target reflectance measurements for calibration of lidar atmospheric backscatter data

Target reflectance measurements for calibration of lidaratmospheric backscatter data

Michael J. Kavaya, Robert T. Menzies, David A. Haner, Uri P. Oppenheim, and Pierre H. Flamant

Wavelength and angular dependence of reflectances and depolarization in the 9-11-ym region are reportedfor four standard targets: flowers of sulfur, flame-sprayed aluminum, 20-grit sandblasted aluminum, and400-grit silicon carbide sandpaper. Measurements are presented and compared using a cw CO2 grating-tun-able laser in a laboratory backscatter apparatus, an integrating sphere, and a coherent pulsed TEA-CO2 lidarsystem operating in the 9-11-,m region. Reflectance theory related to the use of hard targets to calibratelidar atmospheric backscatter data is discussed.

1. Introduction

Aerosol backscatter measurements at CO2 laserwavelengths are important for assessing the feasibilityof an earth-orbiting tropospheric wind measurementtechnique using CO2 Doppler lidar to provide data forforecasting and for studies of transport processes. 1' 2 Acoherent laser radar has been constructed using an in-jection-locked TEA-CO2 laser transmitter which isgrating tunable from 9 to 11 ,um to measure troposphericaerosol backscatter coefficients as a function of altitudeand wavelength.

A standard hard target is desired to aid in the cali-bration of the responsivity of the lidar system and toallow quantitative comparison of our backscatter datawith data taken by others. An ideal target would beeasy to fabricate, reproducible, durable, and have awell-known bidirectional reflectance-distributionfunction (BRDF)3 at all wavelengths in the spectralregion of interest. The target's BRDF and the lidarsystem-target geometry could then be combined withthe target pulse return data to calibrate aerosol back-scatter data. Although hard targets are frequently usedto calibrate lidar systems, there is a surprising lack ofpublished information about their reflectance proper-ties, particularly the BRDF.

In this paper we review the reflectance theory of hardtargets and apply it to typical lidar geometry. Ex-pressions are presented for both a hard target pulsereturn employing the BRDF and an aerosol backscatter

The authors are with California Institute of Technology, Jet Pro-pulsion Laboratory, 4800 Oak Grove Drive, Pasadena, California91109.

Received 16 March 1983.0003-6935/83/172619-10$01.00/0.(© 1983 Optical Society of America.

return. The method of using the target data to cali-brate backscatter coefficients is given. The implica-tions of various assumptions about the BRDF are dis-cussed, including the assumption of Lambertian re-flectance. Other aspects of the calibration process aretreated, including the lidar system telescope overlapfunction, atmospheric attenuation, wavelength-de-pendent parameters, the data acquisition electronicsand the interrelationship between the BRDF, labora-tory backscatter reflectance data, and integratingsphere measurements. Finally, we report on thewavelength and angular dependence of the reflectanceand depolarization of four targets: sublimed flowersof sulfur, flame-sprayed aluminum, 20-grit sandblastedaluminum, and 400-grit silicon carbide sandpaper.Data are presented and compared using an integratingsphere, a cw CO2 laser in a laboratory backscatter setup,and the coherent lidar system at a range of 2 km. Thereflectance vs angle curves of the targets in a backscattergeometry are compared with each other and to an idealLambertian surface.

II. Reflectance Theory

The geometric reflectance properties of a flat, uni-form, isotropic surface can be described by the bidi-rectional reflectance-distribution function (BRDF)[sr-1 ] defined by Nicodemus et al. 3 as

dLr(0i0i;0r,,r;Ei)fr(Oki;rkr) - Ei(Oioi) (1)

In Eq. (1) Lr is the reflected radiance (W . m-2 sr-1 ) inthe direction (Or~qr) due to the incident irradiance dEi= Li cos0i dwi (W . m-2) confined to the solid-angleelement dwi in the direction (i,oi), 0 is the polar anglebetween the ray and the average surface normal, is theazimuthal angle between the ray's projection in thesurface and a reference direction in the surface, and thesubscripts i and r on L, E, 0, and 0 refer to the incident

1 September 1983 / Vol. 22, No. 17 / APPLIED OPTICS 2619

and reflected radiation, respectively. The radiance inthe direction (,0) is defined by

L(Ok)- d (2)dA cos9 dw

where d2 b is the element of radiant flux [W] throughthe element of area dA in the direction (0,k) and withinthe solid-angle element dci. The element of projectedarea perpendicular to the ray direction (0,O) is dA cos6.Equation (1) does not treat interference, diffraction,transmission, absorption, fluorescence, or polarizationeffects, and it is assumed that the illumination ismonochromatic, uniform, and isotropic. The BRDFis an unmeasurable derivative capable of values from0 to infinity. Real measurements always involve anaverage of fr over finite intervals, e.g., dwo and dX.

Nicodemus et al. 3 define nine reflectances, allowingfor directional, conical, or hemispherical geometry ofthe illuminating and reflected radiation. The mostbasic quantity, the biconical reflectance, is defined as

P(wi;wr)

ff fr h(0i ,k0i;Ot,0r) cosi cosOtdwidw,

f cosOidwi

where p(i;wr) is the ratio of the radiant flux in thedirection (rqr) within r to the incident flux in thedirection (i,ki) within wi. (We will avoid the use ofprojected solid angle d = cosO dw as it is nonphysicaland can lead to confusion.4) A Lambertian surface isone for which the reflected radiance is isotropic (Lr isconstant, independent of 0r and r) regardless of howit is irradiated, and thus its BRDF fd is necessarily aconstant. From Eq. (3) we see that fr,d(Gidi;or\,r) =p(coi;27r)/7r.

