lidar measurements of rotational raman and double scattering

Lidar measurements of rotational Raman anddouble scattering

A. Cohen, M. Kleiman, and J. Cooney

The analysis of unusually strong Raman backscattering signals from clouds shows that such signals cannotbe merely related to filter on-line leakage. Theoretical calculations of Raman double scattering in an atmo-sphere with high optical depth values are presented, and it is shown that the Raman multiple scattering ef-fect is not negligible. The results of the calculations are in good agreement with the experimental data.

1. Introduction

The use of rotational and vibrational Raman scat-tering for atmospheric measurements such as temper-ature, water vapor, pollution, visibility, and turbidityhas been discussed in recent papers. 1-5 This techniqueis limited by the relatively weak backscattered Ramansignals. Since the backscattered on-line signals areconsiderably stronger, special arrangements have to bemade to reject these signals when Raman scatteringmeasurements are performed if one wishes high accu-racy ( 1.0%). In the lidar technique this is done byplacing interference filters or monochromators in frontof the Raman optical channels, and in the case of vi-brational Raman a high degree of rejection can beachieved. However, in the measurement of tempera-ture profiles, based on the use of pure rotational Ramanlines, special problems arise because the characteristicsof the filters can provide the required degree of rejectiononly with great difficulty. Therefore, in a so-calledRaman signal to distinguish between the real Ramanpart and the leakage or intrusion of the laser line anon-line measurement has been suggested.6 This mea-surement can provide the required data to remove theerror due to leakage and thus achieve an accurateanalysis of the measurements.

In this paper we discuss a situation involving multiplescattering in Raman measurements. This requires

special treatment. Multiple Raman scattering occursin an atmosphere with high optical depth values.

We present experimental data of rotational Ramanbackscattering in the presence of a cloud and a theo-retical analysis of these data, assuming only single anddouble scattering. It will be shown that, for high valuesof turbidity, multiple scattering effects are not negli-gible not only for on-line measurements but also forRaman scattering measurements.

II. Single and Double Raman Scattering Intensities

The intensity of a rotational Raman line of the di-atomic molecules excited by a linearly polarized light

oa and scattered in the direction 0 iS 7

IRaman(O) = (7 - sin2 O cOs2 s)Qkn, (1)

where so is the angle between the scattering plane (de-fined by the directions of the incident and the scatteredbeams) and the polarization plane of the incident light,and Qkn is the symmetrical part of the polarizabilitytensor. Thus, when the incident light is polarizedparallel (III) or perpendicular (II) to the scatteringplane, intensities of the Raman scattered light are, re-spectively,

I1lRaman(O) = I(6 + cOs2 0)Qkn,

I Raman = 7IQkn (2)

J. Cooney is with Drexel University, Department of Physics & At-mospheric Science, Philadelphia, Pennsylvania 19104; the other au-thors are with Hebrew University of Jerusalem, Department of At-mospheric Sciences, Jerusalem, Israel.

Received 9 September 1977.0003-6935/78/0615-1905$0.50/0.© 1978 Optical Society of America.

Let us describe the incident and the scattered intensitiesby use of the modified Stoke's vector8

I)

V

The linearity polarized incident laser beam, relative toits plane of polarization, is

15 June 1978 / Vol. 17, No. 12 / APPLIED OPTICS 1905

Backscatter

SecondScatter-ng

3oe

Cloud Base

The power, scattered at angle 0 by a volume AV, andincident on the second volume AV2 , in case (a), is de-scribed by the vector IM(O), related to I by the scat-tering matrix' 0

/Pi

PM(O) =I°o2

0 0 0P2 0 0

0 P 3 -P4 :

0 P4 P3

IM(O) = PM(O)L(p)IO AV exp[-6M(R + R1,2 )],R1,2

where

/ cos2

sin2 oL(ep) = -sin 2 v

0

sin2

so 1/2 sin2(pcos2

p - 1/2 sin2sosin2s cos2so0 0 ,

0O0

1

Fig. 1. Double scattering geometry. FOV refers to the lidar receiverfield of view.

00I = fA

0

The single Raman backscattering ( = r) from a cloudvolume V8 at height above the cloud base, illuminatedby a lidar (see Fig. 1), is

-Raman 2 8 IQ exp(-aRI) exp(-WM), (3)

where A is a lidar constant, R, is the mean distance ofthe volume from the lidar, and 8R, 5M are the extinctioncoefficients for the Raman-shifted and the lidar wave-lengths inside the cloud.

