shuttle lidar resonance fluorescence investigations 1: analysis of na and k measurements

Shuttle lidar resonance fluorescence investigations.1: Analysis of Na and K measurements

Shoou-Dyi Yeh and Edward V. Browell

A Shuttle lidar technique based on the detection of backscattered resonance fluorescence radiation has beennumerically modeled and applied to the measurements of sodium (Na) and potassium (K) number densityin the upper atmosphere (80-110 km). The simulations use recently defined lidar system parameters andtake into account the effect of saturation of atomic absorption due to the high intensity of laser pulses. Suchan effect is shown to be important in daytime measurements, when there is a need to narrow the laser beamdivergence in order to reduce the background light. When the saturation effect is important, an optimallaser beam divergence can usually be found as a result of a trade off between the reduction of signal return(due to saturation) and the reduction of background level (by narrowing the receiver field of view). A proce-dure for calibration of the saturation effect is discussed. The Shuttle lidar measurement capability for Naand K is compared to conventional techniques and requirements for conducting scientific investigations inthe mesosphere.

I. IntroductionMeasurements of alkali atoms (Na and K) in the

upper atmosphere (80-110 km) have been demon-strated using ground-based lidar systems.' These lidarmeasurements have achieved better spatial resolutionthan conventional passive photometric methods andprovided useful information for the understanding ofatmospheric processes such as vertical exchange andwave motion among others. Lidar systems are alsomore versatile than the passive techniques in that lidarsystems can more easily make measurements of thevertical distribution of these atomic species at night andduring the day with degraded resolutions. With therecently proposed evolutionary Shuttle-borne lidarsystems2 3 this capability may be extended to coverwider geographic areas needed to define Na- and K-layer characteristics with 3-D mapping achieved onsequential orbital passes. Hence one objective of thispaper is to assess the performance and application ofa recently defined Shuttle lidar system3 for the mea-surements of sodium (Na) and potassium (K) in the80-110-km region.

A second objective of this paper is to study the effectsof high-intensity laser beams on the lidar measure-ments, especially those due to the saturation in the

When this work was done, S.-D. Yeh was with Systems & AppliedSciences Corporation, Hampton, Virginia 23666; he is now withUniversity of Kentucky, Department of Physics & Astronomy, Lex-ington, Kentucky 40506. Edward Browell is with NASA LangleyResearch Center, Hampton, Virginia 23665.

Received 7 December 1981.

atomic absorption of laser photons. High-intensitylaser radiation has been known to cause saturation inatomic transitions among other things4; however, it hasonly recently been discussed in connection with lidarmeasurements.1 In this paper we show that for thesystem considered saturation of atomic absorption isnot an important factor in nighttime measurements butcould cause a systematic error of 40% or more for day-time measurements. In cases when saturation is im-portant we show that an optimal laser beam divergencecan usually be found as a result of a trade off betweenthe reduction of signal return (due to saturation) andthe reduction of background light (due to narrowing thereceiver field of view). Results of such a trade off mustbe considered in the design of a Shuttle-borne lidarsystem.

In this paper we discuss the lidar equation for reso-nance fluorescence measurements and the varioussources of measurement error. The saturation effectand its calibration are described, and an estimate of theerror in the effective resonance fluorescence cross sec-tion is given. The alkali atom number density profilemodels and the lidar system parameters used in themeasurement simulations are discussed along with thesimulation results.

II. Resonance Fluorescence Lidar EquationThe measurements of alkali atoms make use of the

detection of resonantly backscattered photons from theatomic species of interest. The detected signal (numberof photoelectrons) per laser shot can be written as

1 July 1982 / Vol. 21, No. 13 / APPLIED OPTICS 2365

P K= (Az2 (0o + naeff) exp(-2r), (1)(ZL -Z2

where Az = vertical range bin size,ZL = lidar altitude,

z = altitude of the observation point,/% = backscattering coefficient due to mole-

cules other than the species of interest,n = number density of the species to be mea-

sured,Ueff = effective backscattering cross section per

molecule by the species to be measured,T= optical thickness from z to ZL can be cal-

culated asfL att(z)dz;

atot(z) is the total extinction coefficient ataltitude z,

KS = product of a collection of system-depen-dent parameters ArElijqX/(hc),

Ar = area of receiver,El = energy per laser pulse,7 = system optical transmittance,q = quantum efficiency of detector,X = wavelength,h = Planck's constant, andc = speed of light.

