Polarization of the reflectivityof paints and other rough surfaces in the infrared

Uri P. Oppenheim and Yoram Feiner

In this study the IR reflectivity of painted and rough surfaces was investigated, and an attempt wasmadeto represent the surfaces by a complex refractive index. A CO2 laser was used as a collimated source inthe thermal IR region, and the polarization properties of reflected radiation were measured. Thesamples chosen were flat surfaces of sandblasted aluminum, concrete, painted metal, and asphalt.Values of the bidirectional reflectance function were obtained in the two orthogonal states of polarization,based on sulfur as the Lambertian standard. Many samples, such as painted metals, showed specularbehavior and could be characterized by Fresnel equations. For some of these surfaces optical constantswere calculated from the reflectivity measurements. Good agreement was obtained between thecalculated and measured values of the percent of polarization for these surfaces.Key words: Polarimetry, reflectometry, infrared, surface roughness.

1. Introduction

One can obtain thermal images by detecting IRradiation that is emitted and reflected from objects ina scene. The relevant wavelength region is around10 µm, so a CO2 laser that operates at 10.6 µmmay beused to investigate this region. It should be notedthat for outdoor measurements the IR polarization ofa scene is different from that in the visible. Lightfrom the 1cloudless2 sky in the visible is stronglypolarized, in particular when observed at 90° from theSun, whereas in the IR the skyshine is not polarizedand the scene is observed by radiation that is emittedand reflected by objects in the scene. It follows thatin order to study polarization in the IR it is enough tostudy the polarization of reflected and emitted radia-tion from surfaces that make up the scene withouttaking the sky into consideration 1assuming a cloud-less sky2. One can go one step further and forhemispherical or specular reflection use the relationses 5 1 2 rs, ep 5 1 2 rp, where e and r are theemissivity and reflectivity, respectively, and s and pare the perpendicular and parallel components of theradiation field, respectively. In other words, one canlearn about the emitted radiation by studying thereflectivity of the surface. Since the latter is simpler

The authors are with the Department of Physics, Technion–IsraelInstitute of Technology, Haifa 32000, Israel.Received 30 November 1992; revised manuscript received 26

April 1994.0003-6935@95@101664-08$06.00@0.

r 1995 Optical Society of America.

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to investigate, we used reflected and scattered radia-tion only.It is well known that man-made objects 1vehicles,

roads, buildings2 have smooth surfaces that producepolarized radiation in the IR. It follows that byplacing a polarizer in front of the detector of an IRradiometer or imager the scene may be altered.When one views an object against a cluttered back-ground in this way, rotating the polarizer will notchange the background 1which is randomly polarized2but will change the intensity of the object. Thus apolarized image may show contrast whereas an unpo-larized image shows none.As a first step toward applying this idea it was

necessary to learn more about the polarization of thereflectivity of smooth but nonspecular surfaces of thekind mentioned above. It should be noted that inthe IR the wavelength is much larger than in thevisible, so the ratio between the rms roughness of thesurface and the wavelength is much reduced. Sur-faces that are rough in the visible become effectivelysmooth in the IR. As a result, polarization is moreprominent in the IR than in the visible and istherefore important in thermal imaging. Anotherconsequence of the longer wavelength is that it isdifficult to find a Lambertian 1diffuse2 surface in theIR. A surface made up of flowers of sulfur is prob-ably the only surface known to be closely Lamber-tian.1,2Torrance and Sparrow3 suggested that the reflectiv-

ity of a rough surface could be divided into specularand nonspecular parts. Recently it was shown by

Stagg and Charalampopoulos4 that the specular partmay indeed be described by Fresnel equations andthat optical constants n and k may be fitted to such asurface. In the present study a known method5,6 formeasuring optical constants of absorbing materialswas used with improvements7 and was applied toseveral samples. In this method the sample wasirradiated by a beam polarized at 45° with respect tothe plane of incidence, and the reflected intensity wasmeasured at four polarization azimuths with respectto the plane of incidence. From these intensities theoptical constants were found by straightforward calcu-lation. The advantage of this type of analysis is thatonce the optical constants of a surface are known, thespecular reflectivity can be calculated for any angle ofincidence and plane of polarization. It was foundthat painted surfaces could be analyzed in this way.The present study also presents results of bidirec-

tional reflectivities of rough surfaces in the IR.Curves of bidirectional reflectance distribution func-tion 1BRDF2 versus scattering angle are presented forthe s and p components of the radiation. New resultsfor the BRDF of man-made surfaces, such as sand-blasted aluminum, concrete, and asphalt, are pre-sented for both polarization components.

