# Lidar-inversion technique based on total integrated backscatter calibrated curves

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Lidar-inversion technique based on totalintegrated backscatter calibrated curves

Gilles Roy, Gilles Vall6e, and Marcelin Jean

The integrated backscatter signal from a smoke cloud contained in a chamber is studied as function of themeasured concentration. An analysis based on the total backscattered signal leads to the determinationof calibration curves specific to the material and to the lidar system. This procedure leads to a lidarinversion technique based on a calibrated total integrated backscatter curve. The limitation of thetechnique is discussed in terms of the maximum optical depth permitted for acceptable results.

Key words: Lidar, smoke, obscurant.

1. IntroductionOver the past few years there has been a growinginterest in the field of remote sensing of smoke cloudswith lidar systems. The use of scanning lidar sys-tems for remote sensing of gas' or aerosol emissionsfrom smoke stacks is a subject of growing interestwith new environmental protection legislation. Scan-ning lidar systems have also been considered for theremote detection of chemical2 or biological3 4 5 agents.A scanning lidar system known as the laser cloudmapper (LCM) has been used at the Defence ResearchEstablishment Valcartier for the evaluation of screen-ing military smokes. As for all instruments thequestion of calibration has to be addressed.

Until the far-end solution introduced by Klett,6 theinversion of lidar returns to obtain extinction coeffi-cient profiles was plagued by instability and inaccura-cies. The instability of previous solutions is found tobe caused by mathematics. The far-end solution ismore stable in all respects and for most practicalsolutions than the near-end solution. Bissonnette7has shown that a stable solution is one for which theboundary value is assigned at the range where therange-corrected lidar signal is a minimum providedthe extinction value is nonvanishing at that point.This last condition is generally not respected whendealing with smokes and obscurants. Moreover theseclouds usually present a multiple-scattering effect

The authors are with Energetic Materials Division, DefenceResearch Establishment Valcartier, P.O. Box 8800, Courcelette,Quebec GOA 1RO, Canada.

Received 30 July 1992.0003-6935/93/336754-10$06.00/0. 1993 Optical Society of America.

because of their high density. Evans8 introduced in1982 a fairly general and robust technique for inver-sion of the lidar equation. This technique is basedon the measurement of the total backscatter signal.In single-scattering theory the integrated normalizedbackscatter has a maximum value. If this value isexceeded as a result of multiple-scattering contribu-tions, then numerical compensation is applied to keepthe signal within the allowable limit (conservation ofenergy). The method allows to some extent correc-tion for multiple scattering and for the down time ofthe detection system (including the logarithmic ampli-fier). The algorithm is fairly general in the sensethat it is not specific to a given aerosol. However,the numerical compensation is specific to the lidarsystem. This algorithm has been successfully usedwith the LCM to measure the mass concentration ofaerosols. In Refs. 9 and 10, LCM results are com-pared with those of nephelometers. Although thefield trial was not a well-controlled experiment, theconcentration measurements agreed within a factorof 3.

A lidar inversion technique based on total inte-grated backscatter (TIB) calibrated curves is pre-sented. The TIB measurements are performed as afunction of the optical depth for various obscurants ina controlled environment. These calibration curvescould then be used for field evaluation of cloudobscurants. The TIB calibration curves obtainedare general in the sense that it is not necessary to usethe lidar equation to perform the inversion; a linearrelationship is not assumed between the backscatterextinction coefficient (13) and the extinction coefficient(a). However, the TIB calibration curves are specificto the lidar system that has been used to obtain the

6754 APPLIED OPTICS / Vol. 32, No. 33 / 20 November 1993

calibration curves and to the aerosol material and sizedistribution.

This paper is organized as follows. A brief reviewof the basic single-scattering lidar theory and itsinteraction with the TIB is provided in Section 2.Sections 3 and 4 contain a description of the instru-mentation and setup, the experimental methodology,and the concentration measurement calibration.In Section 5 the TIB measurements are presented intheir general form and in a second form to which thelidar equation was applied. Sections 6, 7, and 8present the TIB lidar inversion algorithm, the imple-mentation of the calibration, and the use of naturalatmospheric aerosols as a target background. Thisis followed in Sections 9, 10, and 11 by an analysis ofthe limitations of the TIB inversion technique, ashort discussion of the results, and a conclusion.

2. Basic Lidar TheoryThe range-resolved power-backscattered signal isgiven by the following lidar equation:

P(r) = 1/2PoctF(r)p(r)/r2 exp[-2 f u(r')dr'], (1)where Po is the laser power pulse, c is the speed oflight, tp is the pulse width, and F(r) is the systemoptical characteristic. F(r) is usually considered tobe a constant, r is the distance, (x(r) is the extinctioncoefficient, and (r) is the volume backscatteringcoefficient.

