wavelength dependence of backscattering and extinction of kaolin dust at co_2 laser wavelengths:...

Wavelength dependence of backscattering andextinction of kaolin dust at CO2 laser wavelengths:effect of multiple scattering

Avishai Ben-David

A multiple wavelength, pulsed CO2 lidar system is used to measure spectral backscattering and extinction

of kaolin dust of different optical thicknesses. The measurements show that the wavelength dependence

of spectral backscattering changes with increased multiple scattering, whereas the spectral extinction

remains relatively unchanged. A simple analytical two-stream radiative transfer model is used to

confirm the measurements qualitatively. Several equations were derived from the model to show that in

general the wavelength dependence of backscatter is less dependent on wavelength for a multiple-

scattering case. Therefore, the aerosol cloud becomes a diffuse target that is more flat in its spectral

reflectance as multiple scattering increases. An application to differential absorption detection is

discussed and shows that, in general, the effect of multiple scattering on the backscattered signal from

aerosols will tend to reduce the error in deducing the average path-length concentration of the absorbing

trace gas.Key words: CO2 lidar, differential absorption detection, aerosol backscattering, multiple scattering.

1. IntroductionKnowing the optical properties of aerosol dust isimportant for designing electro-optical systems andfor modeling the effect on propagation of light in theatmosphere. As CO2 lidar technology becomes moreadvanced and is used for multiwavelength measure-ments,' information on the wavelength-dependentbackscattering and extinction of aerosol dust parti-cles is required.

Currently many CO 2 lidar systems that use adifferential absorption detection (DIAL) technique2

are used for the remote sensing of atmospheric tracegases. For atmospheric remote sensing, where thedetected signal is backscattered by aerosols and isattenuated by the trace gas of interest, the wavelength-dependent backscattering coefficient of aerosols is animportant parameter for determining the accuracy ofthe deduced concentration of the trace gas. Thevolume-backscattering coefficient of aerosols in theinfrared is relatively small. Thus only a few fieldmeasurements of backscattering and extinction, usu-ally at only a few wavelengths, are reported in the

The author is with the Science and Technology Corporation,Edgewood, Maryland 21040.

Received 3 March 1992.0003-6935/93/091598-08$05.00/0.© 1993 Optical Society of America.

literature. 3-1 A complete laboratory characteriza-tion of aerosol backscattering, for which only singlescattering contributed to the spectral backscatteringmeasurements, was made by Powell et al. 12

Here spectral field measurements of backscatteringand extinction of kaolin dust are presented in the 9 to11-jim wavelength range. As the quantity of dustincreases, multiple scattering contributes more to themeasured backscattered signal. The measurementswill show the effect of the dust quantity on thespectral backscatter and extinction measurements.A simple analytical two-stream radiative transfermodel' 3 is applied to confirm the measurements andto give insight into the multiple-backscattering andextinction spectra. The effect of multiple scatteringon DIAL measurements will be addressed.

2. ExperimentIn this experiment the CO 2 lidar system transmittedtwo groups of wavelengths at a repetition rate of 10groups per second. Each group contained 10 wave-lengths spaced at intervals of 10 ms. The laser-beam divergence is 3 mrad, the pulse width is 1 jis,the detector-time constant is 0.4 Ris, the amplifierelectronic bandwidth is 5 MHz, the sampling rate is50 MHz, and the receiver field of view is 8 mrad. Adetailed description of the CO 2 lidar system is givenby Ben-David et al.I A hard target made of sand-

1598 APPLIED OPTICS / Vol. 32, No. 9 / 20 March 1993

blasted aluminum (4 x 4 m) was placed at a distanceof 1280 m from the lidar, and an aerosol dust cloud5-10 m in depth was dispersed at a distance 740 mfrom the lidar (i.e., 540 m in front of the target).

Dust was dispersed while the lidar continuouslymeasured the backscatter from the cloud and thereflected signal from the target. Varying the dust-cloud density produced measurements from an opti-cally thin cloud and an optically thick cloud, as shownin Fig. 1. In this experiment backscattering fromthe aerosols is contained to a very small range (5-10m), and the absorption by vapors is along the path(i.e., 740 m to the aerosol cloud or 1280 m to the hardtarget). The long time decay of the backscatteredsignal from the cloud (Fig. 1) is a result of the slowtime response of the infrared detector and is not dueto aerosol dust between the cloud and the target.Measurements from the reflected signal off the hardtarget were used for calibrating of the lidar measure-ments and for measuring water vapor and ozoneaverage path-length concentrations. The aerosol sizedistribution of the kaolin dust was measured andapproximated by a size-distribution function, dn(r)/dr exp({ln(r/(r))2/[2 ln(or)2]}), where r is the aerosolradius ranging between 0.25 jim and 5 m, thestandard deviation is r = 1.682 Gum, and the meanradius is (r) = 0.44 jim.

