spectral reflectance and emittance of particulate ... · n = no + (e/r), (1) where no, the input...

Spectral Reflectance and Emittance of ParticulateMaterials, 2: Application and ResultsJ. R. Aronson and A. G. Emslie

Experimental data on the spectral emittance of particulate minerals, obtained using a Michelson inter-ferometer operating between 300 cm-i and 1400 cm- 1 are compared with the results of a new theory ofthe spectral reflectance (emittance) of such materials. The comparisons show that the theory predictsthe infrared spectra of minerals quite well both for single substances and mixtures, over the wide particlesize range between 0.3 u and 330 . The good agreement suggests that the theory can be used in the ap-plication of remote infrared spectroscopy to such problems as the compositional analysis of the surface ofa planet.

IntroductionFor many ears it has been recognized that in-.

frared spectroscopy provides unique information onthe composition of minerals. This results'from therich vibrational spectra that may be obtained in theinfrared region. While most workers have concen-trated their efforts on laboratory transmission spec-tra, such potentially important remote sensing tech-niques as emission and reflection were i fact inves-tigated by Coblentz' almost three quarters of a cen-tury ago. The advent of the space program reawak-ened an interest in this topic, and a number ofgroups proposed remote infrared spectroscopy as avaluable tool for evaluating planetary surfacemineralogy from orbiting or flyby spacecraft. Theinstrumental capability for obtaining excellent re-mote data has continued to improve, as demon-strated by recent results from the Mariner Mars2

and Nimbus3 orbiting spacecraft.While the reflectance spectra of polished mineral

samples provide many strong features suitable forrelatively simple interpretation, the spectra ofroughened or particulate samples change in impor-tant ways with the degree of roughness or the parti-cle size and packing density. For some time, it wasbelieved by many investigators that the spectra offinely divided minerals approximate blackbody spec-tra and thus contain very little or no informaton asto composition. We showed4 both experimentallyand theoretically that this was not true but that theproblem was simply one of the signal-to-noise ratio.Others 5 ' 6 examined the effects of particle size on

The authors are with Arthur D. Little, Inc., Cambridge, Mas-sachusetts 02140.

Received 8 August 1972.

spectral shape and found that different spectral fea-tures had widely differing behaviors as a function ofparticle size. In some cases7 peaks could even turninto troughs. As the greatest difficulties inherent inthe prospects for remote mineral analysis by infraredspectroscopy were clearly those of interpretation, webegan the development of a new theory of the reflec-tance or emittance of particulate solids several yearsago.8 The current status of the theory is detailed inthe preceding paper9 (hereafter referred to as Part1).

An earlier version of the theory produced relativelygood agreement with experimental data10 in thecoarse-particle regime. The agreement in all parti-cle size ranges has continued to improve through aprocess of successive refinement of the assumptionsas discrepancies appeared in the comparison of theo-retical predictions with experimental measurements.Apparatus

Our measurements have been made on a 7-35 t(1400-300 cm-') Michelson interferometer spec-trometer system, which uses a germanium-coatedCs1 beam splitter and a Barnes TGS pyroelectric de-tector. The samples are heated from below andmounted on a lazy Susan turntable so that alternatemeasurements can be made without breaking thevacuum or inert gas atmosphere. Vacuum measure-ments can be made to investigate the effects of highthermal gradients on the spectra.

The powders are generally supported in a sampletray 0.6 cm deep with a total volume of 3.04 cm3 .This tray is instrumented for temperature measure-ments by embedding a thermistor in the base andstringing two sets of 0.05-cm differential copper-con-stantan thermocouples 0.2 cm and 0.5 cm above thebase (Fig. 1). The gradient between the upper twostations is extrapolated to the nominal surface in

November 1973 / Vol. 12, No. 11 / APPLIED OPTICS 2573

correction for radiation from the shield that is re-flected from the sample.