If the solid angle i confining the illuminating ra-diation is small enough that we can consider fr to beconstant over the limits of integration, Eq. (3) reducesto

p(Oi,0i;Wr) = I (0i,0i;6,0)r cosOrdw, (4)

which is the directional-conical reflectance; i.e., the il-luminating radiation is from a specific direction, and thereflected radiation is measured in a cone of solid angleor- The reflectance measured by an ideal integrating

sphere PIS is given by Eq. (4) with cor = 2,

Pis = p(OiOi;27r) =f f fr(0i'ki;Orc)r) COSOr

X sin0,d0,d0,, (5)

which is the directional-hemispherical reflectance. Ifthe small co assumption is not valid, Eq. (3) should beused for PIS with r = 27r. If the monochromatic illu-mination assumption is not true, an average over AX willbe measured.

In lidar applications both the illuminating and re-ceiving solid angles are very small. For example, a15-cm diam telescope subtends only 7.1 X 10-8 sr at arange of 500 m. Thus we may further simplify Eq. (4)by letting (or - 0 yielding

SGAS ER DETECTOR

Aj G AsAND

Ai Ar

COS Or

Cos 0

(a)

Ar AiAND

Ar S As

GENERAL 8;, ,

COS 1

COLINEAR: 9 = = 6

COS

(b

As AjAND

As < Ar

COS O COS r

(COS )2

(c)

Fig. 1. Pictorial representation of three possible reflectancegeometries: (a) the illuminating spot is smaller than the target andthe detector field of view at the target, (b) the target area viewed by

the detector is smallest, and (c) the target is smallest.

P('04);09rad = W,.r (fr(Oz,(i;Orskr)) coso,. (6)

where (fr) is the average value of fr over the finite solidangle intervals wi and or,.

From Eq. (6) it may be concluded that the receivedpower from a Lambertian target ( = constant) willvary as cosOr. However, this conclusion is not alwayscorrect. It is important to consider the relative sizes ofthe target, the illuminated area on the target, and thearea of the target viewed by the detector as shown in Fig.1. Recall that in Eq. (6), p is the ratio of reflected fluxto incident flux. The incident flux is not necessarilyconstant but is given by the product of the power perilluminated target area and the viewed illuminatedtarget area. Figure 1 (a) depicts the similar cases A <Ar < A or Ai < A < Ar, where Ai = Ai,/cosOi is thearea illuminated by a laser with constant power P, Ar= Aro/cosOr is the area viewed by the detector, and A,is the target area. Note that the illuminated spot issmallest in this case, and, therefore, Oi may not ap-proach 900. The power per illuminated target area isgiven by P cosOi/Ai,, and the viewed illuminated targetarea is given by Ai0/cos6i. Thus the cosi terms willcancel leaving only the cosOr dependence of p in theexpression for received power. In Fig. 1(b) we have thecases Ar < Ai < A or Ar < A < Ai; the receiver field ofview at the target is smallest. Here the power per illu-minated target area is again given by P cos6i/Ai,, butthe viewed illuminated target area is now given byAro/cosOr. When these angular dependences arecombined with Eq. (6), we see that the overall depen-dence of the received power is given by cosOi. As seenin Fig. 1, when a collinear (e.g., lidar) geometry is con-sidered with i = Or = 0, all the above cases exhibit acosO dependence. Finally, Fig. 1(c) depicts the casesA < Ai < Ar or A < Ar < Ai; the target area is smallest.Once again the power per illuminated target area isP cosQ/Aio, but the viewed illuminated target area isjust A. When these factors are combined with Eq. (6),we obtain a cosi cosOr dependence. In this case thecollinear geometry yields a (cosO)2 dependence. It is

2620 APPLIED OPTICS / Vol. 22, No. 17 / 1 September 1983

clear that the geometry of any reflectance experimentis very important, especially when laboratory targetreflectance data are used to characterize targets, whichare in turn placed in a lidar geometry for calibratinglidar systems. Seldom in the literature is the geometryof a reflectance experiment defined in terms of the casesof Fig. 1. The Lambertian reflectance behavior ispredominantly given as cosOr (small Ai), although ex-amples of cosoi-cosOr (small As) can be found 5 6 as wellas coss (small Ar), especially in astronomy.7

We report later in this paper on target measurementsmade using (1) an integrating sphere, and (2) a cw CO2laser in a collinear backscatter geometry (i = 0 r = 0),where Ai Ar < A and where 0 varied from 0 to 80°.The latter data provided collinear 0 dependence of eachtarget's reflectance, showing various deviations fromLambertian (cosO) dependence. It is tempting to as-sume that each target's 0 dependence curve could bescaled absolutely by using the integrating sphere dataand the area under the 0 dependence curve. However,this is not possible for surfaces with a general BRDF.The integrating sphere data depend on the BRDF asshown in Eq. (5), while the backscatter data will dependon Or as shown in Eq. (6):

S(ft;) r*(f,(Oi,0¢J;O',*<)) cosoers (7)

where primes are used to differentiate from the anglesin the integrating sphere case. We may let 01 = O'r = 0and O = O' = i, where we use the collinear geometryand the isotropic property of the target (Jr independentof qi). If we now multiply S(0) by sinG and integrateover 0, we obtain

I = S() sinOdO

'/2wr J (f(O,4ci;O,,P)) * cosO sino * dO. (8)

In comparing Eqs. (5) and (8) we see that we may notuse PIS to scale S(0) unless certain conditions hold.First, the backscatter experiment's solid angles mustbe small enough to allow the assumption that (r) = fr.Second, Jr must be independent of Or to allow the pa-rameter Or of Jr in Eq. (5) to be set equal to Oi. Finally,Jr must be independent of Oi to allow the parameter Oiin Eq. (5) to be set equal to Or. Under these conditionsthe integrals of Eqs. (5) and (8) are proportional to eachother. However, the requirement that fr(0i,'ki;0r,4'r)be independent of O, i, and kr is nearly as restrictiveas the Lambertian assumption of constant Jr (i.e., in-dependent of all four parameters).