3. Radiative Transfer ModelA detailed radiative transfer model is given by Bisson-nette14 for the propagation of a narrow light beam(i.e., a laser beam) in aerosol media; another suchmodel for an infinite plane-parallel beam (e.g., theSun) is given by Herman and Browning. 15 Althoughthese computations are quite accurate, they are com-plex, time consuming, and do not exhibit explicitdependence on the parameters of the problem. It istherefore advantageous to use a simple analyticalmodel, even though it compromises the accuracy ofthe calculation, to help develop greater understand-

1 laser pulse cloud target

c: 0.8-

v0.6-CDN

E 0.4-

0.2-

0 0.3 -0.6 0.9 1.2 1.5 1.8distance [kin]

Fig. 1. Pulse shape for the laser pulse (solid curve), and thebackscattering from an optically thin kaolin-dust cloud (A) and anoptically thick kaolin-dust cloud (). The location of the cloudand target are shown. The return signal from the target is aresult of a two-way extinction through the cloud.

ing of the behavior of the relevant parameters of theproblem.

A two-stream model (see van de Hulst, 3 Chap. 14)in which the scattering is divided into strictly forwardand backward scattering (i.e., transforming a three-dimensional problem into a one-dimensional prob-lem) is used. This model is for a steady-state illumi-nation and not for a time-dependent source of incidentradiation. A radiative transfer problem is consid-ered to be at a steady state if the source of radiationremains constant in the time required for a photon totransverse the scattering medium (i.e., there is suffi-cient time to establish a steady state). In this exper-iment the cloud depth is 5-10 m, so a photon takes- 30 ns to transverse the medium, whereas the laser

pulse is 1,000 ns in length (240 ns from zero energy tomaximum peak power and then a slow decay in theremaining 760 ns; Fig. 1). Therefore, approximat-ing the time-dependent radiative transfer problemwith a steady-state assumption is reasonable. Theslow time response of the receiver, which smears outthe backscattered laser pulse (see the target backscat-tered-pulse profile in Fig. 1 relative to the transmit-ted laser-pulse profile), will further improve thesteady-state assumption because single-scatteringevents and multiple-scattering events will be detectedby the receiver at the same time. This model is asimple analytical radiative transfer model for aninfinite plane-parallel incident beam (e.g., the Sun asa source) and thus does not take into account the fieldof view of the receiver and the receiver's geometry,which effect the magnitude of the detected multiple-scattering signal. Nevertheless, the model is usefulto study, qualitatively, the spectral backscattering ofa multiple-scattering problem, as will be shown inSections 4 and 5.

At this writing there is no exact method to computescattering properties from arbitrary irregular parti-cles. Solutions for scattering from shapes such asinfinite cylinders and spheroids16-18 were developed.An example of the irregular shapes of dust particles isgiven by Hill et al. 16 in Fig. 1 and by Pinnick et al. 19 inFigs. 7-9 below. These figures demonstrate thedifficult task of trying to model the shape of dustparticles. However, Mie theory, which applies tospherical particles, can be used to calculate scatteringproperties from irregularly shaped particles with asize parameter of 2rr/X < (3-5), where is theincident wavelength. 2021 For the kaolin-dust aero-sol size distribution used in this experiment, thelargest size parameter is less than 4, and mostparticles have a size parameter less than 0.3. Theoptical properties of the kaolin-dust aerosol sizedistribution at the 20 wavelengths used in the experi-ment were calculated with Mie theory and are shownin Fig. 2. The wavelength-dependent complex refrac-tive indices were taken from Powell et al. 12 In Fig. 2g denotes the asymmetry factor (i.e., the average ofthe cosine of the single-scattering angle), T the extinc-

20 March 1993 / Vol. 32, No. 9 / APPLIED OPTICS 1599

CPcu

a)N

coE0

Ca

tN

wavelength [m]

Fig. 2. Optical parameters computed by using the Mie theory forthe measured kaolin-dust aerosol size distribution: single-scattering albedo a (a), asymmetry factor g (+), extinction opticaldepth T (), scattering optical depth 'r (A), and volume back-scattering coefficient p (x).

tion optical depth, ;, the scattering optical depth, anda = ,/r the single-scattering albedo.