The transfer function relates radiance N(v) tospectral output voltage E(v) obtained by Fouriertransformation of the interferogram. We assumethat the formula is linear and of the form

N = No + (E/R), (1)

where No, the input radiance that produces zero out-put signal, is equal to the radiance of the instrumentin the direction toward the sample. To determineNo and R we replace the sample successively by twoblackbodies at temperatures T, and T2. Then, fromEq. (1)

Fig. 1. Sample tray (not to scale). EB, = No + (E1/R),

e-B2 = No + (E2/ R),

order to provide a first estimate of the surface tem-perature. Thermistors located on the interferometerdetector case, on the black shield that surrounds thesample chamber, and on the experimental black-bodies provide the other temperatures required fordata reduction.

The experimental blackbodies are constructed ofaluminum and have concentric 300 V-grooves cutinto the surface. They are coated with Parsonsblack paint (Eppley Laboratory) because previousresults using Nextel black paint (Minnesota Miningand Manufacturing Co.) indicated the presence ofspectral features near 1090 cm-' and 460 cm-',owing to the presence of small glass beads in theNextel paint. The Parsons black standard was runagainst a Cabot Corporation Carbolac-1 black pow-der sample (9-m/i carbon particles) as well as Nex-tel-coated standard, and the data indicate a spec-trally flat emittance for the Parsons standard from1400 cm-' to about 500 cm-'. The emittance of theParsons standard then appears to fall monotonicallyreaching apparent values of about 0.97 near 350cm-lData Reduction

The data reduction procedure involves Fouriertransformation of the interferograms of the sampleand the two experimental blackbodies which are runat temperatures close to that of the sample and dif-fer by about 5C. High signal-to-noise data are ob-tained with a sample surface temperature about150C above the near-ambient interferometer andshield temperatures in about 20 min with a spectralresolution of about 3 cm-1.

The spectral emittance (v) of the sample is thespectral radiance N,(v) of the sample divided by thespectral radiance B,(v) of a blackbody at the sametemperature as the sample. We calculate B,(v) fromthe Planck function using the inferred surface tem-perature of the sample. We determine N,(v) fromthe measured output spectrum E(v) of the sampleby means of the instrument transfer function and a

where E, E2 are the emittances of the blackbodies,which would allow for small departures from perfectblackbody behavior. From Eqs. (2) and (3) we ob-tain for R(v) and No(v):

R(v)= (El - E2)/(EBl -EB2) (4)

andNo(v) = 1IE B + e2B2- (1 /R)(E, + E2)1. (5)

With the sample in place we determine the net ra-diance Ns of the sample from the measured spectraloutput Es by means of Eq. (1)

N = No + (E./R) (6)

and where R and No are known from Eqs. (4) and(5). On combining Eqs. (4)-(6) we can express N,directly in terms of the measured quantities El, E2,and Es:

N. = 12(,Bl + e2B2) +

1(e-,e 2B2)((2E, - EI-E 2)/(EI-E2)). (7)Finally, the emittance E, of the sample is comput-

ed from the formulae = N.,- B[1 -(Q / 1- B(Q / 7 /

- B[1B-1(Q-//7r)] - B(Q /7 , (8)which is based on simple radiative transfer consider-ations. Here BC is the radiance of the cavity orshield (assumed to be a blackbody) at temperatureTC surrounding the sample, Bi is the radiance of theinterferometer aperture (also assumed to be a black-body at temperature Ti), Bs is the Planck functionfor the temperature T of the sample, and Q is thesolid angle subtended at the sample by the interfero-meter aperture. The cavity walls are coated with3M Nextel black paint, which, together with multi-ple reflections, should make it an almost perfectblackbody. In the data reduction up to the presentwe have assumed that the blackbodies are indeedblack, so that ei= 2 = 1.

2574 APPLIED OPTICS / Vol. 12, No. 11 / November 1973

Phenolic Tubing

(2)

(3)

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Fig. 2. Comparison of theoreticaland experimental reflectance of

corundum powders.

400 300

As the surface of the powder cannot be microscop-ically smooth (we draw a spatula edge across thepowder surface to prevent gross roughness), and asthe depth of origin of the radiation is a function ofthe optical constants at the various frequencies, wecannot expect the definition of the surface to be veryexact. Further, the position of the stretched ther-mocouple wires has some error and the possibility ofa poor equilibrium between the radiation field andthe shiny thermocouples is quite likely.