Usually the signal return P, is measured, and fromthe idar equation [Eq. (1)] the number density n of thespecies of interest can be deduced by

n = 1 [P, (ZL - pZ)2 ](+2i) - 3 (2)

In doing so we have to know ceff, K5, Az, (ZL - )2 , ,and /0 to some accuracy. The uncertainties in thesequantities, in addition to the error in signal measure-ment, will propagate and become the measurementerror of n. In Sec. III we discuss the uncertainties inthese quantities and how they are treated in the simu-lations.

III. Error AnalysisThe system-dependent constant K requires cali-

bration, which can be done by measuring the signal re-turn from a region of the atmosphere where the back-scattering is strong enough, the molecular density isknown to good accuracy, and it is optically thin from thelidar observation altitude to the calibration region. Theregion chosen is often near the altitude of 30 km, whereRayleigh backscattering provides a good signal, and themolecular density is known to within 3%.5 It is opticallythin from the observation point at 110 km to the cali-bration point at 30 km so that transmission error in-troduced in the calibration process will be negligible.However, it must be noted that, if a wavelength withinthe strong absorption band of an atmospheric speciessuch as ozone is used, the transmission error will becomeimportant. The measurement of Mg+ ion using a2796-A wavelength is a good example and will be con-sidered carefully in a subsequent study.

Using the lidar backscattered signal [Eq. (1)] from thecalibration and observation points, to eliminate theconstant K5, one can write the number density of thespecies of interest as

n = - (PQ3 - 30),Oeff

(3)

where P = [PS(ZL - Z) 2]/[Pc(zL - Zc) 2 ] is the ratio ofrange-corrected signals between the observation andcalibration points; Q = exp[-2(rc - r)] is the two-wayattenuation factor between the observation and cali-bration points; r and rc are optical thicknesses from thelidar to the observation and calibration points, respec-tively; f3c is the backscattering coefficient at the cali-bration point, which is predominantly Rayleigh; and ois the backscattering coefficient at the observation pointdue to molecules other than the species of interest.

From Eq. (3), and following the technique describedin Ref. 6, the error in the number density n/n can bewritten in the following form:

(3n 2 = 30,.eff2 + f(LP)2 + (6Q12+ (foA \21 +

n (eff P Q ) ki30, J f leffl

+ (1oI 2f 10 12.\ 30 I ef (4)

In the case of measurements of Na and K in the upperatmosphere, terms containing 30/n O-eff are negligiblesince t0/nOeff - 10-6 << 1. The [5Q)/Q]2 term is alsonegligible because the optical thickness between theobservation and calibration points is small when thecalibration point is chosen at an altitude of -30 km.This assumption introduces an error of less than -0.5%in the number density error.7 Equation (4) may thenbe approximated as

(3nl2 (6ceff)2 + (fp)2 + kLoc_)n } \ aeffl vP # \oc (5)

Thus Na and K concentration uncertainties are mainlyfrom the uncertainty in signal measurement, the un-certainty in the effective cross section, and the uncer-tainty in the molecular number density at the calibra-tion point. As will be seen from simulations later in thepaper, the most important uncertainty is the signalmeasurement error.

The complete error expression [Eq. (4)] is used in thesimulation program to calculate the error. The mo-lecular density error is assumed to be 3%, and thetransmission error (Q)/Q is calculated following amethod presented in an error analysis of aerosol mea-surements by Russell et al.

7 Since it is not an impor-tant error source in our case, we will not discuss it fur-ther. The signal measurement error is calculated byassuming Poisson processes for the arrivals of signal andbackground photons. Thus

_____p + I P +PI\(6P)K(P+pB2 + P ) (6)

where PB is the background level (number of photo-electrons), and P and P are the signal levels from theobservation and calibration points, respectively.

The uncertainty in the effective resonance fluores-cence cross section also contributes to the error of the

2366 APPLIED OPTICS / Vol. 21, No. 13 / 1 July 1982

measured number of densities of Na and K as shown inEq. (4). This uncertainty is due to the uncertainty inthe temperature at the observation point. A discussionof the estimate of the temperature and fluorescencecross-section uncertainties is given in Sec. IV.

