When are spectral reflectance curves comparable?

ICARUS 49, 109-119 (1982)

When Are Spectral Reflectance Curves Comparable? JONATHAN GRADIE AND JOSEPH VEVERKA Laboratory for Planetary Studies, Cornell University, Ithaca, New York 14853 Received September 28, 1981; revised December 17, 1981 Spectral reflectance curves of flat laboratory samples of the carbonaceous chondrite Allende, a basalt, and the ordinary chondrite Bruderheim measured in a bidirectional geometry are shown to differ from those measured using an integrating sphere. In general, reflectance curves obtained by the bidirectional method are redder than those obtained with an integrating sphere. The degree of difference increases with increasing absolute reflectance. When spectral reflectance curves obtained by the two methods are compared to the reflectance curves expected for spherical and aspherical planets covered with the same materials, it is found that in general the integrating sphere measurements provide a better match to a planet at small phase angles. As the phase angle increases, bidirectional reflectance curves provide a closer match.

basalt. In this paper we use our extensive measurements on three materials of planeA basic problem in comparing laboratory tary interest--a basalt, a carbonaceous spectrophotometric measurements with tel- chondrite, and an ordinary chondrite--to escopic observations of solar system ob- address three specific questions: (1) How do the spectra of flat laboratory jects is that the two sets of measurements are commonly made under quite different samples measured in a bidirectional geomephotometric conditions. Often, laboratory try differ from those measured using an inmeasurements are made on a flat sample, at tegrating sphere? (2) How do such spectra compare with particular incidence and emission angles (i and ~). At the telescope the observation is those measured in the disk-integrated mode either that of the disk-integrated light (for for a spherical planet covered with the objects too small to be resolved ade- same material? (3) How does the shape of the planet quately), or of some portion of the illuminated disk for which the photometric geom- affect disk-integrated spectral measureetry may be quite different from that used in ments? A brief discussion of the third question the laboratory. Gradie et al. (1980) and Gradie and Veverka (198 la) have demonstrated has already been given by Gradie and that photometric geometry does affect the Veverka (198 lb). Our experimental method has been deshapes of spectral reflectance curves, sometimes, as in the case of sulfur, quite scribed by Gradie et al. (1980). In sumdramatically. This fact also follows from mary, the materials studied, a basalt (r, = theoretical considerations (e.g., Hapke, 0.22) from Gardener, Montana, the C3 car1981) when one recalls that the optical con- bonaceous chondrite Allende (rn -- 0.11), stants of the surface material must change and the ordinary chondrite L6 Bruderheim with wavelength unless the spectral (r, = 0.26), were ground in ceramic mortars and sieved to appropriate particle sizes. reflectance curve is flat. As an example, Fig. 1 illustrates the ef- The basalt and ordinary chondrite were fect of changing the incidence angle, and washed in methanol to remove adhering hence the phase angle (a), on the spectral micron grains and dust particles. All samreflectance of a flat sample of powdered ples were carefully leveled, then dusted I. INTRODUCTION

109 0019-1035/82/010109-11 $02.00/0 Copyright© 1982by AcademicPress,Inc. All rightsof reproductionin any formreserved.

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Wavelength (microns) FIG. 1. Bottom: The spectral reflectance o f basalt (particle size 45-75/~m) normalized at h = 0.55 /~m. I n c i d e n c e a n g l e , i = 4°; e m i s s i o n a n g l e , ~ = 0% a n d p h a s e angle ~x = 4 °. Top: R a t i o o f the n o r m a l i z e d s p e c t r a l r e f l e c t a n c e o f b a s a l t v i e w e d at t w o o t h e r a r b i t r a r y g e o m e t r i e s to the c u r v e at i = 4 °, ~ = 0 °, s h o w n at b o t t o m .

with a thin coating o f the same particle size. The three materials were chosen because they represent approximate analogs to the surfaces o f the Moon, C asteroids, and S asteroids, respectively. Measurements of the scattering properties between 0.4 and 1.2/xm were made over incidence and emission angles ranging from 0 to 60°, and phase angles from 0 to 120°.