Ill. Calibration of Atmospheric Backscatter Data

If the BRDF of a calibration target is sufficientlyknown, lidar target return data may be used to calibratelidar atmospheric backscatter data. This calibrationtechnique and its limitations will now be discussed.

Consider a lidar system directed at a calibrationtarget which is at a range R and an angle 0 to the beam.For large R8, collinear geometry may be assumed withboth the transmitting and receiving telescopes sub-tending very small solid angles, making Eq. (6) valid. A

large target is assumed so that either Fig. 1(a) or (b)applies. If the transmitted pulse starts at time t = 0and ends at t = T with a power profile of Pt (t) [W], thereceived signal power [W] is given by

PI, (t) = Pt -) * * * X A O(R,)

Rs

X exp 1-2 f a, (r)dri I (9)

where A is the effective receiver area, A - R. 2 = (r is thesolid angle at the target subtended by the receiver, i isthe system's optical efficiency, O(R,) is the range-dependent telescope overlap function8 defined as thepercentage of the transmitted pulse energy which is inview of the receiver, o (r) [m-1 ] is the total volume ex-tinction coefficient of the atmosphere, 2R8/c is theround-trip transit time of light, and p [sr-'] is thetarget parameter defined as the reflected power persteradian toward the receiver divided by the incidentpower. (Other sources of received power at time t, suchas aerosol backscatter, multiple scattering, Ramanscattering, resonant fluorescence, and fluorescence areneglected. 9 ) It is common to find expressions for Pr,8 (t)that give the factor p as either p, p/7r, or (p cosl)hr,where p is called the reflectivity of the target. We mayuse the theory of Sec. II to more exactly define p*.Under the assumptions leading to Eq. (3), e.g., uniformand isotropic illumination and target surface, we seethat the general expression for p* in Eq. (9) is

P*(w;f) =

fr(Oi,04i;r,4,) cos0i cosOdwidw,

(10)

Wo. X cosoidwi

If small solid angles can be assumed, Eq. (10) be-comes

P*(OiOi;Or,,r) = ((0i,0i;0r,'r)) - cosO, (11)

and if collinear geometry is used, Eq. (11) becomes

P*00,0¢)= ((O,;Ok)) -cosO. (12)If the geometry of Fig. 1(c) applies, cos0 is replaced bycos20 in Eq. (12), and if the target may be consideredLambertian, r(Oi ,ki;OrOkr) is replaced by p(coi;2r)/r,and the average value brackets may be dropped. It isapparent that considerable calibration error may resultfrom replacing p* in Eq. (9) with either p, p/7r, or even(p cos0)/7r when the experimental geometry resultingin the reported value for p is unknown; when the centerwavelength, bandwidth, and polarization of the illu-mination may have differed from that in use; and whenthe target surface is most likely not Lambertian or re-producible.

Now consider the same lidar system directed into theatmosphere. The received power [W] due to aerosolbackscatter is given by

P,,b(t) =f t/ Ptt-2 C- * $(R) O(R). (t-,)/2 I, c R

exp[-2 Sa ab (r)drdR, (13)


where the volume backscattering coefficient : (m- -sr-') is defined as the fraction of incident energy scat-tered in the backward direction per unit solid angle perunit atmospheric length,10 ab (r) is most likely differentfrom a, (r) due to natural fluctuations and the differentbeam paths employed, the appropriate sources of re-ceived power which were neglected in Eq. (9) are againneglected, and the integration over R indicates that thereturn signal at time t is due to a slab of atmosphere ofthickness cr12 centered at Rb = c(t/2 - r/4). (Becauseof the R 2 and exponential terms, there is a range-dependent weighting function in the integrand whichfavors the tail of the laser pulse.) If we assume theentire integrand except Pt (t) is approximately constantover the range of integration, Eq. (13) may be simplifiedto

P,,b(t) Rb 0(R) exp [2 a '(r)drj 2O(Rb)= * ____ , -Is R2 O(Rb) [ Rb C

exp - 2 Jab (r)dr

(16)

For accurate evaluation of 3(R) at all ranges, the tele-scope overlap function and the total attenuation coef-ficients must be well known. If we let ab (r) = as (r) andRb = R8, we obtain

(R =Prb(t) p* 2Is c

(17)

where t = 2R,/c + T/2. No knowledge of the overlapfunction is needed to evaluate the backscatter coeffi-cient at the range of the calibration target.

Pbb(t) = e(Rb) - * -O(Rb) exp 1-2 a X t it 2J dRR2 o(t-7)/2 Pt C

= 1(Rb) 2 1 *0(Rb) * exp {-2 R ab(r)drl - f Pt(t)dt.

If the pulse power profile Pt (t) is assumed rectangular'with power Po, the integral in Eq. (14) becomes Pr,which is the more common form of the lidar backscatterequation. 10

Equations (9) and (14) express the received power vstime for the cases of a calibration target s and aerosolbackscatter b, respectively. However, the receiver maygenerate a voltage which is not directly proportional topower. For example, a heterodyne receiver coupled toa linear IF amplifier and a linear rf detector producesa voltage proportional to the square root of the receivedpower V = G p 1/2 , and a heterodyne receiver with alogarithmic IF amplifier and the same rf detector wouldyield V = log (G . pl/2). Additionally, dc offsets mayoccur. The recorded signal must be processed appro-priately to obtain a quantity proportional to the re-ceived power (e.g., subtract the offset and square theresult). Other considerations include the total numberof pulse returns which were added in each case andvariations in the transmitted pulse power profile. Theremainder of this discussion will assume that these stepsare taken.