IV. Effective Cross Section and its UncertaintyThe atomic absorption line of Na and K has a

Gaussian line shape in the upper atmosphere due toDoppler broadening, and the emitted laser energy is notmonochromatic; hence not all the laser energy is ab-sorbed with the same probability. We can, however,maximize the absorption by locking the laser line to theabsorption peak of the atom. In such a case an effectiveabsorption cross section is obtained by convolving thelaser line shape with the atomic line shape. Since theDoppler profile is temperature dependent, the effectivecross section will depend on the temperature, and anuncertainty in the temperature will lead to an error inthe effective cross section.

To estimate the uncertainty in the effective crosssection we assume a Gaussian line shape for the laserenergy:

- - exp(-4 ln2AA 2/7Y2),

where AX = X - X0 is the wavelength separation fromline center X0, and Yj is the laser linewidth (FWHM).The laser line centers for sodium and potassium mea-surements are 5890 and 7699 A, respectively. The laserlinewidth is taken to be 1 pm in accordance with therecent GE study.3 The atomic Doppler line shape isgiven by

- - exp(-4 ln2AX2/y2),

where the Doppler width (FWHM) is given 'YD = [(2ln2kT)/(Mc2 )]j/2 X0 , and

where k = Boltzman constant (1.38 X 10-23 J/K),T = temperature (K),

Xo = line center (A),M = molecular mass (mass number X 1.67 X

10-27 kg), andc = speed of light (3 X 108 m/sec).

The effective cross sections for Na and K obtained byconvolving the Gaussian laser line shapes with theDoppler absorption line shapes are shown in Table I fortemperatures ranging from 100 to 350 K. For a givenuncertainty in temperature one can estimate the un-certainty in the effective cross section from Table I. Forexample, at a temperature of 200 K ± 25 K the error inthe Na effective cross section will be approximatelyfrom -3.4% to +4.1%. The simultaneous measure-ments of the temperature at the observation regionusing a Na absorption cell method with the same lidarreturns have been discussed by Blamont et al. ,8 in whichan uncertainty of 25 K was obtained using lasers ofmodest energy. Hence we will use this uncertainty inour simulations, which amounts to -4% in the effectivecross-section error.

Table 1. Temperature Dependence of Doppler Linewidth and EffectiveAbsorption Cross Section

af (effective absorptionTD(Doppler width in pm, cross section in 10-12

T(K) FWHM)a cm 2) b

Na K Na K100 0.884 0.89 8.38 6.20150 1.08 1.09 7.59 5.62175 1.17 1.18 7.31 5.38200 1.25 1.26 7.02 5.2225 1.33 1.34 6.78 4.98250 1.40 1.40 6.52 4.83300 1.53 1.54 6.07 4.53

a YD is given by 2[(4 1n2)kT]Xo/(Mc2).b Both laser line shape and the atomic spectral line shape are taken

to be Gaussian. Laser linewidth of 1 pm locked to the atomic spectralpeak is assumed.

V. Saturation Effects

A. Rate Equation AnalysisSince a high-intensity and well-collimated beam is

used in the lidar measurements of Na and K, it is pos-sible that saturation of the resonance fluorescence mightbecome important in such measurements. This isespecially true in daytime operation, when it is neces-sary to keep the receiver field of view small (andtherefore the laser beam divergence small) to reduce thebackground lighting level. The usual lidar equation[Eq. (1)], where the signal is proportional to the energyof the pulse, does not take the possible saturation effectinto account. When saturation is important, the signaldoes not increase linearly with the laser energy; how-ever, it increases more slowly or stops increasing, i.e.,saturates, at a certain level. This saturation is due tothe stimulated emission into the laser mode, which de-creases the number of excited-state atoms available forfluorescence isotropically (and hence into the backwarddirection).

The following analysis follows Megie et al.' and as-sumes a rectangular laser pulse. Other types of pulseshape have also been considered by the same authorsto show some effect on saturation. For the purpose ofsimulations and theoretical estimates of the saturationeffect on the signal measurement a rectangular pulseappears to be adequate.

