Transcript
Page 1: Lidar-inversion technique based on total integrated backscatter calibrated curves

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. Introduction

Over 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. Bissonnette7

has 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

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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 Theory

The 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:

rU(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 TIBhas 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 Setup

The 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

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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 Calibration

The 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 Measurement

The 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-

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bOfl 0

01h oo o v u 0LO ~ ~ On000 9

0 0.1 0.2 0.3 0.4 0.5 0.6

[C] 1, (g/m2

)

(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 EP

0~~~~

00

0 0.5 1 1.5 2 2.5 3

20.9 0 0.800 0.7leo 0.6 M 0.5

0.4

o 0.3C0 0.2

� 0.1c 0

0

_! 0.35

o 0.30o 0.250m 0.2

la 0.156)c; 0.1

) 0.05

0

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)

11 0 %L~gQ r

0 0.5 1 1.5

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

6) 0.5- 0.450 0.40)

- 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 coefficwill be fully addressed in Section 9. provides ini

6. Calibration With the Total Integrated Backscattering refers to theThe left side of Fig. 4 shows the range-resolved general hobackscatter signal S(r) and its associated TIB U(r). gven mateiOn the right side of Fig. 4, the TIB U(T) as a function gE uation cof the optical depth (T) is shown. Using these curves, inversion tewe will establish an equation that provides the extinc-tion coefficient value as a function of the distance r.

The optical depth is related to the TIB through a A. Calibraticfunction f(U). On the other hand, U is a function of It is assunr, i.e., U(r): applicable.

T = f[U(r)]. (8) provided by

Differentiating Eq. (8) yields

2 2.5 3

0O ~~~~ 0 o o 0 CE o 0

0 ° D r n

2 3 4 5 6

[c] 1, (g/m 2 )

(f)(a) Fog-oil, (b) graphite flakes, (c) brass flakes, (d)

*ssion dT/dr is the range-resolved extinc-ient per unit of length, where dU/dr:ormation on the specific cloud and df/dUcalibration curve.

ression for the extinction coefficient isvever, the expression df/dU is specific to arial and to the dispersion technique used.I will be referred to as the TIB lidarchnique.

)n of the LCM With the c* Curves

led that the classical lidar equation isTIB at a point i inside the cloud is

the following equation:

Ui(ri) = C*(1 - ). (10)

dT/dr = df/dU x dU/dr. (9) An increment AU, in the TIB associated with an

20 November 1993 / Vol. 32, No. 33 / APPLIED OPTICS 6757

' 0.4

0.35-0

00 0.3 -o 0.25 -m 0.2

la 0.1564)

0.1

) 0.05)

4)0.28

O 0.2

00i 0.15eD

0.1

6)0 0.05

6)0

_ 1.4

0 1.20

C.m o10

CO 0.8

0.6

_0.4

0) 0.2

O 0

l l l

iE

Page 5: Lidar-inversion technique based on total integrated backscatter calibrated curves

m . 366E01 + 9.03E-03b * 5.41E-02 +I- 4.10E-03se(y) . / 2.59E02F - 1.64E03dl- 1.17E+02

0.1 0.2 0.3 0.4 0.5 0.6

1 - exp(-2 a [C] )

(a)

. 0.9

0.0

' 0.6-0

0.4

.0 0.3

4- 0.1

0.7 0.8 0.9 . O 0.2 0.4 0.6 0.8

1 - exp(-2 a [c] )

(d)

m * 2.29E-01 4- 4.28E-03b -2.31E-024+13.11E-03se(y) + 1.43E-02F - 2.86E+03dl - 3.28E+02

0

0.2 0.4 0.6 0.8 1

1 - exp(-2 a c] I)

(b)

m - 1.21E+004+-3.73E-02b -1.86E-01 4- 2.73E-02se(y) .+/ 1.40E-01F - 1.06E+03df .1.49E+02 0.5

o 0.45o 0.4

CM0 0.35

0.30.2

o 0.21

I ~ ~ ~ ~ ~ ~ ~0.0500.2 0.4 0.8 0.8 1 .s

1 - exp(-2 a [c] 1)