For all of these reasons we chose to estimate oursurface temperature by a radiative expedient basedon what is generally known as the principal Chris-tiansen frequency.",12 When the refractive index nof a substance approaches unity and the absorptionindex k is quite small (10-2), the amount of sur-face reflection is negligible and the refractive scatter-ing is mininal. Thus the emittance is maximum andclose to unity. This combination of the optical con-stants occurs at slightly higher frequencies than thefirst principal reststrahlen band. It cannot in prin-ciple occur for a mixture of materials as the locationof the Christiansen frequency will be different foreach species. Even two orientations of birefringentminerals have slightly different Christiansenfrequencies. We take the value for the average ofthe two orientations of corundum to be 1020 cm-'and for quartz to be 1360 cm-' from data of Bark-er' 3 and Spitzer and Kleinman.' 4 We assume that

the only significant temperature error in our data re-duction scheme is that of the surface temperature.We then use the extrapolated surface temperatureas a first estimate of the true surface temperatureand calculate an emittance spectrum. The comput-er program is constructed so that this temperaturemay be varied and the procedure is to make the re-quired changes in this temperature so as to provide aunit emittance at the principal Christiansen fre-quency.

We have found that the extrapolated surface tem-perature and the temperature derived by the Chris-tiansen frequency technique differ by a few tenths ofa degree in cases of relatively low temperature gradi-ents (about 5/cm to 100/cm as measured by ourupper differential thermocouple) that occur in atmo-spheric pressure runs. Under conditions of hightemperature gradients (vacuum) the procedure isquite inaccurate, and we plan to discuss this in a fu-ture communication. All the data are plotted as re-flectance (R = 1 - E) for convenience in comparisonwith the theory. The validity of this procedure,which is simply an application of Kirchhoff's law forinfinitely thick media, has been previously shown."Comparison of Theory and Experiment

As discussed in Part 19, our theory consists of twosubtheories. The first, which is based on geometri-cal optics supplemented by certain wave optics con-


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120i F(ElC) = .32 F(EIC) = .16 -- *- 10 F(EC) = .20 F(EIIC) = .10Coarse Particle Theory Bridged Theory

-- 60 F(EIC) = .32 F(EIc = .16 3.5p F(ElC) = .16 F(E1lC) = .08Coarse Particle Theory Bridged Theory

30p F(ElC) = .26 F(EIIC) = 13. 0.3p F(ElC) = .12 F(EI1C) = .06Coarse Particle Theory Fine Particle Theory

~-..l' .....

- ----- --

01-1. ,

I I

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Fig. 3. (a) Scanning electron micrograph of steplike asperities.30-i corundum, 740. (b) Scanning electron micrograph of

steplike asperities and additional fines. 120-A corundum, X370.

siderations, is applicable in the coarse-particle regionwhich extends down to particle sizes roughly compa-rable with the free space radiation wavelength. Thesecond, a fine-particle theory, is based on the Lo-rentz-Lorenz theory of dielectrics and Rayleigh scat-tering by particles immersed in the medium whoseoptical properties are set by the Lorentz-Lorenzfield. In order to bridge the two theories for thoseparticle sizes falling in the ill-defined region betweenthe regions of clear applicability of either theory, wehave at present resorted to a simple empirical bridg-ing formula that gradually merges the results of thetwo subtheories.

Figure 2 shows a comparison of the experimentaland theoretical results for corundum powders. The