The next step in calculating (R) is to evaluate theintegral of the target return data given in Eq. (9). Thisis given by

Is = f2R/c+,J2Rs/c

Pr,s(t)dt

=p*. - 0(R,) exp [-2 , S(r)drj~~~~f d

x JfPt(t)dt. (15)

(If an integrating ADC is used and if the sampling pe-riod t is longer than the pulse duration , the integra-tion in Eq. (15) will automatically occur with an addi-tional factor of lt. Care should be taken, however,since the return pulse may overlap two adjacent sampleperiods and/or the ADC may have a decay time >t 8.)Comparison of Eqs. (14) and (15) yields

(14)

IV. Experiments

As stated earlier, the ideal calibration target wouldbe inexpensive, easy to fabricate, durable, reproducible,and have a well-known BRDF. It was also shown inSec. II that quantitative characterization of a targetusing integrating sphere data and laboratory back-scatter 0 dependence data is only possible if fr is inde-pendent of Oi, i, and r; a very restrictive conditionthat is satisfied by Lambertian surfaces. Therefore, aLambertian target would greatly facilitate the calibra-tion process.

We chose four target surfaces for this work: sublimedflowers of sulfur (), flame-sprayed aluminum (FSA),20-grit sandblasted aluminum (SBA), and 400-grit sil-icon carbide sandpaper (SC). Sulfur flowers has beenproposed as an infrared standard of reflectance,' isrelatively Lambertian,5' 6 and has been used to calibratelidar systems at 10.6-,um wavelength.2 Flame-sprayedaluminum,' a more durable surface, has been used asa lidar target.' 4 (The recipe for FSA given by Bran-dewie and Davis'4 did not explicitly include the alumi-num alloy employed or the grit size of sand used forsandblasting the aluminum.) Sandblasted aluminumhas also been used in lidar systems 5"16 and has beendescribed as Lambertian despite earlier contradictorydata.5 Finally, 400-grit silicon carbide sandpaper, acommon and inexpensive material, has also been usedas a lidar target.' 2

Integrating sphere reflectance data from 1-13 um forthe four surfaces are shown in Fig. 2. The Labsphere5-cm diam integrating sphere had a diffuse gold coatinginside, and all sample reflectances were compared to adiffuse gold standard plate using the substitutionmethod. A globar source at 14000C was first focusedon a circular variable filter (CVF) and then on thesample inside the sphere. The angle of incidence i ofthe radiation illuminating the sample was 45°. A


-5V-"' FLOWERS ~~~~OF SULFUR

o 60 -z

l- 20 GRIT SANDBLASTED ALUMINU

20-400 GRIT SILICON CARBIDE

00 1 2 3 4 5 6 7 8 9 10 11 12 13 14

WAVELENGTH (MICRONS)

Fig. 2. Integrating sphere measurements of PjS for flame-sprayedaluminum, sublimed flowers of sulfur, 20-grit sandblasted aluminum,

an 400-grit silicon carbide sandpaper.

[ HgCdTe DETECTOR

ZnSe POLARIZER

'| BaF2 LENS, f - 30 cm

ZnSeIS.As S ,"~~~~~.-. , yai

TARGET jr rn] POWER

'-'XLJ METERHe-Ne LASER

,M

CO2 LSER NaCB. S. CHOPPERFig. 3. Laboratory collinear backscatter apparatus.

number of CVFs with a wavelength resolution of AX =X/50 were used to cover the wavelength range. Three0.95-cm diam holes in the sphere provided for (1) theentrance of the light, (2) the sample to be measured, and(3) a 6 X 6-mm area thermocouple detector which didnot directly view the sample.

We were primarily interested in the wavelength de-pendence of the reflectance in the 9-11-gm region. Theflame-sprayed aluminum appears to be independent ofwavelength in this region, sandblasted aluminum ex-hibits a small dip at 10 gm, and the silicon carbide re-flectance increases with increasing wavelength.'7 Thesulfur reflectance in the 9-11-jum region is lower thanthat reported by Kronstein et al." but agrees reason-ably well with the later results of Blevin and Brown.18For example, at 9 gm Kronstein et al. 11 report a sulfurreflectance of 0.8, and Blevin and Brown' 8 give a valueof 0.6. The flame-sprayed aluminum is the most re-flective of the four targets at the longer wavelengths.

The laboratory collinear backscatter apparatus isshown in Fig. 3. The passively stabilized linearlypolarized, cw CO2 laser is grating tunable in the 9-11-gm region. The laser radiation was chopped at 100 Hzand was directed onto both the target surface and apower meter with a ZnSe 50% beam splitter. The ver-tical polarization of the laser was perpendicular to theplane of incidence at the target. A 30-cm focal length5-cm diam BaF2 lens was used to image the target sur-face onto an LN2-cooled HgCdTe infrared detector. Apreamplifier and lock-in amplifier (not shown) werethen used to obtain the signal magnitude. A ZnSe po-

larizer which had a >500:1 extinction ratio and 10-mmdiam aperture was positioned next to the detector andwas used to select backscattered radiation with polar-ization either parallel or perpendicular to that of theilluminating beam. (The different reflection coeffi-cients of the beam splitter for the two directions of po-larization were measured, and the data were appro-priately scaled.) The target was carefully positionedto align the center of illumination with the axis ofrotation. The beam size at the target was -5 mm indiameter and was smaller than the target even at 0 =800. Since backscatter from the power meter contrib-uted a large background signal, the power meter wasremoved during measurements, and the unblockedbeam was allowed to travel several meters beforestriking anything. Background readings were thentaken with a mirror placed between the beam splitterand the target, also directing that beam across the lab.A small background signal remained which was believeddue to scatter from the surfaces of the beam splitter.This was recorded and later subtracted from the data.The data were also later normalized by the laser power.The finite size of the lens limited the resolution in 0 to3.2°. However, it did help reduce the signal fluctua-tions due to speckle, with an estimated 100 speckle lobesbeing averaged. Nevertheless, six measurements weremade at each angle within ±0.5' in order to reduce theeffects of speckle.