2. Theory

The theory of reflection from different types of surfacehas been described in detail in the literature.1,2,8,9Here only the basic ideas and useful expressions aresummarized.When radiation falls on a rough surface it is scat-

tered into a hemisphere. Different kinds of partialreflectivity can be defined. The kind that is relevantto this study is the directional–conical reflectivity,which is the fraction of radiance that comes from acertain direction and is reflected into a cone inanother direction.The reflection properties of a surface can be de-

scribed by the BRDF, which is defined as10

BRDF ; f 1ui, fi; ur, fr2 5dLr1ur, fr2

Li1ui, fi2cos uidVi1 1sr2 .

Here Li and Lr are the incident and reflected radi-ances, respectively. The direction of the incident andreflected radiation is defined by the polar angles1ui, fi2 and 1ur, fr2, respectively. The solid angles thatcontain incident and reflected radiation are definedby Vi and Vr, respectively.The BRDF contains the radiance 1watts cm22 sr212

that is reflected from the surface in the direction1ur, fr2 divided by the irradiance 1watts@cm22 in thedirection 1ui, fi2. For the case of directional–conicalreflection in which the viewing angle of the detector issmall, the BRDF can be written as9

f 1ui, fi; ur, fr2 5Pr

Pi cos urVr

, 112

where Pi is the power of the radiation that falls on the

surface, and Pr is the measured power at the detectorthat subtends the solid angle Vr. f can assumevalues between zero and infinity and has the dimen-sions 1sr212. Equation 112 is valid for measurementstaken in the plane of incidence with the assumptionthat f and cos ur do not change much inside Vr. TheBRDF of a Lambertian surface is independent of urand is given by

fL 5 r@p, 122

where r is the total 1directional–hemispherical2 reflec-tivity. r and therefore fL are constants of the surfaceand can bemeasured by using an integrating sphere.11When drawing the BRDF of a given surface as afunction of reflection angle, the deviations from astraight horizontal line show how much the surfacediffers from a Lambertian surface.For an optically polished surface there are two

components of the reflected radiation having intensi-ties Rp for the component parallel to the plane ofincidence and Rs for the perpendicular component.For absorbing materials the reflected radiation is

elliptically polarized and a phase difference existsbetween the p and s components. As a result, therefractive index is complex and may be written as n 2ik, where n is the index of refraction and k is theextinction coefficient. Expressions for Rp and Rs as afunction of n and k 1the Fresnel equations2 have beenpublished for the case of absorbing materials.12However, it is not a simple matter to extract values ofn and k from experimentally determined values of RpandRs. Beattie andConn5,6 have developed amethodto do this. Their method consists of measuring twoparameters:

112 r8, the ratio between the parallel and perpen-dicular amplitude components of the reflected beam.

122 D, the phase difference between these compo-nents.

In this method, which was adopted for this study,the specimen was irradiated by plane polarized radia-tion having an azimuth of 45° with respect to theplane of incidence. The intensity of the reflectedradiation was measured for four different orienta-tions of the analyzer, as is explained in Section 3.The values of n and k were then obtained by straight-forward calculations.

3. Experimental

The experimental system that was built allowed us tomake photometric and polarimetric measurements atl 5 10.6 µm. A schematic diagram of the systemappears in Fig. 1 and has been described elsewhere.7Briefly, according to the numbers given to the compo-nents in Fig. 1, the system can be described as follows.A CO2 laser 112 served as the IR source. It could emitunpolarized radiation or plane polarized radiation.The radiation of the laser was chopped by a mechani-cal chopper 122 at 140 Hz. It passed through adiaphragm 172, fell onto the sample 192, which was