120- sample was obtained from the Norton Compa-ny, the 0.3-,4 sample from Adolf Meller Co., and theother samples are LWA powders obtained from theMicroabrasives Corporation of Westfield, Massachu-setts. The particle sizes shown on the figure for theLWA powders are Microabrasives designations ex-cept for the 3.5-pt sample. This is MicroabrasivesLWA 3, but our particle size counts indicated avalue of about 3.8 ,. The shape of the spectrum be-tween 630 cm-' and 900 cm-' and the particle sizeeffect in regions of the spectrum where the particlesare opaque was correctly predicted only after we in-cluded the wave optics additions to the basic geo-metrical optics model to account for the effects ofparticle edges10 and surface asperities. The edge ef-fect which dominates at the lower particle sizes (ds)of the coarse-particle theory produces the 1/d depen-dence of the reflectance spectra in this region of highabsorption by the particles. The fact that the 630-900 cm-' feature persists to relatively large particlesizes (120 It) was explicable only after scanning elec-tron micrographs (Fig. 3) revealed the presence ofsmall steplike surface asperities for this material. Ifthe number of these asperities is proportional to thesurface area of the particles, they will produce no d-dependent effect (see Fig. 4). The surface density ofthese asperities is an adjustable parameter in thetheory. The scale factor for the /d effect of theparticle edges has been chosen, as discussed in Part19, by means of reasonable but somewhat arbitraryphysical assumptions. We have used the same fac-tor for all jagged particles. The general level ob-served in the reststrahlen regions for large particlesin all of our work is higher than predicted by thetheory. We believe this to be the result of deficien-cies in our continuum-type radiative transfer modelas the particles in such regions are highly opaqueand therefore give rise to a large change in the radia-tive fluxes in a single layer of particles, which vio-lates the assumptions of a continuum model. Cor-rection of the theory by means of a discrete layermodel is required, as pointed out also in Part 1.

As reduction of particle size generally results in in-creasing porosity (decreased packing density) andthe fine-particle theory shows a decided porosity-dependent effect owing to the dilution of the opticalconstants by high void fractions, we have carried outseveral experiments with the 0.3-,g powder as a func-tion of packing density. The results showed that aspacking density is increased, the principal effect is toincrease the spectral contrast in the two features at450 cm-' and 580 cm-'. The data shown in Fig. 2for the 0.3-,4 sample were obtained by compressing itgently, thus increasing the volume fraction of mate-'rial to 0.19 from 0.09, which is its state as preparedby our usual techniques.

The spurious feature observed near 930 cm-I in thetheoretical spectra for the 3 .5-,4 and 10-,4 cases wouldbe considerably reduced if a particle size distributionhad been used. It is to be noted that the peak in theexperimental spectrum in this general region shifts

2576 APPLIED OPTICS / vol. 12, No. 11 / November 1973

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to higher frequencies as the average particle size isreduced. This may very well be the effect of a con-tribution by the feature in question. The feature iscaused by the onset of a refractive contribution tothe scattering as the particles become more trans-parent for frequencies approaching the Christiansenfrequency at io20 cm-'. This contribution falls offrapidly as the frequency approaches still closer to theChristiansen point. A similar explanation applies tothe theoretically predicted convex shape of the spec-tra at frequencies above 1020 cm-' contrasted withthe concave shape shown by the experimental data.

Figure 4 shows the theoretical corundum spectraas calculated for the 120-,g and 30-,4 particle sizes byoptions in our program that either, (i) treat the par-ticles as smooth spheres, (ii) include both the effectsof edges and surface asperities, (iii) include edges,but no asperities, and (iv) include asperities but noedges. As can be seen, both edges and asperities arenecessary to account for the particle size dependencein the reststrahlen regions and the shape of the 630-900 cm-' feature in the 120-g particle size sample.The amount of surface asperities used for theseplots is NV = 3 x 10-7 cm (see Part 1). This value,which corresponds to the average thickness of theasperity layer, indicates that a substantial change inreflectance is caused by a relatively small amount ofthese asperities. The effect is caused by the highefficiency of absorption by ellipsoidal particles hav-

700 600 500 400 300

700

Fig. 4. Theoretical spectra of co-rundum powders demonstratingthe effects of edges and surface

asperities.

600 500 400 300

ing n < 1 and k - 1 such as occur in reststrahlenbands. The amount of asperities appears compat-ible with photomicrographs of the particles. In asimilar fashion the scale factor for the d dependencedescribed in Part 1 by the value b /47r is some-what arbitrary and might be slightly adjusted for abetter fit to the data. At the present time b 0.09 isused for all of our theoretical computations. How-ever, as these factors are unlikely to be known pre-cisely for arbitrary unknown samples, we have notyet optimized the fit.