(c)

Fig. 2. Total integrated backscatter as a function of {1flakes, (e) kaolin, and (f) Arizona road dust.

increment Ar is given by

AUi = U,+, - U, = C*(Ti2 - Ti,12)

= c*(Ti + Ti+,)(Ti - Ti+,)-

m - 3.21 E-01 +/ 5.63E-03b - -4.51E-024 4.36E-03se(y) +/-1.41 E-02F * 3.25E+03dO - 2.48E+02

03

0.2 0.4 0.6 0.8 1

1 - exp(-2 a [C] )(e)

m . 3.74E-01 +/- 8.46E-03b .94E-02 +/ 6.04E-03se(y) +/- 3.99E-02F 1.95E+03df - 2.45E+02

0.2 0.4 0.6 0.8

- exp[-2a(c)l]}. (a) Fog-oil, (b) graphite flakes, (c) brass flakes, (d) aluminum

When Ar tends toward zero, we have

(11)

By setting (Ti + Ti+,) = 2(Ti), (Ti - Ti+,) = AT, andusing Beer's law, AT = -(Tj)Ar, we can rearrangeEq. (11) to give the extinction coefficient at i:

Coi = AUi/(2c*(T 12 )Ar). (12)

a(r) = [1/(2c*T2)]dU/dr.

Using Eq. (6), we find

c(r) = [1/(2c*) x 1/(1 - U/c*)]dU/dr.

Using the general form of Eq. (9), we find

df/dU = 1/(2c*) X 1/(1 - U/c*).

6758 APPLIED OPTICS / Vol. 32, No. 33 / 20 November 1993

0

.0co

0)6)

ca

0.4

0.35

0.3

0.25

0.2

0.15

0.1

0.05

0

m. 5.98E01 +l- 1.76E-02b . 2.12E-01 / 9.85E03s.(y) - +- 7.20E-02F- 1.16E03dl - 2.43E+OZ

6) 0.35

3O 0.30COm 0.250CU3ED 0.2 -

0.15

2 O. 1

c 0.05Oa

0

0.25 -.

6)

'U).- 0.25-.UM 0.15-

0)

0.o1

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C O

1 1.66)_ 1.4

0 1.2On0 1US

,m 0.8

0.6

) 0.4

'- 0.2

0.2

- 0.2

1 - exp(-2 a(f)

IC] I)

(13)

(14)

(15)

1

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1.2

4J14.)

0 0.8

M 0. 6 Al flakes

4j 0.4 / Arizona Road dust

° .2/ Kaolin

m 0.26

rf Graphite flakes

Optical depth

Fig. 3. Polynomial best fit of the total integrated backscatteringsignal as a function of smoke-chamber concentration path-lengthproduct.

This last equation can be derived from the moregeneral expression Eq. (9) and the expression for theTIB in the single-scattering limit.

From Eq. (6) we have U = c*(1 - T2) and T=exp(-KT). It follows that

r = f(U) = -1/2 In( - Ulc*) (16)

and df(U)IdU = 1/(2c*) x 1/(1 - Uc*), which isidentical with Eq. (15).

7. Implementation of the Calibration

In Section 6, data obtained from the smoke chamberwere used to define calibration curves for later use inthe field. With proper instrumentation it is possiblein principle to obtain calibration curves in the field.To do so we must set the LCM in the fixed-positionfiring mode. A Nd:YAG transmissometer is set upcolinear with the LCM. A solid target is also set atthe back of the cloud to permit direct transmissionmeasurements with the LCM. Enough data shouldbe collected to cover the full transmission range andto obtain good mathematical fit to the data. Withproper positioning of the transmissometer it is pos-

Distance, r

6)

0'A

.0dcoM

nC

1 2 3

Optical depth,

Fig. 4. Link between a range-resolved backscatter lidar signal andthe total integrated backscatter calibration curve.

sible to cover the full range of transmission. Thefirst step is to plot the LCM target transmissionmeasurements as a function of the Nd:YAG transmis-someter measurement. A straight line with a slopeof 1 should be obtained. The next step is to plot theTIB signal as a function of the Nd:YAG extinctionmeasurement (-In T) or the LCM target extinctionmeasurement. A polynomial fit could be applieddirectly to this set of data, which defines the calibra-tion curve, or the less general form can be obtained bycalculation of the c* constant from a plot of the TIBsignal as a function of (1 - T 2).

