in atm cm. Values of totalabsorptance computed from these equations are be-lieved to be accurate to 4 10%; extrapolations shouldbe avoided.

It is desirable to compare the present results withthose predicted on the basis of various theoretical bandmodels. In view of the regularities in line spacing inthe 2224 cm-' N20 band, it would appear appropriateto use an Elsasser band model,6 for which the total

478 APPLIED OPTICS / Vol. 1, No. 4 / July 1962

0

1:

I-_0

15,

l l li I I l I i I l l l l l l l l l l | I 1 a 1 l l 1 1 1 1 1 ! r

100 N20

2224 cm-' P. in mm Hg

2010 ~' 400.' 71 O. 0i ! l l l | l l l l l l ll100

250-z ~~~~~~~~760

- ~~~~~~~~3000

0.4/0.01 01 I ~~~~~0 100 1000

0.7W Pe w in atmos cm, Pe in mm Hg

Fig. 6. Total absorptance versus wP,0 .7. The limitations of empirical equations are illustrated.

absorptance can be expressed as a function of (WPe)under certain conditions. In order to test the Elsassermodel, the curves in Fig. 7 were plotted from theexperimental data presented earlier; coincidence of thecurves would indicate a function of (WPe). It will benoted that except at the onset of saturation the variouscurves are separated more widely than those in Fig.6. Use of the criteria of Plass7 for the validity of thestrong line approximation [the name given to the ap-proximation when the total absorptance can be ex-pressed as a function of the single variable (wP0 ) ], alongwith data of Goody and Wormell,4 to obtain relationsbetween w and P and the dimensionless parametersemployed in the theoretical expressions made possiblea more quantitative test of the Elsasser model. It wasfound that, for many values of w and P for which thestrong line approximation would be expected to apply,agreement between theoretical predictions and ex-perimental results was not closer than ± 20%.

00 N,0

2224 cm-'

10 _i ,/ ' ICx,. a-- ,

The experimental results show that total absorptanceis less strongly dependent on Pe than on w. Thisweaker dependence on pressure than that requiredby the Elsasser model can be explained qualitativelyon the basis of weak lines in the 2224 cm-' region; forweak lines the effects of w are always greater than thosedue to P. It is possible that the "random Elsassermodel" applied successfully by Plass7 to the ozone spec-trum might also be successfully employed in the treat-ment of the 2224 cm-l N20 band.

Results for Other NO BandsAlthough the 2224 cm-' band is in some respects the

most important N20 absorption band from the stand-point of telluric atmospheric transmission, other spectralregions of NO absorption at 2563, 2461, 1285, 1167, 692,and 589 cm-' were also investigated by methods similarto those described earlier, except for the use of a KBrprism for the last two regions mentioned.

Pein mm Hgi,.* ,- /v ~10

2040

+ 100A 250* 760

3000

10 100 1000 10000

July 1962 / Vol. 1, No. 4 / APPLIED OPTICS 479

wPe in atmos cmxmmHg

Fig. 7. Total absorptance versus wP,,. The limitations of existing theories are illustrated.

11

100

40

D 7iO Pe n mm Hg -

2 _ 1 I I I 1! I- 1 I~ _ _ . 1 , .0,04 1 0.4 I.0 I 1( 40 100

w n tmo cm

Fig. 8. Total absorptance of the 2563 cm-' band versusabsorber concentration for the values of equivalent pressurelisted.

40

Band Intensities

One quantity of fundamental importance in molecularspectroscopy is band strength or band intensity, definedas the integral of the absorption coefficient k(v) over allfrequencies in a band. Although the value of fk(v)dvdepends on population differences between the upperand lower vibrational states and is therefore a functionof temperature, basic information regarding moleculartransition moments can be obtained provided f k(v)dpis known at some definite temperature. Under certainconditions band intensities can be determined fromsome of the data obtained in the present study.

The spectral absorptance A' (v) obtained with aspectrometer of infinite resolving power is given by thefamiliar expression

A (P) = 1 - e-(v) o

Eto

0

A,

1.0

0.1 0.4 .0 4 1

w in tmos cm

400 log

Fig. 9. Total absorptance of the 2461 cm-' band versus ab-sorber concentration for various values of P,.

(7)

However, fA'(v)dv = fA(v)dv, where A(v) is themeasured value of the spectral absorptance and thelimits of integration include an entire band. There-fore, for a situation in which k(v)w < 1 throughout anentire band

f A(v)(dv = f (1 - e-"(v)5v)dv = w flc(v)dv

and

(8)f k(v)dv =fJ to~

In Fig. 8 are summarized the results obtained for the2563 cm-' band. The smoothed curves shown in thisfigure can be used to predict values of total absorptance

to 5% for the range of w and P0 covered whenfiA(v)dv'> 30 cm-l; somewhat greater errors may beencountered for lower values of total absorptance.Similar sets of curves for the 2461, 1285, and 1167 cm-'bands are shown in Figs. 9, 10, and 11, respectively.The data presented in Fig. 10 appear to agree to within