The parameters of the model are the single-scattering albedo a(X), the asymmetry parameterg(X), and the total optical depth r(X) of the aerosol sizedistribution n(r). The probabilities for the scatter-ing process are given byp(X) = a(X)[1 + g(X)]/2 for aforward scattering, q(X) = a(X)[1 - g(X)]/2 for abackward scattering, and by 1 - a(X) for an absorption.Wavelength dependency will be omitted from theequations to follow so that the notations are simplified.Using van de Hulst's notations, we see that UR(T, a, g)is the reflected fraction of flux and UT(r, a, g) is thetransmitted fraction of flux.

For an infinitely optically thick layer, the reflectedflux UR is

UR(r = ca, g)

2 - a(1 + g) - 2[(1 - a)(1 - ag)]'!2

a(1 - g) (

which can be simplified for g = 0 (isotropic scattering)to [1 - (1 - a)1/ 2 ]/[l + (1 - a)'/ 2], and for g = -1(only backward scattering) to 1 - (1 - a2)1/2 Va.For g 1 (only forward scattering) UR is zero, as wecan see by using l'Hpital's rule in Eq. (1).

The reflected flux UR (see van de Hulst,'3 p. 490)can be simplified for an optically thin layer where4(1 - a)(1 - ag)1!2 ] << 1, such that expfi[(1 - a)(1 - ag)1/2 ]} = 1 + 7[(1 - a)(1 - ag)'!2 ]. The nota-tion 7< will be used in all equations to follow toindicate an optically thin layer for which the aboveapproximation is valid. The reflected flux UR for anoptically thin layer is given by

UR( <, a, g) = 2-(1 - g)aT (2)

which for g = 0 becomes aT/[2(l + T) - aT], and forg = -1 becomes aT/(T + 1). The transmitted fluxUT (see van de Hulst,13 p. 490) is simplified for anoptically thin layer to

2UT(Tr, a, g) 2(1 ± r) - ar(1 + g) (3)

For g = 1 the exact transmitted flux is UT =exp[-(1 - a)T], which for a small optical depth T canbe written as 1/[1 + (1 - a),r], as is also confirmed byEq. (3).

Figure 3 shows the reflected flux UR computedfrom the kaolin-aerosol dust parameters of Fig. 2, fora layer with a spectral optical depth 7(X) with differentvalues for the maximum value of T(X). For a layerwith a maximum optical depth larger than 20 thereflected flux is independent of X (i.e., practically aninfinitely optically thick layer). Figure 3 shows thatas the optical depth increases, and therefore themultiple-scattering contribution to UR increases, thewavelength response of UR(X) changes and is shiftedfrom the 9-pm wavelength region to the 10-pmwavelength region. From this figure we can see twodistinct classes of the wavelength-dependent backscat-tered flux. The first is for an optically thin layer(T < 5), and the second is for an optically thick layer(7> 5).

The change of the wavelength-dependent backscat-tered flux can be qualitatively explained by the single-scattering optical properties of the kaolin dust in Fig.2. Figure 2 shows that the scattering optical depthpeaks at 9.5 ,um, but the fraction of absorption(1 - a) in the 9-p1m wavelength range is much larger(factor 2) than the fractional absorption in the 10-pmwavelength region. Therefore, although multiplescattering increases the number of photons collectedwith the receiver by redirecting photons into the fieldof view of the receiver, the distribution between the

0.8-

N0.6-

"CU0,&- 0.4-C

0.2

9.0 9.5 10.0 10.5 11.0

wavelength [Am]

Fig. 3. Reflected fraction of flux for a layer with spectral opticaldepth 'r(\) taken from Fig. 2 and normalized to the followingvalues: 0.1 (L), 1(+), 2 (*), 5 (E), 10(x), and 20 (A).


9-pm wavelength and the 10-[Lm wavelength is notequal because of the higher fractional absorption inthe 9-,um wavelength relative to the 10-pLm wave-length. Thus, more photons at the 10-.Lm wave-length are redirected to the receiver than photons atthe 9-jim wavelength. As a result, the spectralreflected flux will shift its peak to the 10-jim wave-length region with increasing multiple scattering (i.e.,increased optical depth).