The rate equation for the upper (excited) state pop-ulation ne(t) is given by

dne _e Q 1 N(thr(Q)dt tN (ZL -Z)

2Q2 e

ZL-e - ( ) (7)

where the first term accounts for the spontaneous decayof the excited state, the second and third terms are dueto absorption from the ground state and stimulatedemission from the excited state, respectively, and

n = excited plus ground state population,Q1 = one-way attenuation factor from the lidar to

the observation point,Q = laser beam divergence (solid angle),


I-z

al

< R0

Cr NRz

I-.5

.5

, UNSATURATED _

/,,,~~~ . , .,

LASER ENERGY (ARB. UNIT)

Fig. 1. Comparison of saturated and unsaturated backscatteringsignals for calibration of saturation effect. The solid curve representsthe signal from a resonance cell containing the gas species of interest,the dashed curve is the straight-line extrapolation extending fromthe low-intensity limit of the measured curve, representing the un-saturated signal. El is the laser energy which gives a power densityin the resonance cell equal to that in an actual shuttle lidar mea-

surement. The saturation factor is obtained as NR/NR.

tN = natural lifetime of the excited state, typically10-8 sec,

N(t) = number of laser photons at time t, andaeaf = effective absorption cross section (=4 7roeff).

For a rectangular pulse of duration tL and total numberof photons No,

N()No/L, 0 < t < tL, 8N(t) = o, 8tL

Equation (7) can be solved with the initial conditionne (0) =0 to yield

,nt' [1 -exp(-t/t')], 0 < t < tL,

ne(t) = (9)

-t' [1 - exp(-tL/t')] exp[(tL - t)/tNI, t > tL,,2t,

where1 1 1 (ZL - Z)2 QtL-=-+- and ts =

t' tN ts 2Q NOu~ef

Sometimes t is referred to as the saturation time andis the characteristic time of an occurrence of the stim-ulated emission (or absorption). When t is smallcompared with tN, the natural lifetime of the excitedstate, stimulated emission occurs more often than thespontaneous emission, and the saturation effect be-comes important. From the expression for t, one easilysees that the saturation time is inversely proportionalto the laser power density and the absorption crosssection. This suggests that to reduce the saturationeffect we should make the pulse longer or make thebeam wider for a constant pulse energy. The pulsedurations used in this paper are 13 nsec for Na and 10nsec for K.

The number of fluorescence photons collected at thereceiver for a range bin size of Az is given by

ArQiQAt pAz/c n,(t)

47r J tN

+ NO 1 _ tN tN/ts1 + tN/tA , tL + tN/ts

X {exp [-- (1 + tN/ts)]-i) (10)

whereArQ'

N= 1 ( na(f2AzNo

is the number of backscattered photons collected at thedetector when no saturation is considered. It is easy tosee from Eq. (10) that the important parameters are tNand t. When t >> t (low power density limit), NR

NR. There is no saturation. When t<< tN (high powerdensity limit),

NR N t I - [exp(-tL/ts) -1

Saturation will decrease the backscattered signal.

B. Calibration of the Saturation EffectAs seen from the above analysis saturation tends to

decrease the backscattered fluorescence signal level. Ifthis is not properly taken into account, it would lead toan underestimate of the number density of the speciesunder measurement. This systematic error can be aslarge as 40% for the lidar system we are considering.Furthermore, the decrease in signal level will decreasethe signal to noise ratio from its unsaturated value, andin the simulation saturation has to be properly consid-ered.

The systematic error can be corrected by calibrationusing a resonance cell containing the gas sample of in-terest (Na or K in our case). To ensure the same pulseshape and roughly the same beam shape the same lasersystem that is to be used in the Shuttle is transmittedinto the resonance cell. The backscattered fluorescencephotons from a certain spot in the cell are measured.By varying the intensity of the laser beam, the measuredbackscattered signal will be similar to the solid curve inFig. 1. The dashed curve is the straight-line extrapo-lation extending from the low-intensity limit of the

120

110

100

C- 90

80

70c

.5No EXT COEFF ( 10iKM)

1 2K EXT COEFF ( 16 KM )

1.5 2

Fig. 2. Number density profiles of sodium and potassium used inthe simulations.


__1

I.. I I I .. I N- --,,,1,,N,, ,

,

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

I

Table I. Shuttle Lidar System Parameters Assumed in the Simulations

Parameter Na K

Wavelength (Am) 0.589 0.770Energy per pulse (j) 0.25 0.12Pulse duration (Asec) 0.013 0.01Pulse repetition rate (Hz) 10 10Laser linewidth (pm) 1 1Laser beam divergence (mrad) 0.18,4.72a 0.108,4.72a

Area of receiver (M2) 1.11 1.11

Receiver bandwidth (nm) 0.01 0.025Optical transmission (%)3.05b 3.16bPMT quantum efficiency (%) 20 12Receiver FOV (mrad) 0.23,6.0ac 0.137,6.0ac

