Lidar systems are widely used for remote sensing ofoceans and the atmosphere. The analysis of the li-dar echo is relatively simple when the received en-ergy is due mainly to single scattering, since in thiscase a simple relationship relates the lidar echo to theoptical properties of the sounded medium. How-ever, in some cases of relevant interest the opticalthickness of the sounded medium is so large that themultiple-scattering effect on the lidar echo cannot bedisregarded. This is the case, for example, for lidarsounding of clouds. In these conditions the interpre-tation of the lidar echo becomes difficult.However, the relevance of the problem has induced
many researchers to study the effect of multiple scat-tering on lidar echoes and some researchers are co-operating within the workshop group calledMUSCLE ~multiple scattering lidar experiments!with the aim “to stimulate experimental as well astheoretical work to better understand and make useof the measured multiple-scattering lidar contribu-tion for maximizing our information on lidar probing
The authors are with the Dipartimento di Fisica dell’Universita’degli Studi di Firenze, Via Santa Marta 3, 50139 Firenze, Italy.Received 20 November 1995; revised manuscript received 12
of cloud and fogmicrophysical parameters.”1 A com-parison among seven different calculation methods~three analytical and four numerical! that were usedto solve the same problem has been published re-cently ~see Ref. 1 and related papers!: significantdifferences were observed among the results obtainedwith different methods. Even the comparisonamong numerical procedures based on Monte Carloapproaches ~Monte Carlo results are often assumedas a gold standard in the study of photon migrationthrough scattering media! give different results insome cases.One common feature of the different approaches
pursued is that they need some form of approxima-tion or specialization to make the solution computa-tionally possible or affordable. The validation of theresults is therefore necessary. In the conclusions ofRef. 1 it was also stated that “the difficulty in imple-menting corrections is to determine which is the truesolution. More measurements in well controlledand varied conditions are now necessary.” However,when lidar measurements are carried out for actualatmosphere or seawater, it is almost impossible tohave sufficient knowledge and control of the govern-ing parameters. This is especially true for thescattering and absorption properties of diffusers ~ho-mogeneity, size distribution, concentration, shape,refractive index!.It is our opinion that measurements in sufficiently
well-controlled conditions, which are necessary to
20 September 1996 y Vol. 35, No. 27 y APPLIED OPTICS 5435
validate the theories, can bemade only on laboratory-scaledmodels. The similarity principle ~Sections 2.4of Ref. 2! allows one to scale a real problem to alaboratory model. The laboratory-scaled model ofan optical system sounding a cloud should have thefollowing characteristics: ~1! the geometric lengths~cloud distance and thickness, receiver area, lightbeam diameter! should be reduced by the same scal-ing factor K to reduce distances of the order of kilo-meters to the order of meters; ~2! the angular field ofview of the receiver and the divergence of the lightbeam should be kept unchanged; ~3! the diffusingmedium in the scaled model should have both thesame optical thickness and the same scattering func-tion as in the unscaled medium. Therefore thewavelength of radiation and the size of the diffusersshould be kept unchanged ~so that the scatteringfunction remains unchanged!, whereas the volumeconcentration of diffusing particles ~and thus thescattering and absorption coefficients! should be in-creased by the same scaling factor K by which thegeometric quantities have been reduced. When asystem such as the lidar is considered, for which thetime resolution of the received energy is needed, thetime scale on which the scattering events occur alsocomes out scaled. If a time resolution of the order ofnanoseconds is necessary for a lidar sounding actualclouds, the corresponding time resolution for the lab-oratory model should be of the order of picoseconds.In a previous paper3 we demonstrated that, by us-
ing a picosecond laser and a fast detector such as astreak camera, lidar measurements on laboratory-scaled clouds are possible. Preliminary experimen-tal results were also presented, showing theincreased effect of multiple scattering on the lidarecho when the turbidity of the cloud increases. Theresults were referred to a cloud at a fixed distancefrom the lidar system and to a receiver having a fixedfield of view. The results were also used to have afirst validation of the Monte Carlo procedure devel-oped by our group,4 to deal with the depolarization ofthe lidar echo that is due to multiple scattering.In this paper we present new experimental results
that refer to a wider range of experimental condi-tions. In particular, measurements were carried outfor two different values of the lidar–cloud distanceand several values for the field of view of the receiver.We carried out measurements by using a linearlypolarized light pulse. Both the parallel ~Pp! and thecross-polarized ~Pc! components ~with respect to thedirection of polarization of the emitted radiation!were measured.