Figure 4 shows -ln[UT] = T*, which can be viewedas the effective optical depth of a layer with an opticaldepth T caused by the multiple-scattering contribu-tion to the transmitted flux.22 This figure showsthat the wavelength dependence of T is practicallyindependent of wavelength, which can be explainedby the fact that scattering in the forward direction ismuch less sensitive to the refractive index of theaerosols than scattering in the backward direction(see, e.g., Coulson,23 p. 67).

4. MeasurementsMany sets of kaolin-dust backscattering were mea-sured on 8 October 1991 (10:40 a.m.) at DugwayProving Ground in Utah. Acquisition time for the20 wavelength measurements took less than 1 sec.The aerosol cloud was dispersed continuously, andwith a wind velocity of 1.5 m/s a steady flow of aerosoldust traversed the laser beam. The kaolin dust waspreanalyzed for its size-distribution function (seeSection 2) and was mixed well. Thus it is assumedthat the disseminated cloud was homogenous (i.e.,the same size distribution was present throughoutthe dissemination), and that all 20 wavelengths sam-pled the same dust-cloud condition (i.e., the sameconcentration of dust during one set of measure-ments).

Among the 20 wavelengths, those selected forwater-vapor DIAL detection in the 9-jim region were9R14 and 9R12; for the 10-jim region they were1OR22, 10R20, and 10R18, and for ozone DIALdetection they were 9P14 and 9P22. These wave-lengths were used to check the consistency and

0.8-

0N= 0.6-

0E.0.4-

0.2-

9.0 9.5 10.0 10.5 11.0

wavelength [m]Fig. 4. Effective optical depth T*(A) for a layer with spectraloptical depth T(X) taken from Fig. 2 and normalized to the followingvalues: 0.1 (U), 1(+), 2 (*), 5 (E), 10(x), and 20 (A).

C 0.8-CU

0~~~~0

0.6 H20

C0.2-,6

0

EC') 0Q4

CO ~~~~~H20

0 9.5 16.0 10.5 11.0wavelength [Am]

Fig. 5. Normalized atmospheric transmission measured with ahard target at a distance of 1280 m.

accuracy of the lidar measurements. Figure 5 showsthe normalized atmospheric transmission measuredfrom backscattering off the sand-blasted aluminumtarget at 1280 m prior to dust dissemination. Theabsorption wavelengths for water vapor (9R14 and1OR20) and ozone (9P14) are indicated in this figure.From the water-vapor absorption coefficients24 (mea-sured at 300 K and 13.3 mb water-vapor partialpressure), the partial pressure of the water vapor wascomputed to be 4.1 mb from the 9R14 and 9R12wavelength pair, 4.3 mb from the 1OR20 and 1OR18pair, and 4 mb from the 1OR20 and 1OR22 pair. Ameteorological station located a few hundred metersfrom the site measured 5.3 mb (temperature = 16 'C).A temperature correction2 5 of -2.6%/C (measuredfor 6.6 mb water-vapor' partial pressure, for thetemperature range of 10-27 C) to the absorptioncoefficients given by Grant24 results in lidar measure-ments of the partial pressure of water vapor of 5.74mb, 6 mb, and 5.6 mb, respectively. The tempera-ture-corrected water-vapor measurements are inbetter agreement with the meteorological stationmeasurements. In this paper the water-vapor mea-surements are used to check the overall consistencyof the lidar measurements across the 9- to 11-[imwavelength range and thus to ensure that all calibra-tion procedures of the wavelength-dependent compo-nents are properly done. The ozone concentrationwas computed from the ozone-absorption coefficient 26

to be 34 parts in 109. The Air Force GeophysicsLaboratory atmospheric model27 for a midlatitudesummer predicts 33.4 parts in 109 at a height of 1 km.These measurements show that the lidar systemproduced reliable measurements throughout the 9 to11-jim wavelength region. These measurementsserve as reference measurements for calibrating theeffect of atmospheric transmission on the kaolin-dustbackscattering and target-reflectance measurements(i.e., a two-way path through the aerosol cloud).