The scheme for double scattering calculations usedin this paper is based on the work by Cohen and Gra-ber,9 except that here we consider two types of doublescattering:

(a) Mie-Raman double scattering, in which the on-line laser light is scattered by the cloud droplets andthen the second-Raman scattering appears;

(b) Raman-Mie double scattering, in which Ramanscattering from the air molecules preceeds the Miescattering from the cloud droplets.

The cloud volume contained in the field of view of thereceiver is divided into identical small subvolumes AV.The double scattering occurring simultaneously witha given single scattering echo is calculated by adding theintensities scattered by all combinations of two subvo-lumes inside the field of view of the lidar for which thepathlength of the light propagated within the cloud isconstant and equals the single scattering pathlength.

is the rotation matrix for the modified Stokes vectorthrough an angle so between the plane of polarizationand the scattering plane; R1,2 is the distance betweenthe two scattering volumes AV1 and AV 2, and R1 is thedistance between the volume AV, and the cloud base.

In the second type of double scattering, we can de-scribe the intensity of the first Raman scattering in theform of a modified Stoke's vector by use of Eq. (2):

(6 + cos2 0) coS2 \

IR() 10AV 1 IQ 7sin 2 I2~~~~X exp[-(tMRj + RR,2)]. (5)

Once the first scattering angle 0 is determined, thesecond scattering angle 0* is unique since the doublescattered beam is scattered back to the receiver. Hence,0* = -0.

The intensities of the Mie-Raman and the Raman-Mie parts of the double scattering for a correspondingsingle scattering distance R, are, therefore,

IM-R(Ra) = E AAVAVjI 0 QL [P1M(O)(6 + cos2 0) cos2t

+ 7P2 (0i) sin 2 p] exp[-3M(R + Rij) - RRj] (6)

and

IR-M(R) = E AAVAV1j 0Qt [PlR( - O)( 6 + cos2Oj) cos2(p

+ 7 P2R(7r -i) sin2 f] exp[-bMRi-R(Ri,j + Rj)] (7)

for all i and j obeying

2R = HO + Ri + R.j + Rj,, (8)

where HO is the height of the cloud base, Rj, is the dis-tance between the second scattering volume and thereceiver, kR,M = 27r/XRM is the wavenumber, and wherethe indices R and M indicate the Raman shifted or theMie scattered wavelengths, respectively.

The contribution of the double scattering ID to thetotal Raman signal is ID = IM-R + IR-M.

1906 APPLIED OPTICS / Vol. 17, No. 12 / 15 June 1978

VS

complete calculation requires prohibitively long com-puter time, even for relatively simple cases of doublescattering.

Instead, a large sample of g (<K) pairs are chosen in0 six random steps which determine the two subvolumes< coordinates, replaced by two scattering points. SinceX the total number of pairs N [not necessarily satisfyingc. Eq. (8)] is known, the value of K is calculated by theZ random process in which each random pair of points is,7 checked by Eq. (8). In this process the ratio F = aig,n where a is the number of pairs contributing to the< double scattering, is recorded, and, therefore,

<0

I

C:I

PENETRATION DEPTH (m)

Fig. 2. Lidar on-line backscattering signal from the cloud (6943-Ainterference filter).

CLOUD BASE


(A

0

P1

z

zu1

A_4

z

-

a0ZI

(A-- I

K = F. N.

The larger the value of g, the more accurate is the resultachieved. Therefore, the accuracy required will de-termine the value of g.

IV. Measurement and Comparison with TheoryThe measurements of the on-line and Raman back-

scattering from a cloud were performed by use of theDrexel University lidar system at the NASA WallopsIsland base. In this experiment, three different inter-ference filters were used:

(1) on-line 6943-A filter;(2) rotational Raman 6916-A filter;(3) rotational Raman 6880-A filter.

The lidar return through the 6943-A filter is shown inFig. 2. Returns through the 6880-A filter and the6916-A filter are shown in Figs. 3(a) and 3(b), respec-tively.

The third filter had a lower rejection value for theon-line wavelength relative to the very high rejection ofthe second filter. Hence, the number three filter pro-vided a good example of the leakage effect as opposed

CLOUD BASE

Fig. 3. Rotational Raman backscattering signals. (a) Interferencefilter 6880 A with low degree of rejection. The leakage of the strongon-line signal is present. (b) Interference filter 6916 A with high

degree of rejection.