2. Experimental Setup
The experimental setup used, based on the picosec-ond laser and on the streak camera of the LENS~European Laboratory for Non-Linear Spectroscopyin Florence!, was fully described in Ref. 3. Thesource was a dye laser ~average power '100 mW!emitting linearly polarized pulses ~FWHM ' 4 ps! atl 5 573 nm. The detector was a streak camera thatcould be operated in the synchroscan regime. The
5436 APPLIED OPTICS y Vol. 35, No. 27 y 20 September 1996
FWHM of the instrumental impulse response was'25 ps corresponding to a length of 5.6 mm in water.Thus the resolution of the lidar was 2.8 mm.The cloud model was a cylindrical scattering cell
~length L 5 100 mm, 40-mm radius! with opticalantireflecting windows that contains suspensions ofcalibrated microspheres. The optical receiver isshown in Fig. 1. The radius of the input diaphragmD3 was R 5 0.1 mm. The angular field of view wasdetermined by the radius r of diaphragm D2 in thefocal plane of lens L2 ~focal length f1!. Lens L1 wasused to send the radiation to input slit D1 ~180 mm! ofthe streak camera. Polarizer P was used to measureseparately the components of the lidar echo parallel~Pp! and cross polarized ~Pc! with respect to the di-rection of polarization of the laser beam. The laserpulse was directed on the scattering cell, placed at adistance D from the optical receiver, by means ofmirrors and a 50% beam splitter. By means of apower meter and a second beam splitter at the exit ofthe laser system, a small fraction of the light beamwas used to monitor the emitted intensity.The scatteringmediumwas an aqueous suspension
of calibrated styrene divinylbenzene spheres. Be-cause of water–air refraction the optical receiver actsas an equivalent receiver with the same radius, op-erating without refractive effect, placed at a distanceDeq 5 nwD ~nw is the refractive index of water! and afield of view of a 5 ~1ynw!tan21~ryf1!. Measure-ments were repeated for three different values of a:1.3, 2.5, and 5.0 mrad. These values are typical forlidar systems sounding clouds. We varied the valueof a by rotating a disk on which different diaphragmswere obtained. Measurements were carried out fortwo values of D: 305 and 1800 mm. The radius ofthe receiver was R 5 0.1 mm. For measurements atD 5 305 mm the radius of the light beam at the inputof the cell was r > 0.2 mm with a beam divergence~semiaperture! of b 5 3.5 mrad ~lens L3 was used inthis case to reduce the size of the light beam!. Formeasurements at D 5 1800 mm, r > 3 mm and b 50.7 mrad. In any case the region of the mediumilluminated by the direct beam was within the regionseen by the receiver, also when the smallest value ofa was considered.If the scattering cell is assumed to be a model of a
300-m thick cloud, a scaling factor of K 5 3000 re-sults. The two geometric situations are thus modelsof a lidar system sounding a cloud with thickness L9
Fig. 1. Schematic representation of the lidar system.