Figures 6 and 7 show the wavelength dependence ofthe normalized backscattered signal from an opticallythin and an optically thick kaolin dust-cloud, respec-tively, for different cloud optical depths T7* The


1

0.8-

0 0.6-

~0C.) 0.4-

J0 9.5 10.o 10.5 11.0wavelength [m]

Fig. 6. Measurements of backscattering from an optically thinkaolin-dust cloud with a maximum spectral effective optical deptha* of the following values: 0.24 (x), 0.43 (+), 0.44 (*), and 1.0(M). The theoretical curve (A) is computed from the radiativetransfer model.

optical depth r* was determined from the two-waytransmission measurements through the cloud (i.e.,backscatter signals from the cloud and the targetwere measured simultaneously) and the target-reference measurements shown in Fig. 5. In Figs. 6and 7 the peak value of the wavelength-dependentcloud optical depth T*(X) is given to indicate cloudthickness during measurements of the 20 wave-lengths. The theoretical curve (triangle), computedby the radiative transfer model (Fig. 3), is for anoptically thin layer (= 0.5) for Fig. 6, and for anoptically thick layer (a = 20) for Fig. 7.

Figure 8 shows the backscattered signals for atransition stage between an optically thin and anoptically thick cloud. The theoretical curve (triangu-lar symbol), computed from the radiative transfermodel, is for a layer with an optical depth of T = 5,which is chosen to represent the transition betweenoptically thin and thick layers in the model (Fig. 3).

U)NCi

T0

U)

a)

Qa:90C)

.0

10.0wavelength [m]

a).N

cE

~0

a)

0gC.)

.0

.0

wavelength [m]

Fig. 8. Measurements of backscattering for a transition stagebetween an optically thin and thick kaolin-dust cloud with amaximum spectral effective optical depth T*() of the followingvalues: 1.13 () and 1.27 (x). The theoretical curve (A) iscomputed from the radiative transfer model.

.The wavelength dependence of the effective opticaldepth of the dust cloud measured from the target fordifferent kaolin-dust clouds along with a curve com-puted from the model is shown in Fig. 9. This figureshows that for all clouds optically thin and thick, theeffective optical depth exhibits a similar shape, aspredicted by the model (Fig. 4).

It must be noted that the range of available mea-surements is limited in practice. As the cloud thick-ness increases, the measured signal from the targetdecreases rapidly e.g., forX = 1.3, exp(-2'r) = 0.07, asdoes the signal-to-noise ratio of the measurements.For an optically thin cloud the signal-to-noise ratio ofthe backscatter signal from the dust cloud will besmall and thus the measurements become less reliable.Figures 6-9 show a good qualitative agreement withthe simple two-stream radiative transfer model anddemonstrate the different backscatter spectral re-sponses caused by multiple scattering.

wavelength [m]

Fig. 9. Measurements of spectral effective optical depth r*(X)from a kaolin-dust cloud with a maximum spectral effective opticaldepth 9*(X) of the following values: 0.44 (+), 0.86 (x), 1.13 (*),1.27 (), and 2.07 (v). The theoretical curve (A) is computedfrom the radiative transfer model.

~0N

co0Cq

N1

.0

Fig. 7. Measurements of backscattering from an optically thickkaolin-dust cloud with a maximum spectral effective optical depth9*(X) of the following values: 1.3 (x), 1.8 (+), 2 (*), and 2.3(M). The theoretical curve (A) is computed from the radiativetransfer model.


5. Application to Differential Absorption DetectionIn the DIAL technique, where the average path-length concentration of a gas over a distance L to a

ments. The error Aat in deducing the average path-length concentration from differential reflectivityUR(T, a, g) can be written in a differential form:

Ao = [a ln(UR)/aT]dT + [a ln(UR)/da]da + [a ln(UR)/ag]dg2dorL

target is sought, the laser is tuned to two wavelengths.The first wavelength is chosen so that it will beabsorbed heavily by the trace gas of interest (on-resonant wavelength). The second wavelength ischosen to be outside the absorption band (off-resonant wavelength) of the gas and serves as areference measurement to calibrate the reflectivity ofthe hard target or the backscattering from the aerosolwhen aerosols are used as a diffuse target. Forclosely spaced on- and off-resonant wavelengths, theassumption is made that the target reflectivity, or theaerosol-volume backscattering coefficient, is approxi-mately constant with the wavelength. The effect ofdifferential spectral hard-target reflectance on theDIAL technique was studied by Cvijin et al.28 and byGrant. 2 9

When an aerosol cloud at a distance L is the sourceof the measured backscattered signal (as in thisexperiment), the average path-length concentration aof a gas over this distance is given by

Simplified analytical expressions for Eq. (5) can beof great use for analyzing the effect of multiplescattering on the shape of the spectral reflectivity.It can be shown that for an optically thin layer thepartial derivative is reduced to

a ln[UR(7<)] _a7r

a n[UR(T<)] _

aa

a ln[UR(T<)]

ag

2

2T - (ag + a - 2)X2

2(T + 1)