The phenomenon of additional absorption by theneedlelike dipoles that represent the edges and themore general spheroidal dipoles that represent sur-face asperities was an important innovation in ourcoarse-particle theory. We therefore attempted toprove the reality of these effects by carrying out sev-eral critical experiments. The first of these was acomparison of a single crystal emittance spectrum ofrandomly oriented sapphire with the emittance spec-trum obtained after substantial surface abrasionwith 15-i diamond paste. The results are shown inFig. 5, and a stereo pair of scanning electron micro-graphs of a replica of the surface are shown in Fig. 6.Figure 5 shows that the anomalous shape of the pow-der spectrum in the 630-900 cm-' region can be pro-duced in a single crystal spectrum by providing sur-face asperities.


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Fig. 6. Scanning electron micrographs of replica of abraded sapphire crystal. Photographs rotated to simulate the actual surface(X450).

The second critical experiment was carried out byrunning two samples of corundum beads (Fig. 7).These beads were produced for us by D. Spoonerand R. Bechtold of the Lockheed Electronics Geo-physics section. The mechanism of bead productionis to feed small particles of corundum into a hydro-gen-oxygen flame where partial melting occurs.After air cooling, small amounts of a number ofother A12 03 phases were observed by x-ray diffrac-tion, but annealing at 14000C for more than 4 h re-moved the other phases, resulting in pure a-AI20 3.

Figure 8 shows scanning electron micrographs of thesapphire beads. Surface asperities similar to thoseshown for most samples of crushed corundum (Fig.3) still occur on these beads. Some nonspheroidizedmaterial still exists, principally in the smaller sizedsample, but the particles have been largely de-edged.The changed level of the spectra in the 575-900cm-1 region and the noticeably smaller particle sizeeffect when contrasted with the data for comparable-sized particles in Fig, 2 both confirm the assumedmechanism of edge absorption. We believe that the


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Fig. 7. Experimental spectra ofcorundum beads.

300

130P. 215X

1000X 35Mf 500X

Fig. 8. Scanning electron micrographs of corundum beads.


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residual edges in the 3 5-A beads are largely responsi-ble for the fact that the spectrum of this sample isstill somewhat below the spectrum of the 130-gbeads in the 575-900 cm-' region. We note that thelevel of the spectrum of the 35-,4 beads lies betweenthe level of the 60 -A and 12 0-/i corundum powders.A dendritic growth can be seen in the scanningelectron micrographs of the bead surfaces. This ma-terial is apparently responsible for the shape varia-tion in the 630-900 cm-' region. Such a result is inaccord with a number of theoretical experiments wehave conducted by varying the shapes of the asperi-ties (Part 1).

The empirical bridging formula used in the regionbetween 0.3 g and 12 ,u where both theories are beingextended beyond their range of applicability appearsto provide better results than either theory alone.This can be seen in Fig. 9, where the results of bothindividual theories and the bridged theory are com-pared with experimental results for 3.5-p corundumpowder. The relatively greater strength of the fea-ture near 535 cm-' with smaller particle size can beseen in the experimental data for the 3.5-A and 10-Aparticles (Fig. 2). This is apparently a residue of thestrong fine-particle feature shown by the theory (Fig.9) to peak near 570 cm-, and it was used in an at-tempt to ascertain a reasonable bridging relation-

Fig. 9. Comparison of thebridged theory with the coarse-particle and fine-particle theories

for corundum.

600 500 400 300

ship. This relationship can probably be improvedupon, but its optimization is somewhat dependenton the optimization of the other adjustable factors aswell as the replacement of the monodisperse assump-tion with a more realistic particle size distributionfunction. The real particles, of course, have a sizedistribution, but the theoretical results shown in thispaper are all for monodisperse particles.

Figure 10 shows the theoretical and experimentalresults for quartz powders. Once again the theoreti-cal spectra for the coarser particles do not attainvalues as high as those observed in the experimentaldata in the reststrahlen regions. For the theoreticalruns we assumed no surface asperities, since the1100-1200 cm-' feature in quartz, which is similarto the previously discussed 630-900 cm-1 feature incorundum, is only observed at the smallest particlesizes. However, clinging fine particles are commonlyobserved to be present in samples of larger particlesize. In our theory they would act in much the sameway as surface asperities. The data shown for thesample marked 0-20 A provide a good example of theeffect of such fines. The average particle size forthis sample is near 10 g, but the effect of the largenumber [but small volume fraction (0.007) of parti-cles less than 2.85 Ai] is such as to give a more pro-nounced feature in the 1100-1200 cm-' region than


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Fig. 10. Comparison of theoreti-cal and experimental reflectance

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300

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Fig. 11. Scanning electron micrographs (x95) of 170-,u quartz particles.