Ill. Method of Calculations

The summation

ij

of Eqs. (6) and (7) refers to all possible pairs K of sub-volumes AVi and AVj satisfying Eq. (8). The sizes ofthe subvolumes ought to be as small as possible to re-duce the averaging effect of large volumes. However,when this is done the value of K is so large that the

01


(AD-CrT,

z

z0P1z(A

_

a,

i}

Fig. 4. Multiple scattering effect of the rotational Raman back-scattering signal from the cloud with high optical depth value. In-

terference filter 6916 A with high degree of rejection.


CLOUD BASCI

0

(9)

160 120 80 40 0

PENETRATION DEPTH (im)

Fig. 5. Theoretical calculations of rotational Raman (6916-A) signal from the cloud with low (T = 0.04 at a penetration depth of 20 m) opticaldepth values. The Raman wavelength interference filter has a high degree of rejection at the laser wavelength. -X-X-is single rotationalRaman scattering signal;-O-o-is total Raman scattering signal (single and double scattering). To the right of the cloud base the pure

rotational Raman signal in a cloudless atmosphere is plotted.

C,

0C:0in

VIP1

200 160 120 80

z(A--4

MQa

0


(nC,

M

z-

I)

-4

ED

z(A--4

a:

-C

I-0C0

CD

(Am

PENETRATION DEPTH In)

Fig. 6. Same data as in Fig. 5, except that high [(20) = 0.6] optical depth values are presented.

)

-4inz

(A

0

C~~~~~~

> ~~C:

200 160 120 80 40 0

PENETRATION DEPTH (in

Fig. 7. Theoretical calculations of the rotational Raman (6880-A) and the laser wavelength (6943-A) scattering from a cloud with low [(20)=0.06] optical depth value. The Raman wavelength interference filter has a relatively low degree of rejection at the laser wavelength. -

X-X- is single rotational Raman scattering signal; -0-0- is total scattering signal (Raman and on-line wavelength scattering).

to the multiple scattering effect from the cloud as seenthrough filter number two. For theoretical calculationsof the Raman-Mie, Mie-Raman, and on-line scattering,the following parameters of the cloud were used:

(a) The size distribution function of the clouddroplets is fr) = ara exp(-brv), where a = 1.0851 X10-2; a = 8; = 3; b = 1/24 - Deirmendjian's cloudmodel C2.

(b) The extinction coefficient inside the cloud:6 M(6 9 4 3 A) = 11.424 km-1 . This value corresponds toa number density of 100 droplets cm-3. It should benoted that although the double scattering process in-volves three wavelengths, the on-line 6943 A, and theRaman lines 6919 A and 6880 A, the extinction coeffi-cient for all wavelengths is assumed to have the samevalue [for example, R (6916 A) was calculated and gavethe result of 11.423 km-'].

(c) The cloud base is assumed to be at height of Ho= 1000 m.

(d) The laser field of view is 1 mrad.(e) The telescope field of view is 5 mrad.We also assumed that the air density (as well as the

cloud number density) is kept constant within the cloud.The computational results are summarized in Figs. 5-7,which correspond to the experimental Figs. 3 and 4.

In comparing the results of the theoretical calcula-tions with the experimental data, one can see, as can beexpected, that in the case of low optical depth values (inour cloud model for = 0.04) Raman-Mie and Mie-Raman double scattering can be totally neglected in thesignal detected through the Raman interference filters[Figs. 3(b) and 5].

On the other hand, for the same cloud parameters(including the optical depth value) and for the samelidar system, the on-line (6943-A) double scatteringcontribution to the backscattered signal is comparablewith the single scattering contribution. Therefore, ifthe Raman interference filters do not have high degreeof rejection,6 the multiple scattering effect is part of theon-line intrusion through the Raman optical channel[Figs. 3(a) and 7].

However, when the optical depth values increase, thecontribution of the double Raman scattering to the totalsignal becomes significant; and, even for an interferencefilter with high degree of rejection, the peak in the re-ceived experimental Raman signal (Fig. 4) is due to thedouble scattering effect. The results of the theoreticalcalculations of the backscattered Raman signal by sucha cloud (with an optical depth value of r = 0.6) arepresented in Fig. 6.


V. Conclusions

The role of multiple scattering in the analysis of lidarechoes from water clouds is also significant even whendealing with Raman scattering in vibrational or rota-tional lines corresponding to air molecules. As can beseen from the calculations, high values of optical depths(r > 0.4) in clouds will not merely reduce, as seemed tobe expected, the Raman echoes from air molecules.Such a reduction of the backscattered Raman signal inthe presence of a cloud indeed occurs, but only whensingle scattering alone should be taken into account(Fig. 5), whereas the multiple scattering is negligible r- 0.06). In other cases, i.e., clouds with higher values

of optical depth, the multiple scattering effect is nolonger negligible; and Raman scattering from air mol-ecules which are excited by the on-line (6943-A) scat-tered radiation from the cloud droplets (and/or on-linescattering by the cloud droplets of the Raman shiftedradiation emerging from the excited air molecules) ismeasured above the noise level. This effect results inproducing a maximum Raman signal close to (above)the cloud base.