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stationary and reached the HgCdTe detector 1112, afterit passed through an infrared polarizer 1102. Thehome-built polarizer consisted of four ZnSe windowsthat stood at the Brewster angle with respect toradiation that passed through it. Its extinction ratiowas 250:1. The stability of the CO2 laser output wasmonitored by the power meter 162 that received radia-tion from the beam splitter 152.The beam size of the laser at the sample was

restricted by the diaphragm and was ,2 mm indiameter. The detector’s field of view at the samplewas larger than the illuminated area on the sample,but smaller than the sample itself at all angles ofmeasurement. According to the analysis of Kavayaet al.8 this configuration dictated a cos ur dependenceof detected radiation for a Lambertian surface. It isimportant to have this geometric configuration whenone makes measurements of angular distribution ofreflected radiation, as has been explained by Kavayaet al.8

4. Measurements and Results

Two types of measurement were made. In each typedifferent properties of the studied samples were em-phasized.

4.A. Measurements of Scattered Polarized Radiation

In this series of measurements the angle of incidenceui was set at a fixed angle of 45° and the incidentradiationwas linearly polarized in a plane perpendicu-lar to the plane of incidence. The infrared polarizer110 in Fig. 12, functioning as an analyzer, was situatedin front of the HgCdTe detector. The scattered radia-tion was measured as a function of the reflectionangle ur, where at each reflection angle the radiationwas measured for two orthogonal orientations of thepolarizer 1parallel and perpendicular to the plane ofincidence2. In this way the effect of depolarization

Fig. 1. Schematic of the experimental system. The numbersindicate the following components: 1, polarized CO2 laser; 2,mechanical chopper 1140 Hz2; 3, Optoswitch made by Motorola; 4,He–Ne laser; 5, Ge beam splitter; 6, power meter made by OphirOptics, Ltd.; 7, diaphragm; 8, rotatable graduated table; 9, sample1stationary2; 10, IR polarizer 1analyzer2; 11, HgCdTe detector; 12,preamplifier; 13, lock-in amplifier; 14, oscilloscope.

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could be examined in addition to the angular distribu-tion of the scattered polarized radiation. The mea-surements were made for the following samples:

112 Sublimed flowers of sulfur. The sample wasprepared by taking sublimed flowers of sulfur andpreparing a slurry by mixing it with acetone. Theslurry was introduced into a recess in an aluminumflat plate and left to dry. Some sulfur was added tothe surface and wiped off again until a smooth,powdery surface resulted. This method was de-scribed by Haner and Menzies1 and produced a sur-face without any measurable specular reflection inthe IR.

122 Sandblasted aluminum. This sample wasmade by taking a 3 3 9 cm2 aluminum plate andsandblasting it with 20-grit sand to a uniform dullfinish. The grain size was estimated as 40 µm.

132 Painted metal. The sample was prepared bycoating an aluminum plate with yellow plastic paint.Several coats were applied until a matte surface wasproduced. The paint was yellow polyurethane plas-tic paint No. 412 made by Tambour, Ltd., Israel.

142 A plane asphalt surface that contained 50%aggregate.

152 A smooth concrete surface. Samples 142 and 152were taken from a building site and were not as welldefined as samples 112–132.

It was desired to present the results as curves of theBRDF versus angle of reflection for each of thesamples. In order to obtain absolute values of theBRDF the following method was used. According toEq. 112 one can write

BRDF 51

PiVr1 Pr

cos ur2 . 132

Whereas the values of Pr and cos ur could be deter-mined by straightforward power and angle measure-ments it was somewhat difficult to get an exact valuefor PiVr. The problem was solved by using a sulfursurface as the reference sample. Since sulfur isLambertian its BRDF is independent of ur and equalsr@p 3Eq. 1224. Equating this result with Eq. 132results in

Pr

Pi cos urVr5

r

p,

and from this

PiVr 5Pr

cos ur

p

r.

The right-hand side contains two factors that couldbe evaluated by the following measurements. Theratio Pr@cos ur was measured for sulfur and wasfound to be constant within experimental error for allangles of reflection ur. The second factor containsthe directional–hemispherical reflectivity, which is aconstant and is usually abbreviated as the reflectivity.

For sulfur there is some uncertainty about the exactvalue of r at 10.6 µm. In an earlier study wedeveloped an integrating sphere reflectometer in theIR,11 and this instrument was used to measure r.The value of 0.73 was obtained for r at a wavelengthof 10.6 µm.For the Lambertian surface of sulfur we then have

fL 5r

p5 0.23 sr21.

