# Target reflectance measurements for calibration of lidar atmospheric backscatter data

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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. IntroductionAerosol backscatter measurements at CO2 laser

wavelengths 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 cosOidwiwhere 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 DETECTORAj G As

ANDAi Ar

COS OrCos 0

(a)

Ar AiAND

Ar S AsGENERAL 8;, ,

COS 1

COLINEAR: 9 = = 6COS

(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 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 illuminatin

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