(6a)

(6b)

g2)a- (6c)

2a + [2a - a2 - a2 g]T

2 + 2(1 - a)T

2(1 + T)(1 - g) - (1 -

ln[UR,(T, a, g)] - ln[UR2 (T, a, g)]2(or2 - a,)L

For an infinitely optically thick layer UR [T = 0], thepartial derivative is reduced to

(4)

where the indexes 1 and 2 denote the on- andoff-resonant wavelengths, respectively, and is theabsorption coefficient of the gas of interest. In Eq.(4) it is assumed that the path length traveled byphotons in the gas is L, and that the scattering occursin the aerosol cloud. Multiple scattering in theaerosol cloud will lead to many different path lengthsthrough the gas. The effect of the gas absorption onUR is easily handled with the radiative transfermodel (Section 3) by incorporating additional absorp-tion of the gas molecules into the scattering proper-ties of the aerosol. A two-component system (absorb-ing gas plus scattering aerosol) can be viewed as aone-component system where absorption and scatter-ing take place by the aerosols (see van de Hulst,13 p.574). However, the denominator L of Eq. (4) shouldbe modified according to the average path-lengthdistribution in the gas. In this study only the effectof multiple scattering on the reflected fraction of fluxUR and its effect on DIAL is considered. The analy-sis to follow shows that the wavelength dependence ofbackscatter is less dependent on wavelength for amultiple-scattering case. Therefore, the aerosol cloudbecomes a diffuse target that is more flat in itsspectral reflectance as multiple-scattering increases;this effect will thus reduce the error in DIAL measure-

a ln[UR(T = 0o)] _

aa

a ln[UR(T = 00)] _

ag

1

a[(1 - a)(1 - ag)]112

(1 - a)1/2

(1 - g)[(1 - ag)]112

(7a)

(7b)

Figure 3 shows that in general as the optical depthof the layer increases, the spectral response of thereflected fraction of flux UR becomes more broad andflat because of multiple scattering. Therefore, theerror Aua will decrease because of the increase ofmultiple scattering. This trend can be seen fromEqs. (6a)-(7b). For an infinitesimal optically thinlayer the error A is

At O

{aln[UR(7<)]/1a}J J 0 + (da/a) - dg/(1 -g)2duL (8)

and the partial derivative of UR with respect toT is inversely proportional to T, e.g., for g = 0,


{a ln[UR(T <)]/aT} T 0 = {2/[2T + (2 - a),r2]}.infinitely optically thick layer the error Au is

Au I =da/{a[(1 - a)(1 - ag)]1121

For an that for water vapor the error in DIAL decreases withthe increase of multiple scattering (increased optical

- dg(1 - a)1/2 /[(1 - g)(1 - ag)]112(9)2duL

which is larger than the corresponding terms in Eq.(8) for an infinitesimal optically thin layer but cannotcompensate for the rapid increase of Act because ofa ln[UR(r <)]/ar.

In a DIAL where the measured signal is from ahard target and the gas of interest is mixed withaerosol dust, the spectral transmission through anoptically thin aerosol layer r[(1 - a)(1 - ag)]112 << 1is important for the accuracy of the computed averagepath-length concentration of the gas of interest.The change in the spectral transmission of the aerosolis

Aln UT(Tr<)] + r 7)

2(1 + r) - ar(1 + g)

2 - a(1 + g)2(1 + r) - aT(1 + g) dr

(1 + g)T

+ 2(1 + T) - aT(1 + g)(10)

Figure 10 shows the error Au(r)/Au(ar = 0.01) fordeducing water vapor and ozone from backscatterfrom kaolin dust (Fig. 3). The error Aac for watervapor was computed from the wavelength pair 9R12and 9R14 in the 9-jim region (square symbol) andfrom the 10R20 and 10R18 wavelength pair in the10-jim region (triangular symbol). For the ozonethe error (asterisk symbol) was computed from thewavelength pair 9P14 and 9P22. Figure 10 shows

1.0

°>0.8-0

N 0.6

R 0.69 0.4-

4 by 0.2-

" 0.0

I 0.1optical

1.0

6'0

0

1.0 < d.4

d , . , , , . 01 0 100

depth

Fig. 10. Error Aa(T)/Aa(r = 0.01) for DIAL detection of watervapor and ozone from the kaolin-dust backscattering signal; water-vapor detection with the wavelength pair 9R12 and 9R14 (U) andthe wavelength pair 10R20 and 10R18 (A); and ozone detectionwith the wavelength pair 9P14 and 9P22 (*).

depth). The negative values in the figure indicatethat the relative magnitude of UR for the on- andoff-resonant wavelengths was reversed as a result ofmultiple scattering.