Gradie et al. (1980) originally fitted their measurements with a lunar-like photometric law of the form Ix(i,~,a)

COS i = Ax • cos i + cos E fa(a) • Fx,

(1)

where Ix is the intensity of the scattered

COMPARING SPECTRAL REFLECTANCE CURVES light at wavelength h; Ax is a constant related to the absolute reflectance;fx(a) is a function which depends solely on the phase angle, or, and is a product of the singleparticle phase function and the shadowing function derived by Hapke (1963) and Irvine (1966); finally, 7rFx is the incident flux. T h e y found such an approach less than satisfactory, especially for the brighter samples, since the quantity //{cos i / ( c o s i + cos E)} does depend explicitly to some extent on the specific values o f / a n d ¢, and not simply on ot as demanded by Eq. (1). In a subsequent paper, Gradie and Veverka (1981b) showed that their measurements can be fit within the experimental error by any o f three more general photometric functions: recently proposed those of Bowell and L u m m e (1981), H a p k e (1981), and Goguen (1981). T h e y found that a function of the general type proposed by Bowell and L u m m e , Ix ~ A ~ [ l z o / ( I z

+

/xo)]fx(ot) + B~,/xo, (2)

where/~0 = cos i , / z = cos E, and Ax and B x are two constants which are independent of a, fits the available data almost as well as the functionally more complicated expressions derived by Hapke and by Goguen. It is this simpler form o f the photometric function which we will use in the present analysis. Comparable calculations have been carried out in a few cases using the more elaborate Hapke and Goguen types o f functions without altering the salient results in any significant way. II. CALCULATIONS Using our laboratory measurements to determine the constants that occur in Eq. (2) (see Gradie and Veverka, 1981a), we are in a position to calculate reflectance spectra for any arbitrary geometry within the range of measurements. The special cases considered are: (1) an integrating sphere measurement

111

for which i = 45 ° and the scattered light is gathered o v e r all emission angles; (2) a spherical body at an arbitrary phase angle; (3) an oblate spheroid at an arbitrary phase angle. The first case is of interest since many o f the spectral reflectance measurements in the laboratory have been made with an integrating sphere (cf. Nash and Fanale, 1977). The second case is intended to simulate typical telescopic observations for many solar system objects. The third case considers the situation where the object is elongated (see also Gradie and Veverka, 1981a,b). In our calculations we assume that each point on the object scatters the incident light according to Eq. (2). III. RESULTS The results o f our calculations, summarized in Figs. 2 through 4, are discussed in order of increasing normal reflectance at 0.55/zm (rn).

(a) Allende (rn = 0.11) The spectral reflectance from 0.4 to 1.2 /zm normalized at 0.55/xm o f a flat sample of the carbonaceous chondrite Allende (particle sizes < 7 5 / z m , observed at i = 4°, = 0°) is shown at the top o f Fig. 2a. Shown in the middle of the figure is the difference, A (in percent), between the normalized spectral reflectance calculated for the simulated integrating sphere measurement and the normalized spectral reflectance o f a flat sample near opposition (i = 0°, ~ = 4°). Equation (2), with the coefficients A~fx(a) and Bx of Gradie and Veverka (1981b), was used in the calculation. The differences between the integrating sphere and the bidirectional measurements are small for this relatively dark sample. H o w e v e r , as already noted by F r e n c h (1980) for samples o f powdered charcoal and montmorillonite, the measured spectral reflectance shortward of 0.5 /zm is redder for the bidirectional measurement than for one made with an integrating sphere.

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X ( microns ) FIc. 2a. Top: Normalized spectral reflectance (h = 0.55 /xm) of the C3 carbonaceous chondrite Allende (particle size <75/xm) observed at i = 4°, e = 0°, and phase angle = 4°. Middle: Percentage difference between the calculated normalized spectral reflectance from an integrating sphere and the normalized spectral reflectance of the flat sample observed bidirectionally at i = 4°, ~ = 0°, and phase angle = 4°. Bottom: Difference in percentage between the calculated normalized spectral reflectance of an Allende-covered spherical planet and the normalized spectral reflectance of the flat sample (i = 4°, = 0~) at three phase angles.