Absorption cross section (cm 2) 9.0 X 1 0 -1 2 d 6.6 X 1 0 -1 2 dMass number 23 39

a The first number represents daytime operations, the second number represents nighttime operations. The daytime beam divergencesare the optimal values discussed in the text. The nighttime beam divergences are limited by the telescope field of view.

b Three aluminum mirror surfaces, four uncoated lens surfaces, and an interference filter are assumed, see Ref. 3.c These values are 1.27 times the laser beam divergences.d Peak absorption cross sections at 200 K.

measured curve representing an unsaturated signal.Since the area of illumination by the laser beam is pro-portional to the square of the distance from the emitterto the observation point, we can determine one point E1in Fig. 1, which gives a power density at the observationpoint in the cell equal to that in an actual atmosphericmeasurement. If, for example, El is the laser energyused in the Shuttle case and d is the distance from thelaser to the observation point in the cell, E = Eld2 /(zL- z)2. The saturation factor fs can be obtained fromFig. 1 to be NR/N'. In using Eq. (2) to deduce thenumber density the measured signal should be dividedby f.

VI. Simulations

A. Models and ParametersLarge seasonal and diurnal variations of the alkali

atom densities are often observed in the 80-110-km re-gion.9 For the purpose of the simulations we take thenominal models from the study of Megie et al. 1 shownin Fig. 2.

The system parameters used are in accord with therecent GE study,3 and are listed in Table II.

The background lighting level is calculated by takingthe solar continuum radiation outside the atmosphere(1700 W m-2,m-l for Na at 5890 A, 1185 W m-2 m-1

for K at 7699 A)10 multiplied by a factor which includesthe effects of Na and K Fraunhofer lines"1 in the solarspectrum, small bandwidths of the detector used, anda two-way attenuation factor down to the surface andback to the lidar. The Fraunhofer factor depends onthe bandwidth of the detector used; a reasonable esti-mate of 35% for sodium and 50% for potassium is used.A surface albedo, taken to be 100% in the simulationsto represent the worst case, is to take care of the re-flection from the surface or cloud. The moonlit back-ground in the nighttime operation is taken to be 10-6times smaller than the daytime case.

B. ResultsThe simulation results for the measurements of Na

and K are shown in Figs. 3-8. Figure 3 shows the signallevel/shot/km vertical range for both daytime andnighttime operations. One will notice the reduction ofsignal level in the daytime case due to the saturationeffect resulting from the narrowing of the laser beamdivergence in an effort to reduce the backgroundlighting. The saturation factor defined earlier, A =

NR/N', is shown in the inset from 70 to 120 km for thedaytime operation. The slight change of the saturationfactor within this range is due to the change in the il-luminated area. There is no saturation in the nighttimecase because of the large laser beam divergence used.The signal level is smaller in the K case than in the Nacase due to smaller amount of K atoms and less laserenergy per pulse.

A trade off situation emerges as a result of the satu-ration effect: on the one hand, we would like to havenarrow beam divergences to minimize the backgroundlevel; on the other hand, we would like to have largebeam divergences to reduce the saturation effect andthus increase the signal level. An optimal laser beamdivergence/receiver field of view can be found to mini-mize the signal measurement error. In Figs. 4 and 5 thesignal measurement error vs the beam divergence isplotted, as well as the saturation factor, for typicalnumber densities of Na and K. For both Na and Kcases a minimum signal measurement error can befound at a certain beam divergence (L = 0.18 mrad forNa, OL = 0.108 mrad for K). These optimal beam di-vergences meet the eye safety requirement as stated inthe G.E. report3 and are used in subsequent simula-tions.

When the optimal beam divergences are used, thedaytime saturation effect is important as can be seen inFigs. 4 and 5. In the Na case (Fig. 4) a saturation factorof 0.65 has to be incorporated in the data reduction,while in the K case (Fig. 5) the saturation factor is-0.57.


120 -

110

X 100Ci

C -C= -

70-0.0

No SIGNAL(+ PHOTOELECTRONS)

5 10 15

0.2 0.4 0.6 08 1.0K SIGNAL ( PHOTOELECTRONS)

Fig. 3. Signal returns (numbers of photoelectrons detected) from theobservation region for daytime and nighttime measurements. Thedaytime signals are lower than the nighttime signals due to the useof a smaller laser beam divergence which causes a larger saturationeffect. (The system parameters used are shown in Table II.) Theinset shows the saturation factor across the altitude region for thedaytime measurement case, there being no saturation in the nighttime

case.