The TIB measurement is specific to a given aerosolsize distribution. If this distribution changes withtime (because of sedimentation, agglomeration, evapo-ration, or air moisture condensation) the TIB calibra-tion is no longer valid.

8. Use of Natural Atmospheric Aerosols as a TargetBackground

The derivation of a calibrated total integrated back-scatter (TIB) curve requires the measurement of theoptical depth. This could be obtained from thetransmission measurement from a suitable target orwith a transmissometer colinear with the lidar firingdirection. These two techniques present the disavan-tage of requiring a target board or a detector systemat the back of the cloud, which is not always possible.For the LCM, ideally a target filling the whole back ofthe cloud is required. This suggests the use of theambient atmospheric aerosol as a suitable target fortransmission measurements. To determine if theatmospheric aerosol background can be used, a lidarsystem with an E = 100 mj laser source, a 10-ns pulsewidth, and a collective optic A of 7r 0.12 M2 isconsidered. The detected power at a position r at theback of the cloud is given by

p(r) = Ec/(2r2 )Af3(r)T2 exp(-2ur), (17)

where T2 is the transmission through the cloud and,8(r) = 0.02cr(r), rural aerosol,'7 70% relative humidity.To be detected, p(r) must be significantly higher thanthe detection system noise. Typically the currentnoise of a logarithmic amplifier is of the order of 1 VLA.A current of 2 ,uA is considered to be detectable. Ifthe detection system generates 0.34 A/W, this corre-sponds to a detectable pm(r) of approximately 0.6 [iW.Arranging Eq. (17), we find

Tm = {2pm(r)r2/[EcAP(r)exp(-2orr)]}/ 2 . (18)

In this equation, T represents the minimumtransmission measurement possible. Figure 5 showsTm as a function of atmospheric extinction for threedistances r (100, 200, and 400 m) from the lidarsystem. The curves show a minimum over a rela-tively large number of atmospheric extinction coeffi-cients. The range of possible transmission measure-ments increases with the atmospheric extinction tothe point where the atmospheric attenuation be-comes significant; then the minimum possible trans-mission increases. T shows a strong dependence

20 November 1993 / Vol. 32, No. 33 / APPLIED OPTICS 6759

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.. ' r = 400 m

* .: +. ***9w.*~44**f*~ r = 2 0 0 m0

r = 100 mn

0 0.002 0.004 0.006Atmospheric Extinction, 1/m

0.008 0.01

Fig. 5. Minimum transmission measurement as a function ofatmospheric extinction.

L 0.18_ 0.16'U 0.14

0.12

01ED 0.08

X 0.080.06-At 0.04

l 0.020)6) U 1-

.

01

03

5 L=8mL = 16 m

0 0 0.5 1 1.5 2 2.5 3 3.5

Optical depth

Fig. 6. Total integrated backscatter as a function of optical depthfor two cloud widths.

on r. As an example, the minimum transmissionmeasurements achievable with an atmospheric extinc-tion of 2.0 x 10-4 m-', which corresponds to avisibility of 15 km, are 0.2, 0.38, and 0.78, when thecloud is within 100, 200, and 400 m of the lidar,respectively. The use of atmospheric backscatter fortransmission measurements is limited to high trans-mission values.