Observations show that for ozone the absoluteerror does not decrease monotonically with increas-ing optical depth. This behavior is due to the factthat for this specific kaolin dust the peak of backscat-tering (Fig. 3) for an optically thin layer is at thelocation of the on-resonant wavelength 9P14 (X =9.504 jim) and is shifted to longer wavelengths withincreasing optical depth (e.g., for 7 < 0.5 the peak isat 9P14, X = 9.504 jLm; at r = 0.5 the peak is at 9P20,X = 9.552 Am; at r = 2 the peak is at 9P22, X = 9.569jum; and at T > 5 the peak is at 10R28, X = 10.195Pum). This specific example shows that multiplescattering will, in general, reduce the error in DIALcomputations. However, for the specific wavelengthpair used in DIAL (as is shown in the case for ozonedetection), because of the specific backscattering spec-tra of the dust the error in DIAL computations doesnot always decrease.

6. SummaryIn this paper backscattering and extinction fieldmeasurements were presented in 20 wavelengths inthe 9- to 11-jim wavelength range from a kaolin dust.The measurements show that the spectral backscat-tering changes when the optical depth of the cloudincreases and the effect of multiple scattering be-comes more pronounced. The peak of the spectralbackscattering shifts from the 9-jim wavelength rangeto the 10-jim wavelength range. The spectral extinc-tion remains relatively unchanged with increasingcloud optical depth.

A simple two-stream radiative transfer model wasused to explain the measurements qualitatively.Several equations were derived from the model toshow that in general the wavelength dependence ofbackscatter is less dependent on wavelength for amultiple-scattering case. Therefore, the aerosol cloudbecomes a diffuse target that is more flat in itsspectral reflectance as multiple scattering increases.This effect will reduce the error in DIAL measure-ments. The simplified equations derived from themodel will help investigate spectral behavior of multi-ple-scattering measurements qualitatively.

This research was performed in the U.S. Army atthe Chemical Research and Development and Engi-neering Center (CRDEC), Aberdeen Proving Ground,Md., and was supported under grant DAAA15-89-D-


I * . .

I...........................................................I --- - -------------------------------.

aC

-0.o2 4-

007. The author thanks Francis D'Amico of CRDECfor data-acquisition software development, RobertKnapp and Silvio Emery of CRDEC for the help indesigning the lidar-pointing mechanism, Steven Got-off and Janon Embury of CRDEC for useful discus-sions, and Felix Reyes of CRDEC for his technicalsupport.

References1. A. Ben-David, S. L. Emery, S. W. Gotoff, and F. D'Amico "A

high PRF, multiple wavelength, pulsed CO 2 lidar system foratmospheric transmission and target reflectance measure-ments," Appl. Opt. 31, 4224-4232 (1992).

2. R. M. Schotland, "Some observation of the vertical profile ofwater vapor by laser optical radar," in Proceedings of theFourth Symposium on Remote Sensing of Environment, J. 0.Morgan and D. C. Parker, eds. (U. Michigan Press, Ann Arbor,Mich., 1966), p. 273.

3. 0. Steinvall, G. Bolander, and T. Clasesson, "Measuringatmospheric scattering and extinction at 10 plm using a CO 2lidar," Appl. Opt. 22, 1688-1695 (1983).

4. H. T. Mudd, Jr., C. H. Kruger, and E. R. Murray, "Measure-ment of IR laser backscatter spectra from sulfuric acid andammonium sulfate aerosols," Appl. Opt. 21, 1146-1154 (1982).

5. R. L. Schwiesow, R. E. Cupp, V. E. Derr, E. W. Barrett, andR. F. Pueschel, "Aerosol backscatter coefficient profiles mea-sured at 10.6 pm," J. Appl. Meteorol. 20, 184-194 (1981).

6. E. E. Uthe, "Lidar evaluation of smoke and dust clouds," Appl.Opt. 20, 1503-1510 (1981).

7. E. E. Uthe and J. M. Livingston, "Lidar extinction methodsapplied to observation of obscurant events," Appl. Opt. 25,677-684 (1986).