5 300 m placed at distances D9 5 1200 m and D9 57800 m, respectively. The corresponding values forR and r are R9 5 0.3 m, r9 5 0.6 m for D9 5 1200 m,and r9 5 10.5 m for D9 5 7800 m. The laboratory-scaled lidar used is thus a model of a typical systemused for measurements on clouds.As explained in Section 1 the scattering coefficient
ss, and thus the particle concentration, in the scaledmodel should be increased with respect to the scat-tering coefficient ss9 of the cloud by the same scalingfactor K by which the geometric quantities have beenreduced. Thus the optical thickness of the scaledand unscaled clouds have the same results: t 5ssL 5 ss9L9. Measurements were carried out at l 5573 nm. At this wavelength the absorption coeffi-cient of water is very small ~sa 5 0.079 m21!.5 Theeffect on measurements is insignificant and the dif-fusingmedium can be assumed as a purely scatteringmedium. The adimensional quantity t was thuschosen to describe the turbidity of the medium. Thescattering medium was a suspension of styrene divi-nylbenzene microspheres with average diameter F 56.4 mm having a standard deviation of 1.2 mm.Figure 2 shows the scattering function that we eval-uated with Mie theory by using a code based on theroutine reported by Bohren and Huffman6 assuminga Gaussian size distribution. Measurements of ex-tinction coefficient and of scattering function at smallscattering angles ~0° , q , 3°!, which we carried outby using the experimental setup and the proceduredescribed in Ref. 7, showed excellent agreement be-tween the experimental results and the results ob-tained by Mie theory with nominal data for thecharacteristics of spheres.8 Approximately 40% ofthe radiation was scattered within q , 3°. Figure 2also reports the scattering function that refers to theC1 cloud model at l 5 532 nm ~the Nd:YAG laserwavelength often used in lidar experiments!. Thetwo scattering functions are quite similar: the re-sults reported are thus representative for typicalcloud conditions. In all the measurements the con-centration of microspheres was sufficiently small sothat the assumption of uncorrelated scattering wasfulfilled.In some figures the experimental results are com-
pared with the lidar echo expected from singly scat-
Fig. 2. Scattering function of microspheres ~F 5 6.4 mm, 1.2-mmstandard deviation! together with the scattering function relevantto the C1 cloud model at l 5 532 nm.
tered radiation. The contribution of singlescattering was evaluated by the convolution of thelidar equation,
I1~t! 5 Ee
vss
2p~p!
pR2
~Deq 1 vty2!2exp~2ssvt!, (1)
with the measured impulse response of the lidar sys-tem. In Eq. ~1!, I1~t! is the energy received per unitof time, t is the time spent inside the scattering me-dium, Ee is the energy of the delta pulse, p~p! is thescattering function in the backward direction, and vis the speed of light in water. The measured im-pulse response is shown in Fig. 3, which also showsthe calculated lidar echoes that are due to singlescattering for three values of t before and after con-volution. The effect of the impulse response of thesystem on the lidar echo is insignificant apart fromthe signal received within t , 25 ps.Both in Fig. 3 and in the following figures time t 5
0 was chosen to correspond to the maximum of thepolarized component Pp of themeasured or calculatedecho. The lidar returns are presented only to 800 pssince at small turbidity the signal measured forlonger times was distorted by the echo caused byreflection and diffusion on the second window of thecell ~the maximum of the echo from the second win-dow was at 888 ps!, whereas at large turbidity thenoise was large. The signal is reported for a dy-namic range that is not larger than 3 orders of mag-nitude. Since an absolute calibration of the receiverwas not available, we report experimental resultsthat were obtained with arbitrary units.
Fig. 3. ~a! Measured impulse response of the lidar system. ~b!Lidar echoes that are due to single scattering @I1~t!yEe, Eq. ~1!#before ~dashed lines! and after ~solid lines! convolution with theimpulse response. The single-scattering lidar echoes refer to D 5305 mm, R 5 0.1 mm, and to three values of t.
20 September 1996 y Vol. 35, No. 27 y APPLIED OPTICS 5437
Fig. 4. Lidar echoes ~parallel plus cross-polarized components! received from cloud models with different optical thicknesses t. Eachpanel refers to different values of the angular field of view a and the cloud–lidar distanceD. The dashed curves represent the contributionexpected from singly scattered radiation.
We obtained the actual value of the scattering co-efficient of the suspension by measuring the attenu-ation of the beam transmitted through the cell ~Fig.1!. With the geometry that we used the contributionof scattering to the measured energy was small andthe accuracy for ss was better than 5% even for thelargest values of ss.