9. Limitations of Total Integrated Backscattering LidarInversion Technique

The TIB value is not unique for a given extinction andtends to level off for high extinction values. Becauseof multiple scattering, the TIB value is a function ofthe extinction coefficient and of the optical pathlength. To evaluate the importance of the mul-tiple-scattering effect, the module NBSCAT'8 ofEOSAEL92 was used. The module NBSCAT is amultiple-scattering propagation model applicable tonarrow light beams transmitted through aerosolclouds. The module calculates the transmitted andbackscattered irradiance profiles as a function of thefield of view, and the on-axis transmitted power andlidar returns for specified receiver geometries. Thealgorithm is based on the radiative transfer model ofBissonnette' 9 and validated against laboratory dataas reported in Bissonnette et al. 16

Using NBSCAT, we calculated the range-resolvedpower,p(r), with the following parameters: distancefrom the cloud, 100 m; collecting optic, wr X 0.12 M 2

;

beam divergence, 0.2 mrad; cloud depth, 8 and 16 m;cloud extinction coefficient, 0.05-0.4 m-'; field ofview, 6 and 10 mrad. The TIB was obtained bysumming the product p(r)r2dr.

Figure 6 shows the TIB aas a function of the opticaldepth for two cloud depths. Note that it is necessaryto multiply they axis by Ec/2, where E is the energyin joules per pulse and c is the speed of light inkilometers per second. For a field of view of 6 mradand at an optical depth of 1.6, the TIB value for the8-m-deep cloud was approximately 15% larger thanthe TIB value for the 16-m-deep cloud. Qualita-tively this can be simply understood.' 6 At largeoptical depths, most of the received backscatter origi-nates from the front end of the cloud, because thebackscatter from regions further into the cloud isattenuated by the cloud in front. Therefore, for thesame optical depth, clouds that are denser in the front

section should produce greater returns. Therefore,for high extinction values, a TIB calibration curvespecific to the cloud depth is required.

The TIB value is also sensitive to the cloud struc-ture. Figure 7 shows the TIB value as a function ofoptical depth for two cloud shapes: a rectangularconcentration profile and a triangular concentrationprofile, both of which were 16 m in depth. In thiscase the TIB value for the rectangular concentrationprofile exceeded the TIB value of the triangularconcentration profile by approximately 6% at anoptical depth of 1.6.

The lidar inversion algorithm described in Section6 refers to a calibration curve specific to a material.It has been shown that because of multiple scatteringthe TIB calibration curves are not unique for a givenmaterial. It is therefore necessary to determine theeffect of the calibration curve on the lidar inversionalgorithm.

The calibration curve was generated with the helpof NBSCAT. The TIB was calculated for a series ofclouds with a rectangular smoke profile. The depthof the clouds was 16 m, and the optical depth variedfrom 0 to 3.2. As above, the cloud was set at 100 mfrom the lidar system; the other parameters wereidentical with those used for Figs. 6 and 7. Therange-resolved backscatter signal from two cloudswith a triangular concentration profile (depth = 16m, optical depth = 1 and 2) were generated. Theinitial cloud structure was recovered from the range-resolved backscatter signal and TIB calibration curvewith the help of the TIB lidar inversion algorithm

!! 0.14 1

CO 01

.X 0.1-0vtow

0.06 -.)0 .0 6) 0.04 -

' 0.02

a)

-

N

* A

.

A

A

H

:U0

0 0.5

* rectangular cloud profileA triangular cloud profile

1.5 2

Optical depth2.5 3 3.5

Fig. 7. Total integrated backscatter as a function of optical depthfor two cloud shapes: a rectangular concentration profile and atriangular concentration profile, both of which were 16 m deep.

6760 APPLIED OPTICS / Vol. 32, No. 33 / 20 November 1993

0.9u 0.8 -

E) .0@

I- V 0.5 -E -

-a 4 0.4 -

,E 0.3-

E 0.2-

0.10 | I I __§ { . I I

Page 8: Lidar-inversion technique based on total integrated backscatter calibrated curves

a) Cloud Extinction Profile_ 12.0 t

b) Ran(0.012

0

0'. 0

97.5 107.5 117.5Distance (m)

Corrected Backscatter Signal p(r) r2

"\. I

I:IJ I

97.5

e) Calibrated TIB, M(U)

3.0

2.0

1.0

0.0

c) Total0.1

0.00 0.04 0.08 0.12Total Integrated Backscatter, }

107.5Distance

I

KI

117.5(m)

Integrated Backscatter U(r)- Y p(r) r2 Ar

9 7.5 107.5 117.5Distance ()