For the two 1equal2 polarization components of fL weobtain one half of this value:

1 fL2p 5 1 fL2s 5 0.115 sr21.

This value is estimated to be accurate to 65%.At this point it was possible to calculate PiVr, which

was a constant of the system. This permitted themeasurement of the BRDF of the other samples,using the same geometry and the same HgCdTedetector as for sulfur, by measuring the reflectedpower Pr as a function of the reflection angle 3see Eq.1324. The results are shown in Figs. 2–5, in whichthey appear together with the BRDF of sulfur, whichwas measured separately for each angle for compari-son purposes. The average value of the BRDF ofsulfur was set at 0.115 sr21 1for each polarization2.The accuracy of the results in Figs. 2–5 was 610%.The subscripts s and p that appear in Figs. 2–5designate the perpendicular and parallel componentsof the BRDF, respectively. Figure 6 shows the sum ofBRDFs and BRDFp on a linear scale as a function ofthe angle of reflection and is denoted by BRDFtot.

4.B. Specular Reflection Measurements: OpticalConstants

Looking at the angular distribution of the radiationthat was reflected from the yellow-painted metal1Figs. 2 and 42 it is evident that the radiation reflectedfrom this surface has a strong specular component 1at

Fig. 2. Logarithmic plot of BRDFs of sandblasted aluminum,yellow-painted metal, and sulfur as a function of reflection angle.The angle of incidence was 45°. Incident radiation was polarizedin the s plane.

45°2. This result was the motivation for makingmeasurements of specular reflectivity of paints over awide range of angles of incidence. The specularreflectivity in such a case was assumed to be given byFresnel equations for absorbing surfaces. As de-scribed in Section 2, the analysis of these equationswas made with the help of a method that was sug-gested by Beattie and Conn5,6 and was also used byus7 with several improvements. The angle of inci-dence 1ui2 was close to the principal angle of incidence1u2. The intensity of reflected radiation was mea-sured for four different orientations of the analyzer:perpendicular, parallel, at 145°, and at 245° withrespect to the plane of incidence. These intensities,which were denoted I1, I2, I3, and I4, respectively, afterseveral manipulations gave the optical constants nand k. This method was previously applied to a plateof UV-grade fused silica.7 The results were n 5 2.01and k 5 0.45 for this material at l 5 10.6 µm. Theseresults agree with those quoted by Palik12 and by

Fig. 3. Logarithmic plot of BRDFs of asphalt, concrete, and sulfuras a function of reflection angle. The angle of incidence was45°. Incident radiation was polarized in the s plane.

Fig. 4. Logarithmic plot of BRDFp of sandblasted aluminum,yellow-painted metal, and sulfur as a function of reflection angle.The angle of incidence was 45°. Incident radiation was polarizedin the s plane.

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Roseler.13 In this study the method was tried onseveral paints at various angles of incidence and wasfound to be self-consistent, i.e., n and k were indepen-dent of angle of incidence. Then it was used to findthe optical constants of a black paint 1Magic SprayEnamel Black paint made by Yenkin-Majestic PaintCo., Columbus, Ohio2. The paint was sprayed ontoan aluminum plate until an opaque layer was obtained.The specular reflectivity of the paint was measuredwith the CO2 laser. This paint was chosen becauseof its highly specular behavior in the IR. We ob-tained n 5 1.52 and k 5 0.46 for this paint. Fresnelcurves were calculated according to these opticalconstants and are shown along with the experimentalmeasurements of the specular reflectivity of thispaint 1Fig. 72. The low experimental values obtainedfor Rp and Rs 1below 0.3 to 80° angle of incidence2reflect the fact that the paint was dull black in thevisible and had a similar low reflectivity in the IR.It was remarkable that the curve of Rp versus angle of

Fig. 5. Logarithmic plot of BRDFp of asphalt, concrete, and sulfuras a function of reflection angle. The angle of incidence was45°. Incident radiation was polarized in the s plane.

Fig. 6. BRDFtot of yellow-painted metal, sandblasted aluminum,and sulfur as a function of angle of reflection. Incident radiationwas polarized in the s plane. Error bars are shown for a selectedpoint on each curve.