a few percent with similar data published by Goody andWormell.4

Figure 12 gives a set of curves showing spectral

absorptance of N2 0 in the vicinity of its V2 fundamentalat 589 cm-' and at the much weaker band at 692 cm-';the spectral slit width employed was approximately6 cm-'. Absorption by the weaker band was meas-urable only for large values of P0 and w, and its totalabsorptance was not plotted as a function of w, sinceso few data were available. Plots of f A (v)dv versus w

for the 589 cm-' band are shown in Fig. 13 and maybe used to estimate total absorptance for other valuesof w and P. within the range covered.

The general features of the sets of curves shown for

various bands in Figs. 8, 9, 10, 11, and 13 are for themost part quite similar to those discussed in detail for

the 2224 cm-' band.

20C r~r fT

I I n mn Hg

100 M7E 6

250

10 o -o 2 1285 c410

CA 1. 4- 0 0

w in almos cm

Fig. 10. Total absorptance of the 1285 cm'concentration.

-P inmm Hg40 -

250 1167 cmf'100 40

10 4~ 20

A

0.4 1.0 4.0 10 40

' in atmos cm

Fig. I1. Total absorptance of the 1167 cm-'sorber concentration.

480 APPLIED OPTICS / Vol. 1, No. 4 / July 1962

versus absorber

100

band versus ab-

40 100

z0

0-1

0U)

b'i0uJ0U

500700 600

WAVENUMBER in cm-'

Fig. 12. Spectral absorptance of the 692 cm-' and 589 cm-'bands measured with a spectral slit width of 6 cm-. The bandswere arbitrarily separated at 655 cm-' in determining totalabsorptance.

400 - _ I~ N Pe In m m Hg I40 -o - 30001

0.4 1.0 4.

w in tmos cm

Fig. 13. Total absorptance of the 589 cm-l band versus absorberconcentration.

In order to obtain the band intensity from (8) by themethods used in the present study, the approximationthat k(v)w < 1 for all frequencies must be valid, arequirement that is satisfied by small values of w andvalues of P sufficiently large that k(v) is small even atthe centers of rotational lines. Under these conditions,the lines are said to be "completely broadened" andthe total absorptance of the band is directly propor-tional to w but independent of P.

The lower portion of the uppermost curve in Fig.5, corresponding to a total pressure of 3000 mm Hg, islinear and has a slope of approximately unity; thusfA (v)dv is directly proportional to w. It will also benoted that the lower portions of the three upper curvesof Fig. 5, which correspond to values of P 250 mmHg, converge at low values of w. Thus, it would appearthat the condition k(v)w < 1 is satisfied under condi-tions applying to the lowest values of w represented inFig. 5. Some question has been raised concerningearlier results of Thorndyke, Wells, and Wilson,8 withregard to fulfillment of the condition that k(v)w. < 1.However, in the present study the data. are sufficientto establish the approximation involved in (8).

At the intercept of the uppermost curve in Fig. 5,f A(v)dv = 0.37 cm-' and w = 2 X 10-4 atm cm.Substitution of these values in (8) gives f k(v)d =1850 (atm cm)-' cm-' for the band intensity of the2224 cm-' N20 band. It should be noted that the useof the intercept values from Fig. 5 involves the "aver-aging processes" used in drawing the smooth curves.Other careful measurements of f A ()dv for sampleswith large P0 and small w indicate that the value statedabove is accurate to i 10%^. A major source of error isthe determination of w; in order to improve theaccuracy of this measurement, short cells were employedto avoid the measurement of small p and in some sam-ples N20 was added from previously mixed samples ofN 20 and N2.

By methods similar to those described for the 2224cm-' band, it was also possible to determine band in-tensities for the 2563, 2461, 1167, and 589 cm--' bands,but even with the smallest values of w employed it wasimpossible to establish the condition (v)w < I forthe 1285 cm-' band. The values obtained for N0band intensities are listed in Table I.

The present result for the 2224 cm-' band is in ex-cellent agreement with the value of 1867 (atm cm)-cm- reported by Thorndyke et al.8 and possibly in fairagreement with the value 1650 reported by Eggersand Crawford, 9 provided uncertainties in both sets ofdata are considered; however, the present resultis definitely larger than the value of 1617 reported byCalloman, McKean, and Thompson.10 The presentresults for the 1167 cm-' band agree within the limitsof experimental error with the value of 10.9 0.9reported by Goody and Wormell4 but are definitelylarger than the value of 8.5 listed by Eggers and Craw-ford. Finally, the value obtained for the 589 cm-'band is somewhat smaller than the value of 40 reportedby Thorndyke et al. but is considerably greater than thevalue 20.9 published by Eggers and Crawford. To theknowledge of the authors no values of band intensityfor the 2563 and 2461 cm-' bands have previously beenpublished. It should be noted that the "scatter"in reported values of band intensity for the variousbands is rather large; further studies would seem to bein order.