6001

0Cit

ar4001

200)

0 .2 4 .6 .8 1.0

LASER BEAM DIVERGENCE mrod)

1.2

The measurement error across the 70-120-km regionis shown in Fig. 6 for Na and K for a single laser shot anda 1-km vertical range. The errors shown in these figuresinclude a 4% uncertainty in the effective resonancefluorescence cross section. The dominant error sourceis the signal measurement error. The errors can bereduced by relaxing the spatial resolutions accordingto the factor (Az X Ax)-1/ 2 , where Az and Ax are thevertical and horizontal resolutions, respectively.

The vertical-horizontal resolution trade off shownin Fig. 7 (for Na) and Fig. 8 (for K) is expressed as theamount of signal integration necessary to achieve cer-tain accuracy requirements. These figures can be usedto determine if the requirement for a scientific objective

S

U)

.8 C-(

4

.6F

4

Fig. 4. Signal measurement error and the saturation factor vs thelaser beam divergence for the case of sodium for two typical altitudesand number densities. The arrow on the abscissa indicates the op-timal beam divergence. The corresponding saturation factor can be

read from the dashed curves.

The laser pulse duration also has an effect on satu-ration. An increase in the pulse length will decrease thepower for a given total pulse energy and thus reduce thesaturation effect and vice versa. Thus the laser pulseduration should be considered when choosing a lasersystem for these measurements.

For nighttime operations, since the backgroundlighting is not an important factor, we can try to increasethe detector bandwidth and thereby improve the opticaltransmission efficiency to increase the signal level.Simulation results for three bandwidths and corre-sponding transmission efficiencies are shown in TableIII. An increase in the detector bandwidth improvesthe signal measurement. The same test for the daytimeoperations confirms that the smallest bandwidths yieldthe smallest signal measurement error, which are al-ready in use in the simulations.

.8

.6 I

0

4C

.2

LASER BEAM DIVERGENCE~m rod)

Fig. 5. Signal measurement error and the saturation factor vs thelaser beam divergence for the case of potassium for two typical alti-tudes and number densities. The arrow on the abscissa indicates theoptimal beam divergence. The corresponding saturation factor can

be read from the dashed curves.

K ERROR (%)

200 400 600 800 1000120

No_

K

_ I SHOT_AZ I KM -

NH

NIGHT-

>^YilX~~ I IS YO 10

0 20 40 60 80 1(00

No ERROR(%)

Fig. 6. Errors in the measured number densities of Na and K acrossthe 70-120-km region. The errors include a 4% error in the effective

cross section and a 3% error in the molecular number density.


I - I a . I I .No

- I SHOT 91kmA7.- _< 5

DAYTIME %1 9 N IOOkm

/ Imkm, 220eCr

- II - ERROR

--- SATURATION FACT(

p/ 91km, 2310cn 3

. @ | P | t | l~. . I I I

. I I

*OR

1000

0

C-

I4

100

10

0.1 0.

- - ~ -Ir I111IrIm 1,rrIr&10km

(220cni3

1 lo% =- ~~20% ---_ -

D0 Na

020~~~~~~~~

K 2 -~~~~~~~~~~~~~~~~~~~~~~-

o N0 -' C~ -

'N- 91 km > 2 0 \_ (

23

10 c3) \\\

I \ ." 1 10 100

HORIZONTAL RESOLUTION (km)

1000

Fig. 7. Horizontal-vertical resolution trade off for Na. The straightlines represent the amount of signal integration (along horizontaltrack integration or vertical range bin integration) to satisfy givenmeasurement accuracies. Three sets of horizontal and vertical lines,labeled 1, 2, and 3, represent spatial resolution requirements for dif-ferent scientific purposes as discussed in the text. Two typical so-dium number densities are chosen to represent the higher and lowerends of the number density encountered in this region. The labelsD1 o, D2 0, N1 o, and N2 0 represent daytime and 10%, daytime and 20%,

nighttime and 10%, and nighttime and 20%, respectively.