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incidence for this matte surface contained aminimumat the Brewster angle.

5. Analysis and Discussion

5.A. Bidirectional Reflectance Distribution FunctionMeasurements

Previous studies of the BRDF in the IR frequentlygave relative rather than absolute or referenced val-ues of the BRDF. It is therefore difficult to compareour results with those of Haner andMenzies,1 Kavayaet al.,8 and Stuhlinger et al.2 Although the Stuhlingeret al. research did include measurements on sulfur, itwas carried out with unpolarized radiation and didnot include incident angles at 45°.The results for the BRDF in Figs. 2–5 can be

discussed from two main points of view.

5.A.1. Angular Distribution of Reflected RadiationThe main characteristic of a Lambertian surface isthat the intensity of radiation reflected from it de-creases as cos ur, where ur is the angle of reflection.This condition is equivalent to a constant value of theBRDF as a function of ur 3Eq.1224. From our resultsit is quite clear that only the flowers of sulfur surfaceis nearly Lambertian. Its BRDF is nearly constantin both states of linear polarization. For the othersamples the situation is different. The graphs ofBRDFs 1Figs. 2 and 32 that deal with the radiationthat was not depolarized show that the asphalt,concrete, and sandblasted aluminum surfaces scatterthe radiation over a broad range of reflection angles.These curves rise when the reflection angle is in-creased and continue to grow beyond 45°, showing atypical off-specular peak of roughened surfaces, asobserved and explained by Torrance and Sparrow.3These authors made observations in the visible andsuccessfully analyzed their results with a theoreticalmodel. The painted metal, however, reflected al-most all the radiation at the specular angle, as if itwere highly polished 1see Fig. 62.

Fig. 7. Measurements of specular reflectivities 1Rs andRp2 of blackpaint compared with calculated Fresnel curves for n* 5 1.52 1

0.46i. The experimental error is estimated as 65%.

The graphs of BRDFp 1Figs. 4 and 52 deal with theradiation that was depolarized. For sulfur the behav-ior was similar for both polarizations. For the othersamples one can generally state that the intensity ofthe radiation is much lower than for the perpendicu-lar component, but the angular distribution is muchless variable. This means that the part of the radia-tion that was depolarized was scattered in randomdirections without angular preference.

5.A.2. Conservation of the State of PolarizationAnother characteristic of a Lambertian surface is thatit is able to depolarize incident radiation. In thisstudy the incident radiation was linearly polarized ina plane perpendicular to the plane of incidence.Information about depolarization caused by the sur-faces was obtained from the measurements of BRDFp.It is clearly seen in Figs. 4 and 5 that, whereas thecurve of BRDFp for sulfur is the same as that ofBRDFs, the other curves are much lower. Actually itwas necessary to use a logarithmic scale in order todifferentiate the shapes and magnitudes of the othercurves. The situation is not so for the curves ofBRDFs, which means that most of the surfaces andespecially the painted metal plate did not causedepolarization. Another way of looking at this prop-erty of depolarization can be obtained by drawing agraph of percent of polarization of the radiation thatwas scattered from each surface as a function of theangle of reflection 1Figs. 8 and 92.The percent of polarization is defined as

1Ps 2 Pp2@1Ps 1 Pp2 3 100 or 11 2 Pp@Ps2@11 1 Pp@Ps23 100. Looking at this expression one can distin-guish between the following cases: 112 Smooth sur-faces for which Pp 5 0, since the incident radiationarrives polarized in the s plane and is not depolarizedby reflection. In this case we have 100% polarization.Behavior that approaches this was observed forpainted metal 1Fig. 82. 122 Lambertian surfaces forwhich Pp 5 Ps, since the reflected radiation has no

Fig. 8. The percent of polarization of the reflected radiation fromsandblasted aluminum, yellow-painted metal, and sulfur as afunction of reflection angle with ui 5 45°. Incident radiation waspolarized in the s plane.

preferred plane of polarization. The percent of polar-ization approaches zero in this case, as is seen in Figs.8 and 9 for sulfur. 132 Surfaces for which 0 , Pp , Ps.These surfaces are neither purely specular nor purelyLambertian. The expression 11 2 Pp@Ps2 11 1 Pp@Ps221

