- Email: [email protected]
The Opposition Surge and Photopolarimetry of Fresh and Coated Basalts
Icarus 141, 172–178 (1999) Article ID icar.1999.6150, available online at http://www.idealibrary.com on
The Opposition Surge and Photopolarimetry of Fresh and Coated Basalts Michael K. Shepard Department of Geography and Earth Science, 400 East Second Street, Bloomsburg University, Bloomsburg, Pennsylvania 17815 E-mail: [email protected]
and Raymond E. Arvidson Department of Earth and Planetary Sciences, Campus Box 1169, One Brookings Drive, Washington University, St. Louis, Missouri 63130 Received July 30, 1998; revised February 9, 1999
We present polarization-phase curve measurements and analysis for three basalt samples: fresh, dark red varnished, and dark gray varnished. Each sample displays a prominent opposition surge, countering the widely held notion that only particulate surfaces, and not bare rock, will display this phenomenon. The most likely cause of the opposition surge is coherent backscattering, but the width of the surge suggests that other mechanisms may also contribute. The photopolarimetric properties of the samples, especially the negative branch parameters, are most comparable to those of C-class asteroids. °c 1999 Academic Press Key Words: photometry; polarimetry; surfaces, asteroids; regoliths; surfaces, planets.
INTRODUCTION
A photometric feature ubiquitous to nearly all Solar System objects is the opposition surge—the nonlinear brightening of an object as the phase angle of observation approaches 0◦ . The underlying physics of the phenomenon are not completely understood, and major hypotheses for its existence are (a) interparticle shadow hiding (cf. Hapke (1986) for a discussion and historical review), (b) coherent backscattering (Shkuratov 1988, Muinonen 1990, Hapke 1990, Mishchenko 1991), and (c) specular and/or retroreflections (two reflections) from crystalline or metallic phases (Trowbridge 1978). A combination of shadow hiding and coherent backscattering is currently favored to explain most or all opposition surge observations (Shkuratov and Muinonen 1992, Helfenstein et al. 1997, Hapke et al. 1998). In the models proposed, it is generally assumed that a particulate surface is required to generate an opposition surge, and the strength of the opposition surge is believed to be a function (in part) of regolith porosity. In the laboratory, porous low-density powders are observed to exhibit a stronger opposition effect than compacted powders, and it is widely believed that solid surfaces will not exhibit any significant opposition effect. For example, 172 0019-1035/99 $30.00 c 1999 by Academic Press Copyright ° All rights of reproduction in any form reserved.
the lack of an opposition surge on some darker asteroids, e.g., the Trojan asteroid 1173 Anchises (French 1987) and 3694 Sharon (Dahlgren et al. 1998), has led to suggestions that these objects may lack a regolith and instead consist of a coherent, solid surface (French et al. 1989), or alternatively that their surfaces are smoother than average (Dahlgren et al. 1998). Recently, we measured the polarization-phase curves of fresh and coated basalt in the laboratory. The original intent of those measurements was to investigate the general scattering characteristics, and in particular, the specular reflection characteristics of desert-varnished basalt for comparison with rocks at the Viking Lander sites (Guinness et al. 1997). Quite unexpectedly, these samples displayed prominent opposition effects. We have since learned that a similar observation was reported in the past (Pieters et al. 1990). Below, we report our observations with a brief analysis and discuss the implications for the geologic interpretation of asteroid photometry. 2. OBSERVATIONS
2.1. Samples All of the samples measured in this study consist of basalt from the Pisgah volcanic field in California. The samples are discussed at some length in Guinness et al. (1997), and we summarize here. There are three samples: one coated with a “typical” dark desert-varnish which we refer to here as “dark gray varnish” (DGV); one coated with oxidized clays formed by direct contact with eolian derived sediments, referred to here as “dark red varnish” (DRV); and one sample cut with a rock saw to expose fresh, unweathered basalt (FCB). In general, the samples are competent and contain minimal quantities of vesicles or visible pores (<10% by surface area). Each of the samples were cut into a convenient size for measurement, rinsed in water, and dried. No other preparation or modification of the surface took place. After their scattering characteristics were measured, each sample was sliced to obtain
173
OPPOSITION SURGE AND PHOTOPOLARIMETRY