1000

100

10

-J

4

0.1 L0.1 10 IoC

HORIZONTAL RESOLUTION (km)

Fig. 8. Horizontal-vertical resolution trade off for potassium. Thestraight lines represent the amount of signal integration (along hor-izontal track integration and vertical range bin integration) to satisfygiven measurement accuracies. The set of vertical-horizontal linesrepresents the spatial resolution requirements appropriate for sci-entific objectives discussed in the text. Two typical potassiumnumber densities are chosen to represent the higher and lower endsof the number density encountered in this region. The labels D50 ,D1 oo, N5 0 , and Nloo represent daytime and 50%, daytime and 100%,

nighttime and 50%, and nighttime and 100%, respectively.

can be satisfied with the lidar system considered. InFig. 7 three sets of horizontal and vertical lines aredrawn to indicate the resolution requirements for dif-ferent scientific purposes. The lines labeled 1, havinga resolution of Az X Ax = 5 X 100 km, are for the pur-pose of measuring parameters, such as the abundancesand large-scale motions, which need an accuracy of 20%.Figure 7 shows that these requirements can be met bythe lidar system under consideration during daytimeand nighttime conditions for a large range of sodiumnumber densities. Similarly, the system can also meetthe requirements labeled 2 in the figure, which are ap-propriate for the study of stratosphere-mesospherecoupling, for example, and require an accuracy of 10%.The requirements labeled 3, having a resolution of AzX Ax = 2 X 20 km, are for measuring parameters, suchas the eddy diffusion coefficient and the study ofsmall-scale motion, which need an accuracy of 10%.Figure 7 shows that the currently considered system cansatisfy these requirements only for high sodium con-centrations (such as 2310 cm-3 at 91 km) but not for lowconcentrations (such as 220 cm-3 at 100 km).

The measurement of potassium has been largely usedfor determining the Na/K abundance ratio, whichprovides information as to the origin of the alkali atomsin this region.1 12 This ratio has a value of -10 for alkaliatoms of meteoritic origin and a value of -50 for thoseof terrestrial origin.12 Due to such a large difference itdoes not require a high degree of accuracy of the Knumber density to differentiate them. The resolutiontrade off shown in Fig. 8 is for measurement errors of 50and 100%. Two lines representing a spatial resolutionof Az X x = 5 X 100 km are drawn in Fig. 8. Thesystem assumed in these calculations can meet the re-quirements for investigating the ratio of Na/K, exceptin the case of low K concentrations during the day-time.

VII. SummaryNumerical simulations of the measurements of so-

dium and potassium atom number densities in the80-110-km region from a Shuttle-borne lidar systembased on the detection of resonantly backscatteredfluorescence photons have been presented. Lidarsystem parameters used in these simulations are con-sistent with the recent GE Atmospheric Lidar Multi-user Instrument System Definition Study.3 Particular

Table Ill. Shuttle Lidar System Performance for Three Detector Bandwidths

Transmission Signal Background SignalBandwidth (nm) efficiency (%) (No. of photoelectrons) (No of photoelectrons)a error (%)

Nab 0.01 3.05 1.58 (1.58)c 1 (0.0014)0 102 (79)c0.2 6.1 3.16 (3.16)c 40 (0.0561)c 208 (57)01 30.5 15.8 (15.8)c 998 (1.40)c 201 (26)c

Kb 0.025 3.16 0.321 (0.548)0 4.79 (0.0091)c 704 (136)c0.2 6.32 0.642 (1.10)c 76.7 (0.146)c 1370 (102)c1 31.6 3.21 (5.48)c 1917 (3.65)c 1360 (55)c

a Background level is calculated to be 1.1 X 1013 photons cm- 2 sec . nm-1 sr-1 for Na with 100% reflecting surface, 35% Fraunhoferfactor, and 4.5 X 1013 photons . cm 2 -sec -nm-1 -sr-1 for K with 100% reflecting surface and 50% Fraunhofer factor.

b Assuming Na at 100 km with 220-cm-3 density and K at 90 km with 293-cm-3 density.c Numbers in parentheses are for nighttime operations.


.1

attention is paid to the saturation effect of the atomicabsorption due to the use of a high-intensity laser beam.The saturation effect is shown to be important duringdaytime measurements, resulting in systematic errorsof -40%, which can be corrected by an appropriatecalibration procedure. It is also shown that an optimallaser beam divergence can be found to minimize thesignal error as a result of trade off between signal satu-ration and background lighting. At the optimal laserbeam divergence the saturation factor is -0.65 for theNa case and 0.57 for the K case.