Figures 4-7 show the collinear backscatter data forthe 1P(20) CO2 laser line (10.591 gim) for sublimedflowers of sulfur, flame-sprayed aluminum, 20-gritsandblasted aluminum, and 400-grit silicon carbidesandpaper (Sancap), respectively. In each graph theabscissa is the polar angle 0 shown in Fig. 3. The leftordinate is proportional to the recorded signal ampli-tude in V/W scaled as indicated. The ordinates of Figs.4-7 may be directly compared. The upper graph ineach figure corresponds to parallel alignment of thepolarizer (vertical), and the lower graph corresponds toperpendicular alignment (horizontal). (Since the ra-diation incident on the target is always polarized per-pendicular to the plane of incidence, parallel or verticalalignment of the polarizer corresponds to reflected ra-diation which is also polarized perpendicular to theplane of incidence at the target.) The mean value of thesix readings at each angle is plotted with a vertical lineof length 2cr. The solid line represents a least-squaresfit of the data to a cosine curve, the theoretical 0 de-pendence of an ideal Lambertian surface. The dashedline gives the percent deviation of the cosine curve fromthe experimental data as indicated by the right ordinate.Several sets of measurements were made with the samesulfur target on different days and for both directionsof target rotation (positive and negative 0). The re-peatability of the calculated percent deviation curve(dashed line) was better than 10% for 0 < 700.

The sulfur target was fabricated by mixing sublimedsulfur (J. T. Baker 4088) with acetone to form a slurry 2

-1.4-g sulfur to 1-mliter acetone. The slurry waspacked into a rectangular well that was machined inaluminum to a 4.4-mm depth. A microscope slide lu-


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bricated with acetone was used to trowel a uniformsurface finish which appeared smooth to the naked eye.The target was then allowed to dry overnight. Asshown in Fig. 4, both the parallel and perpendicularbackscatter signals from flowers of sulfur were ap-proximately Lambertian. The deviation from thebest-fit cosine curve remains <10% out to -0 = 75",except for the parallel data near 40°. About one-thirdof the backscattered radiation was depolarized into theperpendicular direction.

In Fig. 5 we see that the flame-sprayed aluminumparallel polarization signal was slightly larger than thatof sulfur. However, only 20% of the backscatteredradiation was depolarized. The deviation from Lam-bertian behavior was apparent. At 00 the parallel signalwas greater than the cosine curve, while the perpen-dicular signal was smaller. This was probably due tospecular reflection, which preserves the direction ofpolarization.

The parallel polarization 20-grit sandblasted alumi-num data shown in Fig. 6 was slightly smaller than thesulfur data. About 10% of the backscattered radiationwas depolarized, less than with either of the first twosurfaces. The parallel signal deviated significantlyfrom Lambertian behavior, reaching +30% deviationat 40° and -30% deviation at 80°. The perpendicularsignal, however, was approximately Lambertian out to600. Once again, specular reflection near 0° was indi-cated.

As shown in Fig. 7, the parallel polarization back-scatter signal for 400-grit silicon carbide sandpaper was-12 times smaller than the signal for flame-sprayedaluminum. As with the sandblasted aluminum, 10%of the radiation was depolarized. Noting that the rightordinate extends to 100% deviation in this figure, wesee that the sandpaper was further from Lambertianthan any of the first three surfaces. This was due to thenear independence of the backscattered radiation withangle, indicating that mechanisms for retroreflectionoccur.7 Post et al. 12 have used a collinear lidar at 10.6gm to compare the reflectance of 400-grit silicon carbideto flowers of sulfur at 45°. They assumed the sulfur was


I I I I I I I I I

~~~~~~~~~/

- IOP(20)I I I I I I i

I I I I I I I I I

~~~~~~~- ---

_ 400 GRIT SILICON CARBIDE/IPOL. .- _

- 10P(20)I I I I I I I I I

I - I I

400 GRIT SILICON CARBIDE - \i POL.10P(20)

l I I I I I I I I

I I I I I I I I I0.9 _+0.8 _

0.6 - -.

0.4 - I0.1 10IP(2010.0 I I I I I I I I

I I I I I I I I I

Ni :FLAME-SPRAYED ALUMINUM N

I POL. N -- 10P120P N\ -

I I I I I I I I \

*--1 I I I I I I I I I0.9 - 20 GRIT SANDBLASTED ALUMINUM -

, 0.8e of ~~~~~~~//POL.0.8 ,- . 10P120)

0.7 0 - N 0..6

0.2 _0.1

o0 l I I I I

. ._ .U, , , , , , , . . BAA A_lW.O

U.U W. U

.U r .- ' ' ' ' ' ' . AA S.. _

I

: : -* -w.xU.uo

1.0.

_

40.0

30.0 ?20.0 210.0 20.0

-10.0 I'

-20.0 I

-30.0 ul

-40.0

-50.0

- I I I I I I I I I 0u.u0.9 - 40.00.8 - 30.00.7 - 20.00.6- 10.0

0.4.10

0.3 SULFR -20.00.2 _POL. -30.00.1 9P (20) -40.00.0 I I-60.0

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0

0 (DEG.)

Fig. 8. Same as Fig. 4 but at 9.6 Am.

80.0 90.0

4Z_S2

ZC2§cc

13 .3 A

20

00F

0

50.0

40.0

30.0 i20.0 210.0 F4

0.0

-10.0 t~.20.0 -

-30.0 'W

-40.0150.0

50.040.0

^0j:

aXX

1.

0.9

0.8

0.7

00.040.0

30.0 g20.0 Z

10.0

0.0 >

-10.0 I--20.0

.30.0 i40.0

50.040.0

30.0 -

20.0 9

10.00.0 .10.0 !=-20.0

-30.0 01

-40.0460.0

0.0 10.0 20.0 30.0 40.0 60.0 60.0 70.0 60.0 90.0(DEG.)

Fig. 10. Same as Fig. 4 but for 20-grit sandblasted aluminum at 9.6Am.