thin sections for inspection and study of their respective coatings. Sketches of photomicrograph cross sections are shown in Fig. 1a for each sample. Scanning electron micrographs of the DGV and DRV surface coatings were also acquired (Figs. 1b and 1c). These were taken from the same rock samples (although not at the exact location of the thin sections) and were cleaned of surface debris using only compressed air. 2.2. Opposition Surge Figure 2 illustrates the photometric behavior of all three samples. The incidence angle (angle from nadir) for the source (a tungsten lamp) was set and maintained at 30◦ , while the emission angle was varied from +60◦ (forward) to −60◦ (back), in 10◦ intervals. All observations were made in the solar principal plane. From emission angles −25◦ to −35◦ (phase angles −5◦ to +5◦ ), the emission angle was varied in 1◦ intervals (no observation was made at −30◦ ). All observations were made in red light (0.69 µm) and in linear polarizations both perpendicular and parallel to the scattering plane. Radiance factors for all observations were made by normalizing to a spectrahalon sample illuminated at 0◦ and observed at 5◦ . Errors in the measurements were estimated to be 5% relative and 15% absolute. We made a number of measurements at different incidence angles, and these display the same trends and behaviors observed in Fig. 2. Two major photometric features of these samples are worth noting. First, there is a strong specular (quasi-specular for DGV) reflection from two of the three samples (FCB and DGV), evident from the ratio of the reflectance observed in perpendicular polarization to that observed in parallel polarization (the FCB sample had a strong specular component because portions of the surface were polished when cut by the rock saw). This feature was discussed at some length in Guinness et al. (1997). Additionally, there is a significant opposition surge observed from each sample. Guinness et al. (1997) fit the average reflectance (radiance factor) of each sample to a combined Hapke (1981, 1984, 1986) and Fresnel reflection model (Shepard et al. 1993). Their best estimates of the single scattering albedo, w, and opposition surge height, B0 , and width, h, are given in Table I. 2.3. Photopolarimetry To investigate the opposition surge further, we utilized the data collected to generate polarization-phase curves for each sample,
seen in Fig. 3. The polarization, P, was calculated from ¶ rperp − rparallel . P = 100 rperp − rparallel µ
(1)
Where duplicate phase angles were available (e.g., 5◦ on either side of opposition), we averaged the radiance factors prior to calculating the polarization. We are unaware of any systematic polarization (sometimes referred to as parasitic polarization) in the instrument which might lead to errors in the radiance factors, r . However, any systematic errors that might exist in r should be significantly reduced in P by the division in Eq. (1). Figure 4 illustrates the common characteristics of polarization-phase curves: (1) the negative branch which displays a minimum, Pmin at phase angle gmin ; (2) a cross-over or inversion phase angle, g0 , where P goes from negative to positive; (3) a maximum polarization, Pmax , at gmax ; and (4) the ascending slope of the positive branch of polarization, s. (Unfortunately, the commonly used symbol for polarization slope, h, is the same symbol as used by Hapke (1986) for the opposition surge width. We therefore use s here to differentiate between the two parameters.) The polarization-phase parameters (except Pmax and gmax ) for our samples are listed in Table I. Although a general theory of polarization-phase behavior is lacking, numerous laboratory studies have empirically demonstrated that these parameters are related to surface albedo and texture (Dollfus and Geake 1977, Zellner et al. 1977a,b, Geake et al. 1984). For example, it has been observed that there is an inverse correlation between the surface albedo and slope in laboratory samples. This is one of the more valuable relationships discovered and is widely used to estimate the absolute albedos of asteroids and, from these, their diameters (cf., Dollfus et al. 1989). 3. DISCUSSION
3.1. Opposition Surge Based on the observations illustrated in Fig. 2, the widely held notion that only regoliths or very porous substances display an opposition surge must be questioned. As evident from Fig. 1, these surfaces are solid and coherent rock surfaces or essentially solid, amorphous coatings. The electron micrographs reveal
TABLE I Opposition and Surge Polarization Parameters of Our Samples Sample
w
B0
h
Pmin (%)
gmin
g0
s (%/◦ )
DGV DRV FCB
0.42 ± 0.01 0.56 ± 0.01 0.40 ± 0.01
1.36 ± 0.12 0.75 ± 0.10 1.41 ± 0.13
0.04 ± 0.01 0.03 ± 0.01 0.04 ± 0.01
−1.7 ± 0.02 −1.7 ± 0.02 −2.1 ± 0.02
7 ± 2◦ 3 ± 1◦ 7 ± 3◦
20 ± 2◦ 18 ± 2◦ 21 ± 2◦
0.7 ± 0.05 0.2 ± 0.05 0.7 ± 0.05
Note. Values and uncertainties of w, B0 , and h are from Guinness et al. (1997). Uncertainties in Pmin are propagated errors assuming a 5% (relative) uncertainty in radiance factor. All other polarization uncertainties are estimates of the most likely range.