0.0 0,04Total Integrated

E

C

C

Kx

d) Note: p(r]0.012

0.0 "-'97.5

I r2 - dU(r)/dr

(N.*I

107.5Distance

g) dU(r)/dr - dr(U)/dU1 2.0 °

0. 0 1

97.5 107.5Distance ()

117.5

Fig. 8. Full process of the total integrated backscatter idar inversion algorithm.

described in Section 6. Figure 8 illustrates the fullprocess of the TIB lidar inversion algorithm. Figure8(a) shows the original smoke cloud extinction profile.It is 16 m in length and has an optical depth of 1.Figure 8(b) represents the range-corrected backscat-ter signal [p(r)r2 ] calculated with NBSCAT. Figure8(c) represents the range-resolved TIB, U(r). Figure8(d) shows the derivative of U as a function of r,dU/dr; it is identical with Fig. 8(b). Figure 8(e)shows the calibration curve, T(U), for a rectangularconcentration profile cloud and its polynomial fit, and

Fig. 8(f) shows the derivative of the polynomial fit,dT(U)/dU. Figure 8(g) shows the product dU/drdT(U)/dU and the original cloud extinction profile.

Figures 9(a) and 9(b) show the original smokeclouds and the reconstructed smoke clouds for twoclouds having triangular extinction profiles and opti-cal depths of 1 and 2. The reconstructed cloud forthe small optical depth is closer to the initial cloudthan for the higher optical depth. The discrepancyis caused by a mismatch of the TIB of the signal toinvert with the TIB calibration curve (see Figs. 6 and

20 November 1993 / Vol. 32, No. 33 / APPLIED OPTICS 6761

C

E

0x)

Ew

0.0

f) dc(U)/dU

3 0

20

0.

M

E0

.0

0 K(m)

117.5

- l l l l

lge

I

*

Page 9: Lidar-inversion technique based on total integrated backscatter calibrated curves

Optical Depth =1

* SeulesI

0 Serles2

The sensitivity of the method to measurementerror is strongly related to the quality of the calibra-tion curve. The relative error in the extinctionmeasurement can be obtained from Eqs. (9) and (16),i.e.,

Au/, = Ac*/c* + AU/U + AP/P + Ar/r.

Optical Depth = 2

102.5 107.5 112.5Distance (m)

Fig. 9. Original clouds and reconstructed cloudslar extinction profiles with optical depths of 1, 2, a

7). 'Ihe TIB calibration curve is sensitive to clouddepth and structure for optical depths higher than 2,and a small change in the TIB value corresponds to asignificant change in the optical depth. Figure 9(c)shows the original smoke cloud and the reconstructedsmoke clouds for a triangular extinction profile andan optical depth of 2; it is similar to Fig. 9(b) exceptthe TIB calibration curve used is the exact TIB curveof this particular cloud. As expected, the agreementis good. Figure 9(c) shows the sensitivity of thetechnique to small oscillation of the high-order poly-nomial best fit. The oscillations disappear when aseries of linear regressions is used.

The error in range, Ar/r, is typically less than 1%,whereas the relative error in the detected power(AP/P) has a maximum value of 4% for a 4-decadelogarithmic amplifier coupled to an 8-bit A/D con-verter. U is the summation of the range-correctedpower P, and the relative error AU/U is 5%. Therelative error in the calibration constant Ac*/c*,based on Figs. 4(a)-4(f), is approximately 10%.Therefore the error in the extinction measurementshould be less than 20%. However, for high opticaldepths, the TIB calibration curves show a closedependence on cloud depth and structure because ofmultiple scattering. Hence a relative error as highas 70% [see Fig. 11(b)] can occur when there is amismatch between the smoke cloud (structure anddepth) and the selected calibration curve.

10. Discussion of Results

The TIB values were found to be reproducible. TheTIB plotted as a function of the concentration path-

117.5 122.5 length product or the optical depth defines a calibra-tion curve specific to a material, a disseminationtechnique, and the LCM. This calibration curve canbe used for field measurements. However, for opti-cally thick clouds, the TIB value levels off (forextinction values higher than 2). It makes the mea-surements of optically dense clouds inaccurate.