Table I. N20 Band Intensities f k(v)dv

Band Intensity(cm-,) (atm cm)-' cm-'2563 44 62461 11.5 1.52224 1850 ±t 1851167 12.0 ±t 1.2589 33 4

July 1962 / Vol. 1, No. 4 / APPLIED OPTICS 481

P ,, i n11 tmos C

i.�9- 1 3 4 5.66- 28.0 1 1.8 NO

112 47.3- 2 24 94 6392 166 I- 8 51 359 , YU

----------- I_ i ,

0

20

40

60

80

100

The authors wish to express their appreciation to

Wilbur France and E. B. Singleton who assisted in cer-

tain aspects of the present work and to Carl McWhirt

and his colleagues in the Physics shop for their careful

work in the construction of apparatus. Finally, one

of the authors (Dudley Williams) wishes to express his

appreciation to P. Swings and M. Migeotte for the use

of the library and other facilities at the Institut d'Astro-physique, Universite de Li6ge, during the preparation

of this article.

References1. D. E. Burch, E. B. Singleton, and D. Williams, Appl. Opt.

1, 359 (1962). The symbols and nomenclature used in thepresent article were introduced in this reference. In accord

with the new A.I.P. glossary of optical terminology, frac-

tional absorption A (v) is called spectral absorptance in the pres-ent paper and the earlier term total absorption fA(v)dv isnow called total absorptance.

2. J. N. Howard, D. E. Burch, and D. Williams, J. Opt. Soc.Am. 46, 186, 237, 242, 334, 452 (1956).

3. H. W. Thompson and R. L. Williams. Proc. Roy. Soc.A208, 326 (1951).

4. R. M. Goody and T. W. Wormell, Proc. Roy. Soc. A209,

178 (1951).5. W. Benedict, R. Herman, G. Moore, and S. Silverman,

Can. J. Phys. 34, 830, 850 (1956).6. W. M. Elsasser, "Harvard Meteorological Studies No. 6,"

Harvard University, 1942.7. G. N. Plass, J. Opt. Soc. Am. 50, 868 (1960).

S. A. M. Thorndyke, A. J. Wells, and E. B. Wilson, J. Chem.

Phys. 18, 157 (1947).9. D. F. Eggers and B. L. Crawford, J. Chem. Phys. 19, 1554

(1951).10. H. J. Calloman, D. C. McKean, and H. W. Thompson, Proc.

Roy. Soc. A208, 332 (1951).

ANNOUNCEMENT OF PROGRAM ANDREQUEST FOR CONTRIBUTED PAPERSMANGER HOTEL, ROCHESTER, NEW YORKOSA 47TH ANNUAL MEETING, OCTOBER 2 TO 5, 1962

Invited Papers. There will be six invited papers by acknowledged authorities on a wide variety of subjects, including the Purcell

effect, space optics, light waves in nonlinear media, and optical glass. It is hoped that many contributed papers will be offered

on these as well as other topics of interest to OSA members. The dinner speaker will be Crawford Greenewalt, President of Du

Pont, who will show slides of humming birds and high-speed motion pictures of birds and insects in flight.

Rochester, New York, is the home of the Institute of Optics and of many industries of an optical and general scientific nature.

October 2nd therefore has been assigned to plant and other visits. Three full days of invited and contributed paper sessions will

follow. A choice of full-day and half-day trips to other points of interest will be offered on Saturday, October 3rd.

Institute of Optics will hold an open-house all day on Tuesday, October 2nd, with a lecture and program related to education in

optics in the evening.

Ladies' Program. A varied and complete program is planned, including leisurely local and day trips to the Naples Wineries

or the Syracuse China Works.

Hotel. Headquarters will be located in the Manger Hotel, but downtown motel and other hotel accommodation is'available.

Midtown Plaza, just opened with national acclaim, is adjacent to the Manger Hotel and provides unusual facilities for-shopping,

meals, and parking.

Applied Optics semiannual meeting of Editors, Reporters, and Patents Panelists will be held at noon on Thursday, October

4th in the Manger.

Annual Business Meeting. The Annual Business Meeting of the Society will be held on Friday, October 5th.

George Eastman House. Plan to stay Friday evening for an event at George Eastman House, including showing of early movies

and viewing of the recently opened Mees Gallery.

Abstracts of Contributed Papers. An Abstract Form for submission of contributed papers is available from the Executive Secre-

tary. Presentation time will be limited to fifteen minutes. More than one paper by the same author or coauthors on closely

related topics will be accepted only if time permits; the prior choice should therefore be clearly indicated. Because blackboards

are almost useless in a large auditorium, overhead projectors will be substituted. Lantern slides, infinitely preferable, should have

large type and a minimum of information per slide.

Abstracts must -be in theNO POSTDEADLINE PAPERS

Executive Office by July 16, 1962.CAN BE ACCEPTED FOR THIS MEETING.

1155 Sixteenth Street, N.W.

Optical Society of AmericaMary E. Warga, Executive Secretary

Washington 6, D.C.

482 APPLIED OPTICS / Vol. 1, No. 4 / July 1962