For nighttime measurements the use of largerbandwidth filters with higher optical transmission ef-ficiencies can yield better signal measurements. Fordaytime measurement smaller bandwidth detectors arepreferable.

The spatial resolution that can be achieved with thecurrently considered Shuttle lidar system (Figs. 7 and8), e.g., resolution down to Az X Ax = 1 X 2 km for Nanear 91 km, are superior to those typically achieved bypassive techniques of Az X Ax = 2 X 300 km. In ad-dition, the resonance fluorescence lidar technique iscurrently the only remote method for obtaining a directmeasurement of alkali atom densities in the meso-sphere. Passive techniques have difficulty inferring Naand K concentrations from airglow measurements dueto resonance radiation effects along the optically thickline of sight during the daytime and because nighttimeairglow measurements detect only the chemically ex-cited atoms.

The simulation results suggest that the performanceof such a system can meet most of the identified scien-tific requirements for investigation of Na and K in themesosphere with daytime and nighttime measurementsand 3-D profiling. Thus, lidar observations of free Na

and K in the 90-km layer can provide new insights intothe origin, maintainance, and dynamics of this impor-tant region of the atmosphere.

The research reported in this paper was conductedin association with the Shuttle Lidar Study Office at theNASA Langley Research Center and partially sup-ported under NASA contract NAS1-16115.References

1. G. Megie, F. Bos, J. E. Blamont, and M. L. Chanin, Planet. SpaceSci. 26, 27 (1977) and references therein.

2. E. V. Browell, Ed., "Shuttle Atmospheric Lidar Research Pro-gram-Final Report of Atmospheric Lidar Working Group,"NASA 433 (1979).

3. R. V. Greco, "Atmospheric Lidar Multi-user Instrument SystemDefinition Study," NASA CR-3303 (1980).

4. See, for example, J. I. Steinfeld, Molecules and Radiation: AnIntroduction to Modern Spectroscopy (MIT Press, Cambridge,1974).

5. J. Laver, "Approach for Estimating Errors in Density Profiles,"Appendix D of SAGE Ground Truth Plan, NASA TM 80076(1979); P. B. Russell, B. M. Morley, J. M. Livingston, G. W.Grams, and E. M. Patterson in "Improved Simulation of Aerosol,Cloud, and Density Measurements by Shuttle Lidar," Final Re-port, NASA contract NAS1-16052 (1981).

6. See, for example, P. R. Bevington, Data Reduction and ErrorAnalysis for the Physical Sciences (McGraw-Hill, New York,1969), p. 336.

7. P. B. Russell, T. J. Swissler, and M. P. McCormick, Appl. Opt.18, 3783 (1979).

8. J. E. Blamont, M. L. Chanin, and G. Megie, Ann. Geophys. 4,833(1972).

9. A. J. Gibson and M. C. W. Sandford, J. Atmos. Terr. Phys. 33,1675 (1971) and Ref. 1.

10. M. P. Thekaekara, Appl. Opt. 13, 518 (1974).11. R. M. Goody, Atmospheric Radiation (Oxford U. P., London,

1964), p. 417.12. H. M. Sullivan and D. M. Hunten, Can. J. Phys. 42, 937 (1964).

Meetings Calendar continued from page 2338

1982October

? Int. Symp. on the Measurement of Geometrical Quan-tities, Beijing, China Secretariat, Chinese Society for.Measurement, P.O. Box 1413, Beijing, China

4-6 Technology for Space Astrophysics-The Next 30 YearsConf., Danbury D. McCarthy, Mail Station 879,Perkin-Elmer Corp., 100 Wooster Hgts. Rd., Danbury,Conn. 06810

4-8 Effective Engineering Management course, BostonCont. Ed. Inst., 10889 Wilshire Blvd., Suite 1030, LosAngeles, Calif. 90024

4-8 IEEE's Industrial Applications Group, Electrostatics,Electrophotography and Electrostatic Precipitators,San Francisco M. Hirsh, 28 Spier Ave., Rochester,N.Y. 14620

5-8 Holographic Data Non-Destructive Testing Conf., Du-brovnik D. Vukicevic, IFS-Inst. Phys., U. Zagreb,YU/41000 Zagreb, Bijenicka 45, Dubrovnik, Yugo-slavia


continued on page 2404

shuttle lidar resonance fluorescence investigations 1: analysis of na and k measurements

Documents