3 100 assumes values between zero and 100 for 0 ,Pp , Ps. It is also seen that this expression is adecreasing function of Pp@Ps, which means that themore diffuse the surface, the lower its percent ofpolarization. In this study asphalt, concrete, andsandblasted aluminum show this behavior 1Figs. 8and 92. In the case of sandblasted aluminum thepercent of polarization is rather high 170–90%2, al-though its average roughness is approximately 40µm, which is larger than the wavelength. Such arough surface might be expected to be a good depolar-izer. However, its high degree of polarization may bedue to its nonporous surface structure, which does notpermit much interaction with the incoming radiation.It follows from Figs. 8 and 9 that none of thematerialsthat appear in these figures has a Lambertian charac-ter, except for sulfur.The phenomena that were described above can be

explained from a microscopic point of view as follows:radiation that is reflected from a surface is dividedinto two main parts:

1a2 Radiation that leaves the surface after onereflection. The state of polarization of this radiationis usually conserved, and the reflected radiation has aspecular direction or a direction close to it. Thedirection depends on the orientation of the micro-scopic facet that reflects the radiation. This facetmight be parallel to the average macroscopic plane ortilted with respect to it 1see Fig. 102. It is seen thatthe angle of reflection ur is not equal to ui because thereal angle of incidence is v.

1b2 Radiation that enters the material and suffersrefraction, diffraction, and multiple reflections 1seeFig. 112. This figure shows several possibilities ofscattering by a rough surface 1left-hand side of Fig.

Fig. 9. Percent of polarization of the reflected radiation fromasphalt, concrete, and sulfur as a function of reflection angle withui 5 45°. Incident radiation was polarized in the s plane.

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112 and by a porous surface 1right-hand side of Fig. 112.In both cases the scattered radiation leaves thesurface in a direction that is independent of thedirection of incident radiation. Because of the stronginteraction with thematerial, the state of polarizationof the scattered radiation has no preferred plane.An example of such a surface is flowers of sulfur1Fig. 92.

The parameter that determines whether a certainsurface is specular or diffusive is the ratio betweenthe rms size of grains on the surface 1s2 and theincident wavelength 1l2.4 For s@l : 1 the incidentradiation is scattered by the surface. In the IR rangethe wavelength is approximately 20 times longer thanin the visible. The ratio s@l is therefore smaller bythis factor so the surface becomes effectively smoother.There is less interaction between the radiation andthe surface. Most of the radiation is reflected onlyonce 1no multiple reflections2 from a surface that isalmost parallel to the average plane of the surface, soit is directed close to the specular angle. This is seenclearly in the case of painted metal that has anaverage grain size of 1–4 µm 1Fig. 62.In most of the samples studied both specular and

diffuse reflection mechanisms are involved, each withits own contribution, depending on the material andits microscopic structure.

5.B. Specular Measurements

The graphs of the reflectivities of the black paint 1Fig.72 show partial agreement with Fresnel curves. It isremarkable that Rp has a minimum around 57°,which is close to the theoretical principal angle ofincidence for this material 1corresponding to theoptical constants2, which was 56.7°. The points of Rsdo not fit the theoretical curve and only the qualita-tive shapes are similar. However, better agreementbetween experimental points and theoretical curvescan be achieved by calculating from the data in Fig. 7

Fig. 10. Reflection of radiation from a surface tilted with respectto the average plane of the macroscopic surface.

Fig. 11. Several possibilities of scattering by a rough surface.

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the ratios Rp@Rs and the percent of polarization of thespecularly reflected radiation: 31Rs 2 Rp2@1Rs 1 Rp24 3100 1see Fig. 122. This is due to the fact that the ratioRp@Rs for a rough surface is the same as that for asmooth surface of the same material. This wasshown theoretically and experimentally by Stagg andCharalampopoulos,4 who also showed that a rough-ened surface of pure carbon obeyed Fresnel equationsand reached 90% polarization at 3.5 µm. It shouldbe stressed that the expression used here for thepercent of polarization refers to the components of thespecular reflectivity and should not be confused withthe percent of polarization mentioned in Section 5A.2,which refers to the scattered radiation.The conclusion based on specular measurements is

that painted metal behaved like a smooth opticalsurface when it reflected IR radiation, but the agree-ment with Fresnel curves was not complete becausepart of the radiation was scattered. However, theratio betweenRp andRs and the degree of polarizationof the radiation that was specularly reflected did notchange and agreed quite well with the theoreticalcurves.4 Therefore, as long as a specular reflectivitymeasurement is possible from a rough surface, n andk of the material can be derived from polarizedreflectance measurements. It may be assumed thatthese values of n and k are equal to the bulk values,since they are based on a single specular reflectionfrom the grains of the material.