3. Experimental Results
A. Effect of the Optical Thickness of the Cloud
To demonstrate the effect of the optical thickness ofthe cloud on the contribution of multiple scattering tothe lidar echo, Fig. 4 shows the total received energyPp 1 Pc versus time. The figure shows the lidar echomeasured for different values of t. Different panelsrefer to the echoes measured for different values ofthe field of view and of the distance of the cloud fromthe receiver. The contribution expected from singlyscattered radiation is also reported. Since an abso-lute calibration of the receiver was not available allthe echoes were multiplied by the same normalizingfactor for the comparison with numerical results.We normalized measurements at D 5 305 and D 51800 mm separately by equating to one the maxi-mum of measured ~total energy Pp 1 Pc! and calcu-lated returns that refer to a 5 5 mrad and t 5 7.3.The comparison between the measured returns
and the calculated curves representing the contribu-tion expected by single scattering points out the de-pendence of multiple scattering on differentparameters: for the smallest value of t considered ~t5 1.3 for D 5 305 mm and t 5 1.2 for D 5 1800 mm!the contribution of multiple scattering is negligibleapart from the largest value of the angular field ofview ~a 5 5 mrad!, but for larger values of t thecontribution becomes more and more important. As
5438 APPLIED OPTICS y Vol. 35, No. 27 y 20 September 1996
expected the contribution of multiple scattering ismore important for larger values of t and larger val-ues of a. The effect also increases when the lidar–cloud distance increases. These features can beexplained by taking into account that the region ofthe cloud seen by the receiver, from which the lidarsystem can receive radiation, increases when aandyor D increase, whereas the region of the cloud inwhich the first order of scattering occurs, the oneilluminated by the direct beam, is entirely seen forany combination of values of a and D used. Thecontribution of single scattering is thus expected toremain unchanged when the region of the cloud seenby the receiver increases, whereas multiple-scattering contribution is expected to increase. Theincrease is more significant for larger values of t be-cause a wider region of the cloud is illuminated.We note that the shape of the lidar echoes in a
semilogarithmic scale remains almost linear, as ex-pected from a homogeneous cloud in single-scatteringconditions, even when multiple-scattering effects arepredominant. In these conditions the scattering co-efficient of the cloud, obtained from the slope of thelidar echo according to Eq. ~1!, is significantly under-estimated.
B. Effect of the Receiver Field of View
Lidar measurements are often repeated with differ-ent values of the angular field of view a of the re-ceiver. Since the receiver usually sees the region ofthe medium illuminated by the direct beam evenwhen small values of the field of view are used ~thiswas also the case for our measurements!, the echothat is due to single-scattering is independent of a,whereas the echo that is due to multiple scatteringusually increases when a increases. The depen-
Fig. 5. Parallel ~continuous curve! and cross-polarized ~dashed curve! components of the lidar echo measured with different angular fieldsof view a. Different panels refer to different values of optical thickness t and of the cloud–lidar distanceD. The values of a correspondingto each curve are 5.0, 2.5, 1.3 mrad from upper to lower curves, respectively.
dence of the lidar echo on a can thus be used to obtaininformation on multiple scattering.The results obtained for different values of the re-
ceiver field of view are reported in Fig. 5. In eachpanel both the parallel ~Pp! and the cross-polarized~Pc! components of the lidar echo measured with dif-ferent angular fields of view are reported. We usedthe same normalizing factors as for the data reportedin Fig. 4: we normalized measurements at D 5 305and D 5 1800 mm separately by equating to one themaximum of the total energy ~Pp 1 Pc! that refers toa 5 5 mrad and t 5 7.3. As expected, the differenceamong echoes that refer to different values of a arelarger for larger values of t and increase when t in-creases. Variations are larger for the cross-polarized component. Since measurements werecarried out on spherical diffusers, the cross-polarizedcomponent of the lidar echo should be ascribed tomultiple scattering only.
C. Effect of the Cloud–Lidar Distance
Multiple-scattering contribution to lidar returns alsodepends on the cloud–lidar distance D. When D in-creases the region of scattering medium seen by thereceiver increases, and the multiple-scattering con-tribution is expected to increase at least for timessufficiently long when a wide region of the cloud isilluminated. The results obtained for two values ofD are reported in Fig. 6. Both the parallel and thecross-polarized components are reported. Measure-ments were carried out at D 5 305 and 1800 mm.Considering the scattering cell ~100 mm thick! as themodel of a 300-m-thick cloud, the corresponding dis-tances areD9 5 1200 and 7800 m. These are typicalvalues for a ground-based lidar or an airborne lidarsounding tropospheric clouds.To underline the effect of the cloud–lidar distance,
we normalized both lidar returns measured at D 5305 mm and at D 5 1800 mm with the same factorobtained by equating to one the maximum of the totalenergy ~Pp 1 Pc! that refers to a 5 5mrad and t 5 7.3and D 5 305 mm. Measurements at low values of t~t 5 1.3 for D 5 305 mm and t 5 1.2 for D 5 1800mm! show almost parallel curves for the parallel com-ponent for any value of a. In this case the echo isdue mainly to single scattering: the ratio betweenthe echoes at D 5 305 mm and D 5 1800 mm isapproximately equal to ~1800y305!2 as expected fromEq. ~1!. The cross-polarized component Pc remainssmaller than 10% with respect to the parallel compo-nent Pp forD5 305mm, whereas it reaches'20% forD 5 1800 mm and t 5 800 ps, indicating a largercontribution of multiple scattering. Measurementsat t 5 7.3 show that the slope of the curve atD5 1800mm is smaller than the one at D 5 305 mm: in thiscase the multiple-scattering contribution is signifi-cantly larger for D 5 1800 mm especially for largevalues of t.