When the natural atmospheric aerosols' backscat-ter contribution to measured signal is negligiblerelative to the cloud aerosol contribution, the range-corrected backscatter signal can be written as

S(r) = 2c*(c exp[ -2 f u(r')dr'] (2)where c* = [P0CtpF(r)]/4}k; c* is dependent on thelidar system and aerosol type. The value k is thebackscatter-extinction ratio. A linear law has beenassumed; this is generally the case when multiplescattering is excluded and the aerosol size remainsconstant."

The calculation of the total integrated backscatter(TIB), (U), is obtained by performing the integrationof S(r) over r:

r

U(r) = S(r")dr". (3)

When a single-scattering lidar equation is used [Eqs.(1) and (2)], the TIB is reduced to

U(r) = 2c* f u( ")exp[ - 2 f (r')dr']dr's (4)using the definition of one-way transmission to a

distance r, i.e.,

T(r) = exp]-u(r')dr'], (5)and with the change of variable, cr(r')dr' = -dT'/T',we find

U~)=fS d 2 x(2l T'dT/TU(r) = S(r")dr = 2 * Jexp(-2 n T')(-dT'/T')

= c*(1 - T2). (6)Therefore under single-scattering theory, the TIB

has a maximum value equal to c* when T = 0. Alinear regression of the TIB signal U as a function of(1 - T2 ) will provide a value for the material systemconstant c*.

3. Experimental SetupThe experimental configuration consisted of the de-ployment of the lidar system, the field stop target (i.e.,a plywood baffle) at a 50-m range, and the largeoutdoor aerosol chamber at a 100-m range. Thelidar experiments were conducted at the DefenceResearch Establishment Valcartier lidar range facil-ity from June to September 1991. Measurementswere made of the backscatter signal from knownaerosol concentrations located in the aerosol chamber.The aerosol clouds released in the chamber were asfollows: fog-oil, Arizona road dust, kaolin, brassflakes, aluminium flakes, and graphite flakes. Theconcentrations varied from 0.0 to 0.8 g/m3. Thepulsed idar was aligned optically to fire through theopening in the baffle and the central portion of theaerosol chamber (the lidar was not operated in thenormal scanning mode). For this study, laser pulseswere fired through the aerosol chamber for 50 sfollowing opening of the chamber doors. The lidarshots were generated at a frequency of 1 pulse/s, andthe digitizer sampling interval was set at 10 ns. Thesampled propagation path of the lidar was terminatedat a range of 180 m from the transmitter-receiver, arange that corresponds to a sampling requirement of120 data points per lidar shot for the specifieddigitzer-sampling interval.

The LCM'2 used is a monostatic backscatter lidarsystem that is equipped with a ruggedized Q-switchedNd:YAG laser (1.5 mrad divergence) for the transmit-ter. The laser supplies pulses of near-infrared radia-tion at the fundamental wavelength of 1064 nm; eachpulse has a nominal peak energy of 30.0 mJ and aduration of 10 ns. The range-resolved backscatteredlight is collected by the receiver telescope optics and isfocused on a sensitive silicon-avalanche photodiodewith an electrical output signal that is conditionedthrough a 4.5-decade logarithmic amplifier and digi-tized by a 100-MHz Biomation transient recorderwith an 8-bit resolution.

There is some off-axis scattering of the laser beamfrom the transmission optics of the LCM. A field

20 November 1993 / Vol. 32, No. 33 / APPLIED OPTICS 6755

stop was required to avoid detecting backscatter ofthis off-axis radiation from the smoke chamber struc-ture. Thus the field of view of the instrument waslimited to 10 mrad.

The smoke chamber was 7.3 m long, 2.4 m high,and 2.4 m wide. It was built with black paintedplywood. The styrofoam doors at both ends of thechamber were controlled by two independent garage-door openers. It took 9 s to open or close the doorscompletely. Two small mixing fans were located inthe chamber. They were operated during aerosoldissemination and were switched off prior to openingthe doors to minimize the escape of aerosol from thesmoke chamber. The dissemination was achievedwith a pneumatic nozzle13"4 for all the materialsexcept the fog-oil, for which a Pepper Fogger (Smith& Wesson) was used. Five He-Ne (0.6328 tum)transmissometers were mounted at a right angle tothe LCM firing axis. A single laser source was splitinto five beams with beam splitters. The path lengthsacross the chamber were each 2.4 m. The pathlengths were 1.2 m apart and were at the same heightas the LCM laser beam. The detectors' field of viewwas 16 mrad. The transmission value of each trans-missometer was read every second.