6. Conclusions

Rough surfaces, such as concrete and asphalt, havebeen shown to scatter IR radiation to a considerabledegree, although the state of polarization was mostlyconserved. The BRDF for several of these surfaceswas measured in this study, but no unique behaviorcould be formulated. These surfaces were neitherideal diffusers, following Lambert’s law, nor idealreflectors.However, otherman-made surfaces, such as painted

metals 1vehicles2, have been shown to have strongly

Fig. 12. Experimental data and theoretical curves of Rp@Rs 1opencircles2 and the percent of polarization 1filled circles2 of reflectedradiation from black paint. The experimental error is estimatedat 65%.

polarized optical properties in the IR region. To afirst approximation they could be characterized bytheir optical constants 1n and k2 and their reflectingbehavior described byFresnel equations. Good agree-ment was found between the calculated and observeddependence of the degree of polarization on angle ofreflection 1Fig. 122.

This researchwas supported by the Fund for Promo-tion of Research at the Technion. The authors aregrateful to Dan Sheffer of the Electro-Optics Divisionof the Technion Foundation whomade the IR reflectiv-itymeasurements of sulfur with an integrating spherereflectometer. We thank Matty Katz for fruitful dis-cussions.

References1. D. A. Haner and R. T. Menzies, ‘‘Reflectance characteristics of

reference materials used in lidar hard target calibration,’’Appl. Opt. 28, 857–864 119892.

2. T. W. Stuhlinger, E. L. Dereniak, and F. Q. Bartell, ‘‘Bidirec-tional reflectance distribution function of gold-plated sandpa-per,’’Appl. Opt. 20, 2648–2655 119812.

3. K. E. Torrance and E. M. Sparrow, ‘‘Theory of off-specularreflection from roughened surfaces,’’ J. Opt. Soc. Am. 57,1105–1114 119672.

4. B. J. Stagg and T. T. Charalampopoulos, ‘‘Surface-roughnesseffects on the determination of optical properties of materialsby the reflection method,’’Appl. Opt. 30, 4113–4118 119912.

5. J. R. Beattie and G. K. T. Conn, ‘‘Optical constants of metals inthe infrared: principles of measurement,’’ Philos. Mag. 46,222–231 119552.

6. J. R. Beattie and G. K. T. Conn, ‘‘Optical constants of metals inthe infrared: experimental methods,’’ Philos. Mag. 46, 235–245 119552.

7. Y. Feiner and U. P. Oppenheim, ‘‘Measurements of opticalconstants of absorbing materials in the infrared,’’ InfraredPhys. 33, 289–292 119922.

8. M. J. Kavaya, R. T. Menzies, D. A. Haner, U. P. Oppenheim,and P. H. Flamant, ‘‘Target reflectance measurements forcalibration of lidar atmospheric backscatter data,’’ Appl. Opt.22, 2619–2628 119832.

9. M. J. Kavaya, ‘‘Polarization effects on hard target calibrationof lidar systems,’’Appl. Opt. 26, 796–804 119872.

10. F. E. Nicodemus, ‘‘Directional reflectance and emissivity of anopaque surface,’’Appl. Opt. 4, 767–773 119652.

11. D. Sheffer, U. P. Oppenheim, and A. D. Devir, ‘‘Absolutemeasurements of diffuse reflectance in the a0@d configuration,’’Appl. Opt. 30, 3181–3185 119912.

12. E. D. Palik, ed., Handbook of Optical Constants of Solids1Academic, Orlando, Fla., 19852, Chap. 4, p. 70.

13. A. Roseler, ‘‘Spectroscopic ellipsometry in the infrared,’’ Infra-red Phys. 21, 349–355 119812.

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