I n t h e l o w e r p o r t i o n o f Fig. 2a, the n o r malized spectral reflectance of a spherical p l a n e t c o v e r e d w i t h A l l e n d e m a t e r i a l is c o m p a r e d w i t h the b i d i r e c t i o n a l r e f l e c t a n c e o f t h e flat s a m p l e n e a r n o r m a l i n c i d e n c e a n d e m i s s i o n (Fig. 2a, top). A s the p h a s e angle i n c r e a s e s , t h e s p h e r i c a l p l a n e t bec o m e s r e d d e r , r e l a t i v e to the flat s a m p l e .

T h e t o p p o r t i o n o f Fig. 2b s h o w s this " p h a s e r e d d e n i n g " effect f o r a s p h e r i c a l planet compared with the measurement of the s p e c t r a l r e f l e c t a n c e w i t h an i n t e g r a t i n g s p h e r e . I n b o t h c a s e s , the effects a r e less t h a n 15% u p to p h a s e a n g l e s o f 60 °. T h e l o w e r h a l f o f Fig. 2b d e m o n s t r a t e s t h a t effects o f a s p h e r i c i t y o n s p e c t r a l

C O M P A R I N G S P E C T R A L R E F L E C T A N C E CURVES

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FIG. 2b. Top: Difference in percentage between the calculated normalized spectral reflectance of an Allende-covered planet and the calculated normalized spectral reflectance from an integrating sphere, at three phase angles. Middle: Difference in percentage between the normalized spectral reflectance of the broad side of an Allende-covered spheroid (axes B = C and A/B = 3) and the normalized spectral reflectance calculated for an Allende-covered spherical planet at three phase angles. Bottom: Difference in percentage between normalized spectral reflectance calculated for the end view of the spheroid and the spherical planet at three phase angles. reflectance are of minor importance for d a r k s a m p l e s . H e r e , t h e s p e c t r a l reflectance of an elongated spheroid (axes B = C, A / B = 3) v i e w e d s i d e - o n a n d e n d o n , r e s p e c t i v e l y , is c o m p a r e d w i t h t h a t o f a sphere. The variations are small and essentially phase independent. These trends are consistent with the fact that for Allende the c o e f f i c i e n t s B x a r e s m a l l c o m p a r e d to

Axfx(ot) in E q . (2) ( G r a d i e a n d V e v e r k a , 1981b).

(b) Basalt (r, = 0.22) The normalized spectral reflectance of a flat s a m p l e o f a s l i g h t l y o x i d i z e d b a s a l t ( s e e G r a d i e a n d V e v e r k a , 198 l a ) o b s e r v e d a t i = 4 °, ~ = 0 ° is s h o w n at t h e t o p o f Fig. 3a. T h e p a r t i c l e size is 4 5 - 7 5 m i c r o n s . S h o w n b e -

114

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low is the difference (A), in percent, between the normalized spectral reflectance calculated for an integrating sphere [using Eq. (2) and the coefficients ADex(ot) and Bx from Gradie and Veverka (1981b)] and the normalized spectral reflectance measured for the flat sample in the near-normal bidirectional geometry. The normalized reflectances for the bidirectional measurement are again redder than those calculated for the integrating

sphere. The total variation is 10% from 0.4 to 1.2/xm. In the bottom part of Fig. 3a the differences (A) between the reflectances calculated for a spherical planet relative to the fiat sample are compared at three different phase angles. The flat sample is redder than the spherical planet at very small phases, but the planet becomes redder than the flat sample by t~ = 30°. The differences are most pronounced in the parts of the spec-

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trum in which the reflectance changes most rapidly with wavelength, i.e., shortward of 0.6 ~m. The top half of Fig. 3b compares the spectral reflectance of the spherical planet at several different phase angles with the integrating sphere measurement. At small phase angles, the integrating sphere spectra and those of the spherical planet are almost identical. However, as the phase angle of the spherical planet increases, the planet becomes much redder than the integrating

sphere. The overall effect can be as much as 20% from 0.4 to 1.2 /xm at 60° phase. The effects of asphericity are illustrated in the lower portion of Fig. 3b. Here, the side view of a spheroid (axes A / B = 3, B = C) produces a spectral reflectance nearly identical to that of the sphere at all phase angles less than 60° . However, the spectral reflectance of the end of the spheroid shows differences of up to 7%; these differences decrease with increasing phase.