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is observed for the 4.5-,4 sample. In fact, the lattersample was obtained only after a discrepancy wasobserved between the experimental particle size andthat necessary to produce the feature, using thesame value of b, the scale factor for the 1/d edge ef-fect as was used for corundum. That discrepancyled us to reexamine the particle distribution in the0-20-A sample and the wide distribution found sug-gested that a narrower size range for this importantexperiment was in order. The 4.5-, sample wasthen obtained from Duke Standards of Palo Alto,California. They indicate a 1-4.5-,4 range for thesample. Our particle counts give 4.6 ,u for the vol-ume-averaged size of this material, and it has an ob-viously narrower particle size distribution than the0-20-A sample. The 0-2 0-g sample can be reason-ably well fitted by the theory, if we use an asperityfactor of NV = 1.5 10-5 cm to represent the cling-ing fine particles. This fit tends to confirm our ideathat a small volume of clinging fines represents thesame kind of extra absorption as do surface asperi-ties. This effect was first observed in some of ourearly work, when some large quartz particle sampleswere run as received and after a wet-sieving proce-dure was used to remove the small volume fraction,but large numbers of clinging fine particles. Figure11 shows photomicrographs of the samples of quartzpowders of large particle size (170 g) as received andafter removal of the fines. Figure 12 shows the re-sultant spectra. The very large effect shown in Fig.12 was produced by a quite small volume fraction ofthe fines. As with the surface asperities, the effectappears most significant in regions of high absorp-tion.

As with corundum we note a spurious theoreticalfeature (Fig. 10) slightly to the high frequency side ofthe principal reststrahlen band for samples of inter-mediate particle size (4.5 g and 10 ). This featuredoes not occur in the experimental data which as be-fore is actually for a particle size distribution. Weagain note an apparent shift of the reststrahlen fea-ture toward higher frequencies as the particle size is

reduced and believe that the theoretical feature con-tributes to the shift. It is significant that the fea-ture in question is also produced theoretically in Mietheory calculations12 for the intermediate particlesizes, but with smaller amplitude. Further study ofthis problem is in progress.

Figure 13 shows experimental and theoretical re-sults for garnet powders obtained from Barton Minesof North Creek, New York. The particle sizes usedto calculate the theoretical spectra for these sampleswere obtained by microscopic techniques. They areslightly larger than the analyses given by BartonMines. No surface asperities were invoked in com-puting the theoretical spectra because microscopicexamination showed no need for sch a factor. Theoptical constants used as input parameters for thegarnet data were obtained by fitting the spectrum ofa large polished sample with a set of classical oscilla-tor parameters, using the Lorentz line shape, bywell-known techniques.' 5 The minor discrepancyobserved near 500 cm-' is thought to be caused by aslightly deficient set of dispersion parameters, sincean insufficient number of points were taken in thespectrum of the single crystal to resolve the smallfeature by least-squares analysis.

The experimental and theoretical spectra of twomixtures of quartz and corundum powders are shownin Fig. 14. Each mixture actually represents a mix-ture of four components since quartz and corundumare both uniaxial crystals so that two sets of opticalconstants are required to represent each of them. Inthese cases the experimental data were processedusing the measured sample temperatures instead ofapplying the usual Christiansen technique since thistechnique cannot be justified for the case ofmixtures. It is clear from the theoretical resultsshown in this figure that there is no frequency wherethe reflectance is very close to zero such as wouldoccur at the principal Christiansen frequency for apure sample. The experimental results can be seento confirm this theoretical conclusion. It is worthnoting that the reflectance is close to zero for both


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quartz and corundum individually even though theycan be regarded as birefringent mixtures. The rea-son is that the optical constants for the ordinary andextraordinary rays differ very little. We observethat the departure from zero reflectance is substan-tially greater for the finer particles. Thus arbitrarilysetting the lowest point in the spectrum of a mixtureat zero reflectance or unit emittance would make asubstantially greater error for the finer particle datathan for the coarser particle data. It is also quitesignificant that for the finer particle sample the low-est point in the spectrum occurs near 1160 cm-'.This corresponds to the Christiansen frequency ofneither component. Thus an identification tech-nique based on the principal Christiansen frequencywould fail for this mixture.