Izo

5I

2

0

UJ s Za F t i

Us, tI.-8 al h a

0.0 10.0 20.0 30.0 40.0 50.0 60.0 70.0 80.0 90.0

B(DEG.)

Fig. 9. Same as Fig. 4 but for flame-sprayed aluminum at 9.6 ,im.

Lambertian and used the reflectance value publishedby Kronstein et al." to arrive at a value for the BRDFof SC. This value of the BRDF should not be extrap-olated to other angles and wavelengths, however, since(a) SC is not Lambertian, and (b) it has a spectral de-pendence.

Measurements were also made at the 9P(20) C02laser wavelength (9.552 gim) and are shown in Figs. 8-11.For example, the flowers of sulfur target data are shownin Fig. 8. As at 10.6 gm the sulfur appears to be Lam-bertian, and approximately one-third of the backscat-tered radiation was depolarized. (Direct comparisonof reflectance ratios between the 9.6- and 10.6-gm datashould not be done due to the wavelength dependentelements in the experimental apparatus.) As can beseen the deviations from Lambertian behavior,the de-polarization ratios, and the relative magnitudes of thetargets at 9.6 gm are similar to that at 10.6 gm.

1.1 I I I I I I I I I 10.00.9- -80.1

0.8 -60.0

0.7 -40.0

0.6 _ _ - -20.0

0.4 -.- 20.0

0.3 40 RT~~L>..I-40.0

0 40GISILICON CARBIDE o-.-- 6.0 P - 0

0.1 SFP205 -80,0°° I I I I I I I I I I -150.0

1.0 i 1 1 1 1 1 1 1 1100.0

0.9 -. 0

0.8 60.00.7 40.0

0.0 - 0.00.4 -- 0___ 20.0

0.3 400 GRITSIL.C 1C Ia -40.00S2 .LPOL. .- -60.00. 9P120) -8.0

I I I I I I I I I ~~~~~~~~~~~-00.0U.U 10. 20.0 30.0 40.0

GIDEG.)

50.0 60.0 70.0 80.0 90.0

Fig. 11. Same as Fig. 4 but for 400-grit silicon carbide sandpaper at9.6 gtm.

Selected ratios of the reflectance data for differenttargets are given in Table I. The integrating sphereratios of PIS are obtained from Fig. 2. The higher re-flectance of silicon carbide at 10.6 gm is consistent withthe figure. Two different ratios are presented for thelaboratory backscatter data: ratios of the integral over0 of the backscatter data multiplied by sing as given byEq. (8) and ratios of the data at 0 = 45°. It was shownin Sec. II that the integrating sphere signal would beproportional to the integral in Eq. (8) only under certainstrict conditions; conditions which did not apply to ourtargets and experimental apparatus. This is supportedby the entries of Table I. For example, the retrore-flection exhibited by silicon carbide sandpaper in Fig.7 would lead to large values for the integral given by Eq.(8). However, in the integrating sphere geometry itmay cause a smaller signal since a larger fraction of theilluminating radiation would exit the sphere through


1.0

0.9

. 0.6

3 a 0.70.6

4 X 0.5

S 0.4E .0.3

0.2

0.1

0.0

t.O,

I I I I I I I I I--- ---

SULFUR- //POL.- W (20)

I I I I I I I I

0.9 _ 20 GRIT SANDBLASTED ALUMINUM -

//POL.0. ~~~~~~s.9P(20)0.7 / 0.6 / -0.5 -

0.4 -0.3 -0.2 -

0.10.0 I I I

.4

04~

. .

0

I I 1 20 GRIT SANDBLASTED ALUMINUM -

lPOL.91(20) -

0.6 -0.5 - = -

0.4 - N5 H0.3 -~~N

02 0.2

.0 I I I I I I I I

,, - 0.4

01 0.2

0.1

0.0

1.0

0.9

-j 0.8

Z 0.7

fI' 2 0.6

I m 0.5

0.4

II- 0.3

01 0.2

0.1

ant ' ,

P0

I

t;

I

Rz0

II

Table I. Ratios of Reflectance Data for Different Targets

S SBA SCMeasurements FSA FSA FSA

Integrating sphere, pis9.6 gm 0.76 0.48 0.042

10.6 gm 0.77 0.50 0.091

Laboratory backscatter

f S(O) sinOdO

9P(20) Il 0.83 0.39 0.0821.1 0.27 0.030

1OP(20) Il 0.78 0.49 0.13l 1.1 0.36 0.054

0 = 4509P(20) II 0.92 0.38 0.088

l 1.1 0.28 0.027lOP(20) Ii 0.94 0.50 0.13

± 1.2 0.37 0.054

the illumination port. In Table I we see that the ratioof silicon carbide to flame-sprayed aluminum is largerfor the laboratory backscatter integral case than for theintegrating sphere case at both 9.6 and 10.6 ,gm. (Theparallel polarization ratios should be used in the com-parison' since the depolarized radiation was a smallfraction of the total radiation.) The laboratory back-scatter ratios for 0 = 45° are presented for referencesince much of the published lidar calibration targetwork has used this angle and since the angle of incidencein the integrating sphere measurements was 45°.

Pulsed lidar measurements were made with flame-sprayed aluminum and 400-grit silicon carbide targets.The 1.83-m (6-ft) square targets were placed at a rangeof -2 km, where both the transmitted beam and thereceiver field-of-view were -0.6 m in diameter.