8. M. J. Post, F. F. Hall, R. A. Richter, and T. R. Lawrence,"Aerosol backscattering profiles at = 10.6 ALm," Appl. Opt.21, 2442-2446 (1982).

9. E. R. Murray, M. F. Williams, and J. E. vander Laan, "Single-ended measurement of infrared extinction using lidar," Appl.Opt. 17, 296-299 (1978).

10. R. G. Pinnick, G. Fernandez, B. D. Hinds, C. W. Bruce, R. W.Schaefer, and J. D. Pendleton, "Dust generated by vehiculartraffic on unpaved roadways: sizes and infrared extinctioncharacteristics," Aerosol Sci. Technol. 4, 99-121 (1985).

11. J. H. Hodges, "Aerosol extinction contribution to atmosphericattenuation in infrared wavelengths," Appl. Opt. 11, 2304-2310 (1972).

12. W. D. Powell, D. Cooper, J. E. vander Laan, and E. R. Murray,"Carbon dioxide laser backscatter signatures from laboratory-generated dust," Appl. Opt. 25,2506-2513 (1986).

13. H. C. van de Hulst, Multiple Light Scattering Tables, Formu-las and Application (Academic, New York, 1980).

14. L. R. Bissonnette, "Multiscattering model for propagation ofnarrow light beams in aerosol media," Appl. Opt. 27, 2478-2484 (1988).

15. B. M. Herman and S. R. Browning, "A numerical solution tothe equation of radiative transfer," J. Atmos. Sci. 32, 559-566(1965).

16. S. C. Hill, A. C. Hill, and P. W. Barber, "Light scattering bysize/shape distributions of soil particles and spheroids," Appl.Opt. 23, 1025-1031 (1984).

17. S. Asano and G. Yamamoto, "Light scattering by a spheroidalparticle," Appl. Opt. 14, 29-49 (1975).

18. R. D. Haracz, L. D. Cohen, and A. Cohen, "Scattering oflinearly polarized light from randomly oriented cylinders andspheroids," J. Appl. Phys. 58, 3322 (1985).

19. R. G. Pinnick, G. Fernandez, and B. D. Hinds, "Explosion dustparticle size measurements," Appl. Opt. 22, 95-102 (1983).

20. J. Heintzenberg and R. M. Welch, "Retrieval of aerosol sizedistribution from angular scattering functions: effect of par-ticle composition and shape," Appl. Opt. 21, 822-830 (1982).

21. J. B. Polack and J. N. Cuzzi, "Scattering by nonsphericalparticles of size comparable to a wavelength: a new semiem-pirical theory and its application to tropospheric aerosols," J.Atmos. Sci. 37, 868 (1979).

22. S. R. Pal and A. I. Carswell, "Multiple scattering in atmo-spheric clouds: lidar observations," Appl. Opt. 15, 1990-1995 (1976).

23. K. L. Coulson, Polarization and Intensity of Light in theAtmosphere (Deepak, Hampton, Va., 1988).

24. W. B. Grant, "Water vapor absorption coefficients in the 8-13[tm spectral region: a critical review," Appl. Opt. 29, 451-462 (1990).

25. G. L. Lopel, M. A. O'Nell, and J. A. Gelbwachs, "Water-vaporcontinuum CO 2 laser absorption spectra between 27 'C and- 10 'C," Appl. Opt. 22, 3701-3710 (1983).

26. M. S. Shumate, R. T. Menzies, W. B. Grant, and D. S.McDougal, "Laser absorption spectrometer: remote measure-ment of tropospheric ozone," Appl. Opt. 20, 545-552 (1981).

27. G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H. Chetwynd,and E. P. Shettle, "AFGL atmospheric constituent profiles(0-120 km)," Rep. AFGL-TR-86-0110 (U.S. Air Force Geophys-ics Laboratory, Hanscom Air Force Base, Mass., 1986).

28. P. V. Cvijin, D. Ignjatijevic, I. Mendas, M. Sreckovic, L.Pantani, and I. Pippi, "Reflectance spectra of terrestrialsurface material at CO 2 laser wavelengths: effect on DIALand geological remote sensing," Appl. Opt. 26, 4323-4329(1987).

29. W. B. Grant, "Effect of differential spectral reflectance DIALmeasurements using topographic targets," Appl. Opt. 21,2390-2394 (1982).


wavelength dependence of backscattering and extinction of kaolin dust at co_2 laser wavelengths:...

Documents