* Serlesi Moreover, because of multiple scattering the TIBo Serle~s2 calibration curve is sensitive to cloud depth and

structure for optical depths higher than 2. Thiseffect could be reduced with the use of a narrowfield-of-view detector. Therefore the TIB lidar inver-sion technique is limited to optical depths smallerthan 2. However, the difference between the de-tected power at two different fields of view wouldallow more precise measurements in dense clouds by

117.5 122.5 taking into account the contribution of multiplescattering. 2 0

for threetriang- Well-controlled measurement of the TIB needs toLnd 2. be performed for various cloud depths to determine

the importance of the multiple-scattering effect.

1 1. Conclusion

The lidar inversion technique in which the totalintegrated backscatter (TIB) is used can be appliedwith confidence for optical depths smaller than 2.For optical depths greater than 2 it is sensitive to thecalibration curve used. For large optical depths,multiple scattering affects the calibration curve. Infield experiments, atmospheric aerosols can be usedto measure transmittance of artificial clouds.

We wish to thank D. Hutt for his helpful com-ments.

6762 APPLIED OPTICS / Vol. 32, No. 33 / 20 November 1993

0.14

0.12

- 0.1: 0.08

t 0.06

V 0.04

0.02

097.5 102.5 107.5 112.

Distance (m)

(19)

0.25

_ 0.2E

0.150-

. 0.1

0.05

0

0.25

0.2

_ 0.15

ii 0.1

0.05

97.5 102.5 107.5 112.5Distance (m)

Optical Depth=2, Cal O.D =2

0 Il r

97.5

Page 10: Lidar-inversion technique based on total integrated backscatter calibrated curves

References1. R. M. Bilbe, S. J. Bullman, and F. Swaffield, "An improved

Raman lidar system for the remote measurement of naturalgas releases into the atmosphere," Meas. Sci. Technol. 1,495-499 (1990).

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10. B. T. N. Evans and G. Roy, "Lidar measurement of concentra-tion and turbulence in battlefield obscurants," in ConferenceProceedings of AGARD, 454, Atmospheric Propagation in theUV, Visible, IR and MM-Wave Region and Related SystemAspects (Advisory Group for Aerospace Research and Develop-ment, Nevilly sur Seine, France, 1989), p. 28-1-28-12.

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13. G. Roy and G. Vallde, "Laboratory evaluation of potentialinfrared screening powders," Rep. DREV R-4427/86 (DefenceResearch Establishment Valcartier, Quebec, 1986), pp. 1-31.

14. G. Roy and G. Vallee, "Laboratory evaluation of infraredscreening metallic powders," in Proceedings of Smoke Sympo-sium IX (Aberdeen Proving Ground, Washington, D.C., 1985),pp. 77-91.

15. C. Bruce and L. F. Hall, Measuring Aerosol Density UsingNephelometry and Dosimetry (Center for Atmospheric Sci-ences, New Mexico State University, Las Cruces, N.M., 1987),Chap. 5, pp. 127-142.

16. L. R. Bissonnette, R. B. Smith, A. Ulitsky, J. D. Houston, andA. I. Carswell, "Transmittedbeam profiles, integrated backscat-ter, and range-resolved backscatter in inhomogeneous labora-tory water droplet clouds," Appl. Opt. 27, 2485-2494 (1988).

17. R. C. Shirkey, R. A. Sutherland, and M. A. Seagraves, "Aerosolphase function data base PFNDAT," in EOSAEL 87, (Atmo-spheric Science Laboratory, White Sands Missile Range, N.M.,1987), pp. 1-76.

18. L. R. Bissonnette, "Multiple scattering propagation moduleNBSCAT," in EOSAEL 92 (Atmospheric Science Laboratory,White Sands Missile Range, N.M., 1992), pp. 1-43.

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

20. L. R. Bissonnette and D. L. Hutt, "Multiple scattering lidar,"Appl. Opt. 29, 5045-5046 (1990).

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