The optical layout of the coherent lidar apparatus isshown in Fig. 12. The Lumonics pulsed TEA-CO 2 laserwas operated at pressures near 760 Torr with an un-stable resonator consisting of a Littrow-mounted re-flection grating and a germanium output coupler.During operation it consistently emitted near-diffrac-tion-limited single-longitudinal-mode (SLM) pulses of1-2 J energy at a repetition rate of up to 0.1 Hz. A cwCO2 waveguide laser was used as the injection oscillator,entering the TEA laser cavity through the front outputcoupler. The cw radiation reflected by the TEA lasercavity was focused onto a detector which provided adiagnostic signal for manual or automatic alignment ofa longitudinal mode with respect to the injection oscil-lator wavelength resulting in consistent SLM opera-tion.'9 The injection oscillator wavelength was fre-quency stabilized by employing the optogalvanic ef-fect20 or, alternatively, an optoacoustic detector(OAD). 2 1 A small portion of the linearly polarized TEAlaser pulse was directed onto a pyroelectric detector forobservation of the pulse power profile. The main por-tion of the pulse was directed into a reflective off-axis5X transmit telescope which had a 15.5-cm output di-ameter. Two steerable mirrors directed the expandedbeam through a rotatable dome on the roof of our lab-oratory and toward the desired target or along the de-sired atmospheric path. The receiver telescope was anf/8 reflecting Newtonian telescope with a maximuminput diameter of 20 cm and a 5-cm diam central ob-scuration. The focal plane of the receiver was imagedonto a HgCdTe photomixer. Both direct detection andheterodyne detection were possible. When heterodynedetection was employed, the signal consisted of only thebackscattered radiation with polarization parallel to thetransmitted beam. When desired, the passively stable

TELESCOPE ASSEMBLY(RECEIVE) (TRANSMIT)

I l

LOCALOSCILLATORCo2LASER

PZT

INJECTIONOSCILLATORWACEO 2

SHUTTER

Fig. 12. Optical layout of the JPL coherent lidar system.


Table II. Ratios of 0 = 450 Backscatter Reflectance Data to = 100Data

Measurements S FSA SBA SC

Laboratory Backscatter9P(20) 11 0.77 0.54 0.42 0.79

1 0.76 0.82 0.75 0.951OP(20) 11 0.77 0.59 0.50 0.98

1 0.76 0.75 0.77 0.96

Coherent Lidar9P(20) II 0.50a,0.50c 0 .6 6 b,0 .6 9 c

1OP(20) II 0.64d '° 8 5 d

a Measurements made on 3 Aug. 1982.b Measurements made on 22 Nov. 1982.c Measurements made on 2 Dec 1982.d Measurements made on 14 Dec. 1982.

CO2 local oscillator could be optogalvanically stabilized,or stabilized at a fixed-frequency difference from theinjection oscillator through the use of a second photo-mixer. The TEA laser transmitter, the waveguide in-jection oscillator, and the local oscillator were all gratingtunable and could be operated at a number of wave-lengths extending from 9.2 to 10.7 gim.

The transmitter and receiver telescopes were care-fully aligned and aimed at the center of the target. Asdiscussed earlier, i = 0 = 0 under these conditions,where i and 0 r are the angles between the target normaland the line of sight to the transmitting and receivingtelescopes, respectively. As with the laboratory back-scatter apparatus, the linear polarization (vertical) ofthe transmitted beam was perpendicular to the planeof incidence at the target. At each angle a largenumber of pulses were fired at the target to reduce theeffect of speckle. (The predicted intensity distributionfunction was a negative exponential since the pulsecoherence length was greater than the surface heightvariations of the target and since the target introducedrandom phase fluctuations >27r.) The return signalswere summed with a transient digitizer/signal averagerand sent to an HP1000 minicomputer for analysis. Thecomputer was used to process the data, e.g., subtract anyoffset, square the data.

Table II lists the ratios of the backscatter reflectancedata at 0 = 45° to the data at 0 = 10° for both the co-herent lidar measurements and the laboratory back-scatter measurements. The agreement between lidardata taken on different days is excellent, especiallyconsidering the deleterious effects of speckle, atmo-spheric turbulence, and changing atmospheric attenu-ation. Fifty pulses were averaged on 3 Aug. 1982, andsixty-four pulses were averaged on the other three days.The agreement between the lidar data and the labora-tory data is also good. An ideal Lambertian surfacewould yield a ratio of cos45/coslO = 0.72. Of the fourtargets, sulfur was the closest to this ideal ratio. Theperpendicular data were usually closer to the Lamber-tian ratio than the parallel data.

V. DiscussionWe have reviewed the reflectance theory of hard

targets and have applied it to the typical geometries ofintegrating sphere, laboratory collinear backscatter, andlidar measurements. The importance of various as-sumptions in each case as well as of the experimentalgeometry was discussed. The measured quantity ineach case was shown to depend on the BRDF of thetarget surface; a function that can only be measuredwith a complex goniometric experimental setup andwhich likely varies with the wavelength, polarization,and bandwidth of the illumination and with the sub-tended solid angles of the illumination and detector.The assumption of Lambertian behavior was shown toresult in considerable simplification of the theory. Thereflectance theory was then combined with the ex-pressions for pulsed lidar returns from hard targets andatmospheric aerosols to show how lidar calibrationtarget data can be used to calibrate atmospheric back-scatter data. The complications in this process thatresult from atmospheric attenuation, the telescopeoverlap function, the receiver electronics, etc. werediscussed. Experimental results were then presentedand compared employing four candidate calibrationtargets; sublimed flowers of sulfur, flame-sprayed alu-minum, 20-grit sandblasted aluminum, and 400-gritsilicon carbide; and three measurement techniques: anintegrating sphere, a laboratory collinear backscattersetup, and a coherent pulsed lidar system. The onlytarget which approached Lambertian behavior wassulfur, which, unfortunately, is probably too fragile forfield work.

Much more work remains to be done in the area ofcharacterizing calibration targets for lidar experiments.In particular, the variations in reflectance behavior withtime for a single target and the variations among dif-ferent samples of the same material should be investi-gated. It is also desirable to standardize the fabricationrecipes of the targets and to find a calibration target thatis both Lambertian and durable.