Signal-to-noise ratio considerations in lidar Ramanscattering measurements, corresponding to our exper-imental system, are discussed in detail by Cooney.'

This result must be taken into account when tem-perature measurements are performed. But, thetreatment of the results is different than that used inthe case of leakage: though in the latter case the leak-age is a measurable quantity and, therefore, can be de-ducted from the Raman signals,6 the multiple scatteringRaman signal presents an average of scattering by airmolecules between the cloud base and the signal scat-tered layer. Hence, the results can no longer represent

one given altitude, but rather the whole layer. Never-theless, to the first approximation temperature profilescan be deduced even in situations of high values of op-tical depth by a method of successive averaging ofoverlapping volumes.

Combined Raman-Mie measurements of the kinddescribed here can permit the use of laser measurementssuch as temperature measurements, even in the pres-ence of enhanced Mie scatter (- > 0.4).

This research was partially supported by the U.S.-Israel Binational Science Foundation under researchgrant 679, and NOAA, U.S. Department of Commerce(Drexel Project 740). In addition this work was par-tially supported by the Meteorology Branch of theNational Science Foundation as well as the GeosciencesDirectorate of the Army Research Office in Durham,North Carolina.

References1. J. Cooney, J. Appl. Meteorol. 11, 108 (1972).2. R. G. Strauch, V. E. Derr, and R. E. Cupp, Remote Sensing En-

viron. 2, 101 (1972).3. H. Inaba and T. Kobayasi, Opto-electronics 4, 101 (1972).4. D. A. Leonard and B. Caputo, Opt. Eng. 13, 10 (1974).5. V. Zuev, G. Krekov, I. Naats, and V. Scorinov, Izv. Acad. Sci.

USSR Atmos. Oceanic Phys. 11, 827 (1975).6. A. Cohen, J. Cooney, and K. N. Geller, Appl. Opt. 15, 2896

(1976).7. G. Placzek, in Handbuch der Radiologie, A. Marx, Ed. (Akade-

mische Verlagsgesellschaft, Leipzig, 1934).8. S. Chandrasekhar, Radiative Transfer (Dover, New York,

1960).9. A. Cohen and M. Graber, Opt. Quantum Electron. 7, 221

(1975).10. D. Deirmendjian, Electromagnetic Scattering on Spherical Po-

lydispersions (Elsevier, New York, 1969).

From the Editor continued from page A144

oriented lakes in New York and Alaska); two volumes of StrangePhenomena (ball lightning, glows in earthquakes, sounds in aurora);two volumes of Strange Artifacts (Stonehenge, ancient inscriptions);and Strange Minds (arithmetical prodigies, dowsing, voodoo). Theauthor does not attempt to interpret these accounts; he simply pre-sents them.

A final item of interest in the Corliss books is HANDBOOK OFUNUSUAL NATURAL PHENOMENA by William R. Corliss (1977,547 pp., $14.95). This is a bound volume, compiled from material inthe six sourcebooks, with 130 added illustrations and index. Hecovers will o'the wisps, sky glows, anomalous halos, lights associatedwith tornados, earthquakes, mirages, and so on. Nothing fake orsleight of hand, simply natural curiosa. This book was also recentlyreviewed, in Bull. Am. Meteorol. Soc. 58,1085 (1977). The reviewerof the Corliss book found it interesting and entertaining, although hefelt that there was little in the chapter on unusual weather phenomenathat a meteorologist would consider unusual if sufficient observationaldata were available for each case. Furthermore he found some essaysrather slanted toward the sensational and mysterious. For example,under Dark Days the author states: "While admitting forest fires tobe the cause of most dark days, we should also ask whether some maynot owe their origins to stratospheric or even extraterrestrial cloudsof obscuring matter." We know that spectacular volcanic eruptionshave introduced enough volcanic ash in the upper atmosphere to makea few weeks of redder sunsets, but there is little evidence that strat-ospheric dust has ever darkened the day. Well, all these books areentertaining, and some are factual and scholarly, all that is neededis to take them with a few grains of salt (thrown over the left shoulder,of course).

JOHN N. HOWARD


lidar measurements of rotational raman and double scattering

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