For both mixtures the shapes of the theoreticalspectra quite adequately represent the experimentaldata. While the general level of the theoreticalspectrum of the mixture of finer size powders is also

600 500 400 300Fig. 13. Comparison of theoreti-cal and experimental reflectance

of garnet powders.

600 500 400 300

in good agreement with the experimental spectrum,the same cannot be said for the spectrum of the mix-ture of coarse powders. Once again, we believe thisdiscrepancy is due to our use of a continuum modelrather than a discrete layer model.

It is worth noting, however, that for remote sens-ing applications where the problem is the inverse oneof determining mineral compositions from spectraldata, the general spectral level is much less impor-tant than the detailed structure of the spectral fea-tures.

The authors are indebted to E. M. Smith and P.C. von Thuna for assistance in the experimental pro-gram and to I. Simon for a number of helpful discus-sions. This work was supported in part by NASAunder contracts NAS 9-10875 and NAS 9-8396 (con-tract monitor, W. Mendell) and the Air Force undercontract F19628-C-0353 (contract monitor, T. Roo-ney).


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WAVE NUMBER, CM-1700

References

1. W. W. Coblentz, "Investigations of Inra-Red Spectra," Carne-gie Institution of Washington, 1905, reprinted by the CoblentzSociety, 1962.

2. R. A. Hanel, B. J. Conrath, W. A. Hovis, V. G. Kunde, P. D.Lowman, J. C. Pearl, C. Prabhakara, B. Schlachman, and G.Levin, Science 175, 305 (1972).

3. R. A. Hanel, B. J. Conrath, V. G. Kunde, C. Prabhakara, I.Revah, V. V. Salomonson, and G. Wolford, J. Geophys. Res.77, 2629 (1972).

4. J. R. Aronson, A. G. Emslie, and H. G. McLinden, Science152, 345 (1966).

5. R. J. P. Lyon, NASA CR100, Washington, D.C., 1965.

600 500 400 300Fig. 14. Comparison of the theo-retical and experimental reflec-tance of mixtures of quartz and

corundum.

600 500 400 300

6. W. A. Hovis, Jr., and W. R. Callahan, J. Opt. Soc. Am. 56,639 (1966).

7. G. R. Hunt and R. K. Vincent, J. Geophys Res. 73, 6039(1968).

8. A. G. Emslie, in Progress in Astronautics and Aeronautics(Academic Press, New York, 1966), Vol. 18, p. 281.

9. A. G. Emslie and J. R. Aronson, Appl. Opt. 12, 2563 (1973).10. 4. R. Aronson and A. G. Emslie, The Moon 5, 3 (1972).11. J. R. Aronson, A. G. Emslie, T. P. Rooney, I. Coleman, and

G. Horlick, Appl. Opt. 8, 1639 (1969).12. J. E. Conel, J. Geophys. Res. 74, 1614 (1969).13. A. S. Barker, Jr., Phys. Rev. 132, 1474 (1963).14. W. G. Spitzer and D. A. Kleinman, Phys. Rev. 121, 1324

(1961).15. H. W. Verleur, . Opt. Soc. Am. 58, 1356 (1968).


'uC.)z

-JU.wu

ExperimentalCorundum 120 p F = .22Quartz 170pM F = .33

-~--Corundum 10 1p F = .125Quartz 10p F = .125

'I_ ~~~~~~~~~~~~-

Wz

-JLUwJ

TheoreticalCorundum 120 p

- Coarse F (EIC) = .14 F EI[C) = .07Particle Quartz 170 pTheory F (EiC) = .20 F (ELIC) = .10

--- Corundum 10 pBridged F (EIC) = .08 F EIIC = .04Theory Quartz 10u

- F (EXC) = .08 F (EIIC) = .04

I \ IV-\

spectral reflectance and emittance of particulate ... · n = no + (e/r), (1) where no, the input...

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