In view of our results to date we plan to calibrate our


atmospheric aerosol backscatter data using the fol-lowing procedure. The laboratory backscatter ar-rangement of Fig. 3 will be used to measure the reflec-tance ratio between sulfur and one of the more durabletargets such as flame-sprayed aluminum. This will bedone at 450 to simulate the integrating sphere mea-surement and at all wavelengths in the 9-11-gm regionthat will be subsequently used for aerosol measure-ments. We assume that the sulfur is Lambertian.Since the integrating sphere measurement of sulfuremploys unpolarized light, backscatter measurementsof sulfur will be made with all four permutations ofparallel and perpendicular, incident and reflected ra-diation. One-half of the sum of these four readings willbe used: S[ss + sp + pp + ps]/2. For the flame-sprayed aluminum only a single measurement will beused with both incident and reflected radiation per-pendicular to the plane of incidence: FSA[ss] to sim-ulate the pulsed lidar geometry. Lidar measurementswill then be made with the large flame-sprayed alumi-num target at 45° close to the time that atmosphericaerosol backscatter data are taken. The backscattercoefficient will then be calculated using Eq. (16), wherep* would be replaced by Pis cos45' - r-1 multiplied bythe FSA/sulfur ratio described above. Note that thePIS is the reflectance of sulfur measured with the in-tegrating sphere and that we have used Eq. (12) and thefact that a Lambertian surface's BRDF is given by fr =

PIs 7rV'

References1. R. M. Huffaker, Ed., "Feasibility Study of Satellite-Borne Lidar

Global Wind Monitoring System," NOAA Tech. Memo. ERLWPL-37 (Sept. 1978).

2. R. M. Huffaker, T. R. Lawrence, R. J. Keeler, M. J. Post, J. T.Priestly, and J. A. Korrell, "Feasibility Study of Satellite-BorneLidar Global Wind Monitoring System, Part II," NOAA Tech.Memo. ERL WPL-63 (Aug. 1980).

3. F. E. Nicodemus, J. C. Richmond, J. J. Hsia, I. W. Ginsburg, andT. Limperis, "Geometrical Considerations and Nomenclature forReflectance," NBS Monograph 160 (Oct. 1977).

4. F. E. Nicodemus, Ed., "Self-Study Manual on Optical RadiationMeasurements: Part I-Concepts," NBS Tech. Note 910-1 (Mar.1976), Chaps. 1-3.

5. J. T. Agnew and R. B. McQuistan, J. Opt. Soc. Am. 43, 999(1953).

6. W. WM. Wendlandt and H. G. Hecht, "Reflectance Spectrosco-py," Chemical Analysis; A Series of Monographs on AnalyticalChemistry and its Applications, Vol. 21, P. J. Elving and I. M.Kolthoff, Eds. (Interscience, New York, 1966).

7. T. S. Trowbridge, J. Opt. Soc. Am. 68, 1225 (1978).8. K. Sassen and G. C. Dodd, Appl. Opt. 21, 3162 (1982).9. R. L. Byer, Opt. Quantum Electron. 7, 147 (1975).

10. R. T. H. Collis and P. B. Russell, Laser Monitoring of the At-mosphere, E. D. Hinkley, Ed., (Springer, Berlin, 1976), Chap.4.

11. M. Kronstein, R. J. Kraushaar, and R. C. Deacle, J. Opt. Soc. Am.53, 458 (1963).

12. M. J. Post, R. A. Richter, R. J. Keeler, R. M. Hardesty, T. R.Lawrence, and F. F. Hall, Appl. Opt. 19, 2828 (1980).

13. Sandblast 6061 aluminum plate with 60-grit sand. Prime withNi alumina bonding agent. Flame-spray with pure aluminumto a thickness of 0.25-0.38 mm.

14. R. A. Brandewie and W. C. Davis, Appl. Opt. 11, 1526 (1972).15. 0. Steinvall, G. Bolander, K. Gullberg, I. Renhorn, and A. Widen,

Proc. Soc. Photo-Opt. Instrum. Eng. 300, 100 (1981).16. G. Bolander, K. Gullberg, I. Renhorn, 0. Steinvall, and A. Widen,

"Studies of Target Signatures with a Coherent Laser Radar,"FOA Report C 30220-El, Linkoping, Sweden (May 1981).

17. W. G. Spitzer, D. Kleinman, and D. Walsh, Phys. Rev. 113, 127(1959).

18. W. R. Blevin and W. J. Brown, J. Sci. Instrum. 42, 385 (1965).19. P. H. Flamant and R. T. Menzies, IEEE J. Quantum Electron.

QE-19, 821 (1983).20. M. J. Kavaya, R. T. Menzies, and U. P. Oppenheim, IEEE J.

Quantum Electron. QE-18, 19 (1982).21. M. J. Kavaya, R. T. Menzies, and U. P. Oppenheim, "Spectro-

phone Stabilization and Offset Tuning of a Carbon DioxideWaveguide Laser," IEEE J. Quantum Electron. QE-19, 000(1983); to be published.

The authors appreciate the assistance of C. Esproles,R. B. Miller, and R. A. Zanteson in this work. We arealso grateful to Abraham Gross for his helpful sugges-tions. D. A. Haner is a Research Affiliate visiting fromCalifornia State Polytechnic University, ChemistryDepartment, Pomona, Calif. 91768. U. P. Oppenheimis a NASA-NRC Resident Research Associate on leavefrom Technion-Israel Institute of Technology, De-partment of Physics, Technion City, 32 000 Haifa, Is-rael. P. H. Flamant is a NASA-NRC Resident Re-search Associate on leave from Laboratoire de Meteo-rologie Dynamique du C.N.R.S., Ecole Polytechnique,91128 Palaiseau, France. The integrating spheremeasurements were made at Technion-Israel Instituteof Technology.

The research described in this paper was carried outby the Jet Propulsion Laboratory, California Instituteof Technology, under contract with the NationalAeronautics and Space Administration.


target reflectance measurements for calibration of lidar atmospheric backscatter data

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