D. Depolarization Caused by Multiple Scattering
The importance of polarization measurements in acloud sounding technique is outlined in Ref. 9. De-polarization of the lidar echo can be due to eithermultiple scattering effects or the nonsphericity ofdiffusing particles. The different cloud phases, ice,water, or mixed phase, can, in principle, be charac-terized by the different polarization of lidar returns.Since in ourmeasurements the diffusing particles canbe assumed spherical, the depolarization of the re-ceived radiation should be ascribed to multiple-scattering effects. Figure 7 presents the measuredratio between the cross- and the parallel-polarizedcomponents: PcyPp. This quantity can be consid-ered as a measure of the depolarization ratio.
20 September 1996 y Vol. 35, No. 27 y APPLIED OPTICS 5439
Fig. 6. Parallel ~continuous curves! and cross-polarized ~dashed curves! components of the lidar echo measured for two different valuesof the cloud–lidar distance: D 5 305 mm ~upper curves! and D 5 1800 mm ~lower curves!. Different panels refer to different values ofoptical thickness t and of the receiver angular field of view a.
The results show some typical features of depolar-ization that are due to multiple scattering: depolar-ization increases as the contribution of multiplescattering to the received echo increases. Thus de-polarization increases with the increase of ~1! theturbidity of the cloud, ~2! the angular field of view ofthe receiver, and ~3! the depth of the sounded region,i.e., of time. In particular, at t 5 0, Pc is smallerthan 2% of Pp in any case considered and increaseswhen t increases, but for large values of t the value ofPcyPp seems to show a saturation effect at leastwithin the temporal window investigated. The de-
5440 APPLIED OPTICS y Vol. 35, No. 27 y 20 September 1996
pendence on a is different for D 5 305 mm and D 51800 mm: for D 5 305 mm the curves that refer todifferent values of a become well separated for t . 50ps, forD 5 1800 mm the curves become separated fort . 200 ps. This is because, for larger values of D,the region of the medium seen by the receiver for afixed value of a becomes wider and the scatteredradiation takes a longer time to exit from this region.For measurements carried out on a suspension of
polystyrene spheres having a mean diameter of f 515.8 mm, we observed significantly different behaviorfor depolarization: a strong depolarization ~'20%!
Fig. 7. Ratio PcyPp between the cross- and parallel-polarized components of the lidar echo versus time for different angular fields of viewa. Different panels refer to different values of optical thickness t and the cloud–lidar distance D. The values of a corresponding to eachcurve are: 5.0, 2.5, 1.3 mrad ~upper to lower curves, respectively!.
Fig. 8. Measurements carried out on 15.8-mm microspheres: effect of nonspherical diffusers on the lidar echo: ~a!, ~b!, and ~c! theparallel ~solid curve! and cross-polarized ~dashed curve! components of the lidar echo measured at different optical thicknesses t and withdifferent angular fields of view a; ~d!, ~e!, and ~f ! the depolarization ratio PcyPp. The cloud–lidar distance was D 5 305 mm. The valuesof a corresponding to each curve are 5.0, 2.5, 1.3 mrad from upper to lower curves, respectively.