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GRADIE AND VEVERKA

(c) Bruderheim (r. = 0.26)

Two important effects are noticeable: (1) the normalized spectral reflectance of the flat sample is redder than that of the integrating sphere for wavelengths shortward of 0.7 p,m, and (2) the depth of the 0.95-/~m feature is deeper relative to the reflectance at 0.7/~m and narrower for the bidirectional than for the integrating sphere measurement. The first effect has already been noted for the other two samples, as well as by French (1980), who found that the spectral reflectance of powdered samples of

The spectral reflectance from 0.4 to 1.2 /~m normalized at 0.55/~m of a flat sample of the chondritic meteorite Bruderheim (particle size 45-75/zm, observed at i = 4°, = 0°) is shown at the top of Fig. 4a. Shown below is the difference, A (in percent), between the normalized spectral reflectance of the flat sample and the calculated normalized spectral reflectance expected for a measurement using an integrating sphere (i = 45°).

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COMPARING SPECTRAL REFLECTANCE

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depth and width of the 0.95-/~m absorption band, has not been noted previously, but is expected since as the reflectance changes with wavelength across this region the relative magnitude of the terms AxFx(t~) and Bx varies. The relative importance of B~ is largest at those wavelengths for which the reflectance is highest. In the lower part of Fig. 4a, the difference (A) is shown for the normalized spectral reflectance calculated for a spherical planet at three different phase angles compared with the normalized spectral reflectance

charcoal/montmorillonite mixtures obtained from a Cary 14 integrating sphere spectrophotometer was less reddened than a flat sample measured at i = 4°, ~ = 0% in the region shortward of 0.6 ~m. Since no difference was found for measurements of an essentially gray sample of powdered magnetite, French postulated that the effect was due to the wavelength dependence of the optical properties of the surface, a suggestion which is confirmed by our measurements. The second effect, the difference in the

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GRADIE AND VEVERKA

measured bidirectionally for the flat sample of Bruderheim. At 4° phase the flat sample is redder than the model planet for h < 0.7 /zm and the 0.95-/~m absorption feature is narrower and deeper for the flat sample. However, as the phase angle increases, the planet becomes redder than the flat sample at h < 0.7/~m. In Fig. 4b, the top graph shows the trends for the normalized spectral reflectances of a spherical planet compared with those measured by an integrating sphere. At small phase angles, i.e., - 4 °, the spherical planet and the integrating sphere show nearly identical spectra except that the spherical planet is slightly redder for wavelengths less than 0.7 /~m. However, as the phase angle increases, the spherical planet becomes much redder than the integrating sphere, and the 0.95-/~m band becomes deeper and narrower relative to the integrating sphere by factors that are twice those for the bidirectional case (above). We conclude that for materials as bright or brighter than Bruderheim (r n = 0.26 at 0.56 /~m), spectral reflectance curves obtained by normal reflectance methods are not equivalent to the spectral reflectance curves obtained by integrating spheres. While the integrating sphere can produce a spectral reflectance curve that matches that of a spherical planet more closely than a bidirectional measurement on a flat sample near opposition, the match becomes increasingly worse as the phase angle increases. In the lower part of Fig. 4b we compare the effects of asphericity on the spectral reflectance. The spectrum of a spheroid of dimensions B = C and A/B = 3 is compared in side view and end view with the spectrum of a spherical planet. The spectrum of the side view shows only slight differences from that of a sphere. But, as already noted by Gradie and Veverka (1981a), the end of the elongated object will show measurable spectral variations compared to a spherical planet. Still, the effects of asphericity are less than 5%, and small by comparison with