FIG. 1. (a) Cross-section sketches of photomicrographs for dark gray varnish (DGV), dark red varnish (DRV), and fresh cut basalt (FCB). The dark and light stippled areas are varnish coatings on two of the samples. Note lithic and mineral fragments in the varnish (after Guinness et al. 1997). (b) Electron photomicrograph of DGV, bar scale is 5 µm. Note the evidence of defoliation and micrometer scale fragments. (c) Electron photomicrograph of DRV, bar scale is 5 µm. Note the rugged nature of the surface (compare with 1a). 174
OPPOSITION SURGE AND PHOTOPOLARIMETRY
175
rugged landscapes at the micrometer scale and there is evidence of defoliation on the DGV. However, these surfaces are clearly not regoliths. It is also evident that smooth surfaces may exhibit an opposition surge—two of these surfaces (FCB and DGV) were smooth enough to display specular or quasi-specular behavior. This contrasts with the observations of Pieters et al. (1990), who observed an opposition surge from a roughened basalt sample, but none from a smooth basalt sample and none from roughened or smooth obsidian samples. Below we briefly discuss the possible mechanisms for the observed behavior. 3.1.1. Specular or retro-reflections. Because at least two samples (FCB and DGV) have significant specular or quasispecular reflections, we cannot rule out the possibility that these might contribute to the observed opposition surge. Indeed, the micrometer-scale foliation on DGV may favor the development of corner or retroreflectors. However, near opposition we expect Fresnel reflectance coefficients of only ∼0.04 if we use the indices of refraction deduced by Guinness et al. (1997). Additionally, if the “facets” contributing to the surge are distributed (as expected) with a preference to slopes clustered about a horizontal mean, we would expect a weaker opposition surge at large incidence angles than at small incidence angles (fewer facets to contribute when i = 60◦ than when i = 30◦ ). Although we have not illustrated the data acquired at other incidence angles in this paper, such a dependence is not observed in our data. Therefore, we conclude that retro-reflections are, at best, only a weak possible contributor to the observed opposition surge in our samples.
FIG. 2. Radiance factor versus emission angle for each sample. Samples were illuminated at an incidence angle of −30◦ (negative emission angles indicate backscatter geometry, positive emission angles indicate forward scattering.) Circles are measurements made in perpendicular polarization, squares are parallel polarization, and the solid line is the average radiance factor. Note the strong opposition surge seen in each sample. Also note the strong quasi-specular and specular lobes in DGV and FCB, respectively, as evident from the large perpendicular to parallel polarization ratio.