was measured even with a small turbidity ~t , 1!.At t , 1 the depolarization was almost independentof time. In these conditions the effect of multiplescattering is negligible and the depolarization cannotbe ascribed to multiple scattering. For thesespheres, the remainder of a three-year-old sample,observations with an optical microscope showedmany clusters of spheres, whereas for measurementswith f 5 6.4 mm the spheres were well separated.For measurements with 15.8-mm microspheres thescattering medium can thus be considered as a mixedphase medium in which both spherical and non-
spherical diffusers are present. The depolarizationwas thus ascribed, at least in part, to the nonsphe-ricity of the diffusers. The results obtained withthese diffusers are not useful for a comparison withnumerical results, since knowledge of the scatteringfunction is lost. Nevertheless, some of these resultsare presented since they can be useful to show thedifferent features of depolarization when nonspheri-cal particles are present. In Fig. 8 the parallel andcross-polarized components of the echoes are shownfor different values of t and a. To point out the effectof nonspherical diffusers on depolarization, we also
Fig. 9. Comparison between experimental ~dashed curves! and Monte Carlo ~solid curves! results. The parallel ~upper curves! andcross-polarized ~lower curves! components of the lidar echo are reported for t 5 7.3 and different values of the angular field of view andof the cloud–lidar distance.
20 September 1996 y Vol. 35, No. 27 y APPLIED OPTICS 5441
show the ratio PcyPp. Note that the nonsphericity ofscatterers is sufficient to explain the results for lowturbidity ~t 5 0.75!: in this case PcyPp is almostconstant when either t or a change. Both the non-sphericity ~to justify the strong depolarization atshort times! and the multiple-scattering effects ~tojustify the increase of PcyPp with time! should beconsidered to justify the results for t 5 3.3 and 4.9.
4. Conclusions
The results of lidar measurements on laboratory-scaled cloud models, carried out to investigatemultiple-scattering effects, have been presented.Measurements were repeated for different values ofthe parameters that affect multiple scattering. Theeffects of both the scattering coefficient of the mediumand the geometric parameters ~receiver field of view,cloud–lidar distance! were investigated. The exper-imental results enabled us to point out the depen-dence of multiple-scattering features on the differentparameters. The scattering medium was homoge-neous and with well-known optical properties. Theresults obtained can thus be useful to validate nu-merical or analytical models. A diskette with theresults is available for researchers interested in thecomparison.A comparison with the results of numerical simu-
lations carried out with the Monte Carlo code devel-oped by our group is in good agreement for a widerange of conditions and provides further validation ofthe calculation scheme. An example of comparisonbetween numerical ~continuous lines! and experi-mental ~dashed lines! results is reported in Fig. 9,which shows the parallel ~upper curves! and thecross-polarized ~lower curves! components of the lidarecho for t 5 7.3 and different values of a. Figures9~a!, 9~b!, and 9~c! refer to D 5 305 mm; Figs. 9~d!,9~e!, and 9~f ! refer to D 5 1800 mm. Since the ab-solute calibration of the receiver was not available, anormalization was necessary to compare experimen-tal and numerical results. We normalized data atD 5 305 and 1800 mm separately by equating to onethe maximum of measured and calculated returns fortotal energy ~Pp 1 Pc! that refers to a 5 5 mrad. Fort 5 7.3 Fig. 4 shows that the contribution of multiplescattering is important especially for large values of t.The excellent agreement observed for the parallelcomponent shows that theMonte Carlo code correctlyevaluates the effect of multiple scattering even whenthe contribution of high orders of scattering becomessignificant. Also for the cross-polarized componentthe agreement is good, especially for large values of t,
5442 APPLIED OPTICS y Vol. 35, No. 27 y 20 September 1996
showing the adequacy of the Monte Carlo code thatwas used to deal with depolarization caused by mul-tiple scattering. Further examples of comparisoncan be found in Ref. 10.Measurements of suspensions in which many clus-
ters of microspheres were present also showed theeffect on the depolarization ratio that is due to thenonsphericity of diffusers.
The authors express their thanks to the director ofthe LENS ~European Laboratory for Non-LinearSpectroscopy! for assistance and permission to usethe laboratory instrumentation. Research at theLENS was performed with the support of EuropeanCommunity contract GE1*CT92-0046. The re-search was partially (40%) supported by the Minis-tero dell’Universita’, Ricerca Scientifica e Tecnologicaproject, Physics of the Atmosphere and Ocean.
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