4. Concentration Measurement CalibrationThe concentration measurements of aerosols withthe transmissometers required calibration. To doso, all the aerosols under study were dispersed in alarge silo-shaped smoke chamber 3,' 4 with a volume of323 M3 . The dissemination technique was identicalwith the one that was used in the mini-range chamber.The aerosol mass concentration was obtained bycollecting the aerosol on filter paper and using an airsampling flow rate of 50 L/min. A large range ofaerosol concentrations were generated inside the silo,and the corresponding nephelometer' 5 and transmis-someter signals were recorded. To be able to deter-mine aerosol mass concentrations with the transmis-someter, it was necessary to determine first the massextinction coefficient of the material. It was ob-tained by plotting -ln(T) as a function of the siloconcentration path-length product. The slope of thecurve obtained was the mass extinction coefficient ofthe material. It has units of meters squared pergram. The silo measurements were then applieddirectly to the mini-range site. Once we knew thesmoke cloud width (lw) along the transmission pathand the mass extinction coefficient (a) of the aerosolmaterial present, the He-Ne mini-range transmissiondata were converted to mass concentration, [c] i.e.,

[C] = ln(THeNe)/(a-HeNelw)- (7)For the convenience of data presentation the con-

centration data will be multiplied by the mini-rangechamber length 1l.The quantity obtained will bereferred to as the concentration path-length product.The values of the mass extinction coefficients arelisted in Table 1.

Table 1. Mass Extinction Coefficients for the Six Materials Studied

Mass Extinction Coefficient (m2/g)Material He-Ne (0.6328 p.m) Nd-YAG (1.06 pum)ARD 0.9 0.1 0.7 0.1AI-40XD 2.2 0.2 2.5 0.2Br-9820P 1.6 0.2 1.8 0.4Fog-oil 7.3 0.7 2.3 0.7Graphite 1.9 0.3 2.2 0.3Kaolin 1.1 0.1 1.2 0.2

5. Total Integrated Backscatter MeasurementThe total backscatter measurement is the integralover r of the range-corrected detected power [Eq. (3)].Figures 1(a)-1(f) show the TIB as a function of thesmoke cloud concentration pathlength product forthe six materials studied. All the curves show thesame characteristic, the integrated backscatter tendstoward a saturation value for high aerosol concentra-tions. According to the basic theory presented inSection 2, the maximum value assuming single scat-tering is c*, where c* is a constant specific to thecombined effects of the material, the disseminationtechnique, and the LCM. The particle-size distribu-tion of the smoke cloud is strongly affected by thedissemination technique used. However, in the pres-ence of a high concentration path-length product thesingle-scattering theory is no longer valid because ofmultiple-scattering events.

The total backscatter measurements can be used todetermine the aerosol and system constant: c*.Figures 2(a)-(f) are plots of the total backscattermeasurement as a function of {1 - exp[-2a(c)f]}, seeEq. (4); a is the mass extinction coefficient at 1.06 jim.According to single-scattering theory, a linear regres-sion should be used to fit the data. The slope of thisline is the c* coefficient. All the materials presentacceptable straight lines.

Figure 3 shows polynominal fits of the TIB signalas a function of smoke chamber optical depth for thesix materials studied. The difference between thedifferent materials is very apparent. The metal flakes(brass and aluminium) give a much stronger returnsignal than the others materials. The x axis is theoptical depth (i.e., at[c]l). In the single-scatteringapproximation a smoke cloud formed of aerosol X hasa unique TIB value for a given optical depth. It istherefore possible to derive a calibration curve spe-cific to an aerosol.

According to the theory developed in Section 2, theTIB has a maximum value of c*. For values ofextinction higher than 2, the TIB levels off. Forhigh extinction values (> 2), multiple scattering startsto be significant.'6 For a highly absorbant material(e.g., graphite flakes) multiple scattering is less impor-tant as much light is absorbed. However, metallicflakes act like little mirrors, so that multiple scatter-ing may be important.

There is experimental evidence that multiple scat-toring causes nonunique total baclscattering measure-

6756 APPLIED OPTICS / Vol. 32, No. 33 / 20 November 1993

bOfl 001h oo o v u 0

LO ~ ~ On000 9

0 0.1 0.2 0.3 0.4 0.5 0.6[C] 1, (g/m 2 )(a)

0 0

0 0.2 0.4 0.6 0.8 1 1.2[c] IJ (g/m 2 )

(b)

0 30 0 1 00a 0 d~p EP0~~~~

00

0 0.5 1 1.5 2 2.5 3

20.9 0 0.800 0.7leo 0.6 M 0.5

0.4o 0.3C0 0.2

0.1c 0

0

_! 0.35o 0.30o 0.250m 0.2

la 0.156)c; 0.1

) 0.050

0 QC] 0 0

P 0 9 00 00o0B 0 ogE o

0.2 0.4 0.6 0.8

[C] 1, (g/m 2)(d)

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[c] 1, (g/m 2 )(e)

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- 0.350m 0.3

0.25'a 0.2CD 0.15(: 0. 10)0 0.05e 0

0

[c] 1, (g/m 2 )(c)

Fig. 1. Total integrated backscatter as a function of the smoke cloud concentration.aluminum flakes, (e) kaolin, and (f) Arizona road dust.

ments.16 For a given optical depth, multiple scatter- The expriing will cause the TIB to be higher. This question tion coeffic...

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