3.1.2. Interparticle shadow hiding. Shadow hiding requires the existence of structure much larger than the scale of the wavelength to cast shadows. As opposition is approached, the shadows of such structures become hidden by the structures themselves, and the surface brightens nonlinearly. Inspection of the fresh basalt (FCB) under a stereomicroscope revealed numerous microscopic pores that may have been responsible for some of the opposition surge in that sample. However, in the other two samples, the coatings on the surface filled in these pores. The photomicrographs of DGV and especially DRV (Fig. 1) show rough surface structure at the 1- to 100-µm scale which may contribute to a shadow hiding surge. However, photometric models which include roughness effects [such as Hapke 1984] reveal that surface roughness alone is not sufficient to create sharp shadow hiding surges, even at unrealistically high roughness values. In addition, the presence of strong specular and quasispecular peaks from DGV and FCB argue against significant surface roughness at scales larger than a few tens of micrometers. Electron photomicrographs of DGV at scales of tens to hundreds of micrometers confirm this. Despite the arguments outlined above, the width of the opposition surge and negative branch (∼20◦ to 30◦ ) are more consistent with a shadow-hiding mechanism than coherent backscatter (Hapke et al. 1998). Therefore, if shadow-hiding is responsible for any of the observed opposition surge, then it must be
176
SHEPARD AND ARVIDSON
FIG. 3. Polarization-phase curve for dark gray varnish, dark red varnish, and fresh cut basalt (top to bottom). Plots on the right are enlargements of those on the left to highlight the negative polarization branch.
OPPOSITION SURGE AND PHOTOPOLARIMETRY
FIG. 4. Illustration of “typical” polarization-phase curve behavior and associated parameters commonly measured and reported.
occurring interior to the surface. The dense basalt and coatings examined here consist of discrete mineral grains, voids, and other discontinuities interspersed in a matrix. Each component has different optical properties, and the matrix may be viewed as an analog to the interstitial vacuum of a regolith. Therefore, it may be possible for some variant on the traditional shadow hiding mechanism to occur in these samples. 3.1.3. Coherent backscatter. Coherent backscatter is essentially a multiple scattering phenomenon, in which two photons take exactly the same path, but in opposite directions, from source to receiver. Their mutual constructive interference near opposition is responsible for the observed nonlinear brightening. Any medium interspersed with refractive index discontinuities, such as our samples, should display the phenomenon. It is therefore likely that coherent backscatter plays a major role in these samples. Coherent backscattering is frequently associated with volume scattering; however, it is also possible for micrometer-scale structures on the surface to cause this effect (McGurn 1990). This latter mechanism is especially feasible for DGV because of its numerous micrometer scale surface structures. The only significant argument against coherent backscatter in these samples is that the width of the opposition surge (∼20◦ to 30◦ ) is much larger than expected and typically observed. Although widths of this size do not preclude coherent backscattering, they suggest that another mechanism is also present, e.g., shadow-hiding. (Hapke et al. 1998). 3.2. Polarimetric Behavior The results of the polarimetric analysis are intriguing. Figure 5, a standard Pmin versus g0 plot, compares our samples to samples measured in a laboratory and to observed asteroids. Area I on the plot encompasses the parameter range observed
177
from bare siliceous rocks, Area II encompasses observations of fine-grained regoliths and powders displaying “fairy castle” structures, and Area III is where most asteroids, dust covered lunar rocks, and coarsely crushed rock samples are observed (Dollfus et al. 1989). All of our samples lie in Area III, not in Area I where they might be expected, and are most comparable in polarimetric attributes to C-class asteroids despite their relatively high single scattering albedos (all samples are significantly brighter in red light than perceived by the eye). Interestingly, the fresh basalt has the most negative value of Pmin in our sample set, and is comparable to the most negative values ever measured. If confirmed, these observations suggest some interesting implications for studies of asteroid regoliths. It is frequently argued that the presence of most asteroids in Area III is evidence for a coarse-grained regolith, i.e., an absence of fines and associated fairy castle structures observed on the Moon, or for bare rock lightly coated with dust (cf. Dollfus et al. 1977, 1989). In our samples, however, we see evidence that fresh or coated rock may mimic these behaviors. While we are not suggesting that these are possible analog surficial materials for asteroids, we do suggest that surface textures other than a coarse-grained regolith, or bare rock covered by a thin layer of fines may be possible. There are several points of caution to note, however. A possible contributor to the strong negative branch is volume scattering. It has been demonstrated that light escaping from an optically smooth surface will be negatively polarized near opposition because of the preference for parallel polarized light to be transmitted out of the surface (cf. Hapke 1993). It is also
FIG. 5. Plot of Pmin versus g0 (cross-over polarization). Areas I, II, and III are where solid rocks, fines, and asteroids tend to plot, respectively. The cross-hatched region, labeled “S-class,” demarcates the approximate boundary for most S-class asteroids, and the hatched region, labeled “C-class,” covers the approximate boundary for C-class asteroids. Our samples are labeled F (FCB), G (DGV), and R (DRV) and fall within Area III and the C-class asteroid region (after Dollfus et al. 1989).