the differences between the spectra of the spherical planet and those measured by the integrating sphere. IV. DISCUSSION We have shown that different methods of obtaining laboratory reflectance spectra can produce slightly different results due to the fact that the photometric functions of materials are wavelength dependent. Such measurements can be compared rigorously with each other and with planetary observations only when these differences are taken into account. The material studied all have reflectances which increase from the blue to the red part of the visible spectrum. We find that bidirectional measurements at small phase angles produce spectral reflectance curves which are redder than those obtained with an integrating sphere. Our results also show that integrating sphere measurements provide a better match to the spectral reflectance curves of spherical planets at small phase angles (a ~< 15°) but that the bidirectional measurements yield a better comparison at large phase angles. Finally, we find that the differences between the spectra of spherical and nonspherical planets are small. The differences discussed in this paper become more significant as the absolute reflectance of the sample increases, and are especially noticeable in spectral intervals in which the reflectance changes significantly. For very dark materials, especially if their spectra tend to be flat, the effects will be small. For example, for Allende the integrating sphere measurements are very similar to those obtained in the bidirectional geometry. Either can be compared with planetary disk-integrated measurements once some allowance for phase reddening is made. Thus, it is unlikely that the effects discussed in this paper are very important in the context of the darker asteroids and satellites. On the other hand, for materials which are as bright as our Bruderheim sample the

COMPARING SPECTRAL REFLECTANCE CURVES effects are larger and more complex, especially if significant changes in spectral shape with wavelength are present. Noteworthy is the fact that the relative depth and width of absorption bands appear to depend on photometric geometry and hence are sensitive to the mode of measurement. For example, in Fig. 4a, the 0.95-~m band for Bruderheim is wider for the integrating sphere measurement than for the bidirectional one. We stress that the variations discussed here are not artifacts of the photometric function chosen to represent the data. The photometric functions described by Hapke (1981) and by Hapke and Wells (1981) imply differences in the spectral curves of materials measured by various laboratory methods, which are closely similar to those described in this paper. Similar differences were also found by French (1980) by comparing directly bidirectional and integrating sphere measurements. The differences in spectral reflectance curves described in this paper should be most pronounced for materials such as sulfur which display steep absorption features in conjunction with large variations in absolute reflectance (Gradie et al., 1980). For multiminerallic substances caution should be used when band depths or contrasts are analyzed for quantitative deductions about relative abundances of absorbers, since the depth depends upon a number of factors, including geometry.

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ACKNOWLEDGMENT This work was supported by NASA Grant NSG7606. REFERENCES BOWELL, E., AND K. LUMME (1981). Radiative trans-

fer in the surface of atmosphereless bodies. Astron. J., in press. FRENCH, L. M. (1980). Photometric Properties o f Carbonaceous Chondrites and Related Materials. Ph.D. thesis, Cornell University. GOGUEN, J. D. (1981). A Theoretical and Experimental Investigation o f the Photometric Functions o f Particulate Surfaces. Ph.D. thesis, Cornell University. GRADIE, J., J. VEVERKA, AND B. BURATTI (1980). The effects of scattering geometry on the spectrophotometric properties of powdered materials. Proc. Lunar Planet. Sci Conf. l lth, 799-815. GRADIE, J., J. VEVERKA (1981a). The effects of scattering geometry on spectral reflectance: Color lightcurves of asteroids (abstract). In Lunar and Planetary Science XII pp. 359-361. Lunar & Planetary Institute, Houston. GRADIE, J. AND J. VEVERKA (1981b). Effect of body shape on disk-integrated spectral reflectance. Proc. Lunar Planet. Sci. Conf. 12th, 1769-1779. HAI'KE, B. W. (1963). A theoretical photometric function for the lunar system. J. Geophys. Res. 68, 4571-4586. HAPKE, B. W. (1981). Bidirectional reflectance spectroscopy. J. Geophys. Res. 86, 3039-3054. HAPKE, B. W., AND E. WELLS (1981). Bidirectional reflectance spectroscopy. II. Experiments and observations. J. Geophys. Res. 86, 3055-3060. IRVlNE, W. M. (1966). The shadowing effect in diffuse reflectance. J. Geophys. Res. 71, 2931-2937. NASH, D. B., AND F. P. FANALE (1977). IO'S surface composition based on reflectance spectra of sulfur/salt mixtures and proton-irradiation experiments. Icarus 31, 40-80.