178
SHEPARD AND ARVIDSON
possible that a slight (but unobserved) tilt of the samples caused a shift in both Pmin and g0 (Shkuratov, pers. commun.). Both volume scattering and an unaccounted surface tilt would also lead to nonzero polarization when extrapolated to zero phase— something observed in DRV and FCB. Another feature of interest is the magnitude of Pmax approached in our data (Fig. 3). Both DGV and FCB show extremely high values of P at large phase angles (40–50%), a factor of four or more times larger than expected from particulate surfaces (∼10%). This is likely caused by the strong component of specular reflection observed from these surfaces. This hypothesis could be tested by repeating the measurements out of the principal plane, where specular reflections are of less importance (this was not possible on the instrument used for these measurements). The DRV sample, which did not display a significant specular component, approaches a Pmax value more comparable to particulate surfaces. 4. CONCLUSIONS
Dollfus, A., M. Wolff, J. E. Geake, D. F. Lupishko, and L. M. Dougherty 1989. Photopolarimetry of asteroids. In Asteroids II (R. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 594–616. Univ. of Arizona Press, Tucson. French, L. M. 1987. Rotational properties of four L5 Trojan asteroids from CCD photometry. Icarus 72, 325–341. French, L. M., F. Vilas, W. K. Hartmann, and D. J. Tholen 1989. Distant asteroids and Chiron. In Asteroids II (R. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 468–486. Univ. of Arizona Press, Tucson. Geake, J. E., M. Geake, and B. Zellner 1984. Experiments to test theoretical models of the polarization of light by rough surfaces. Mon. Not. R. Astron. Soc. 210, 89–112. Guinness, E. A., R. E. Arvidson, I. H. D. Clark, and M. K. Shepard 1997. Optical scattering properties of terrestrial varnished basalts compared with rocks and soils at the Viking Lander Sites. J. Geophys. Res. 102, 28687–28703. Hapke, B. 1981. Bidirectional reflectance spectroscopy. 1. Theory. J. Geophys. Res. 86, 3039–3054. Hapke, B. 1984. Bidirectional reflectance spectroscopy. 3. Correction for macroscopic roughness. Icarus 59, 41–59. Hapke, B. 1986. Bidirectional reflectance spectroscopy. 4. The extinction coefficient and the opposition effect. Icarus 67, 264–280. Hapke, B. 1993. Theory of Reflectance and Emittance Spectroscopy. Cambridge Univ. Press, Cambridge, UK.
Based on these observations, the existence of a strong opposition surge is not sufficient evidence to infer the presence of a regolith. Conversely, the absence of a surge (as for 1173 Anchises or 3694 Sharon) should not be used to infer the absence of a regolith, and other mechanisms for this phenomenon need to be explored (cf. French et al. (1989) for a discussion of some other possibilities). Coherent backscatter is the most likely cause of the observed opposition surge; however, we suggest that some variant on the traditional shadow-hiding mechanism may also contribute. Finally, a preliminary analysis suggests that the polarimetric negative branch and associated parameters of our samples are similar to those of C-class asteroids.
Hapke, B., R. Nelson, and W. Smythe 1993. The opposition effect on the Moon: The contribution of coherent backscatter. Science 260, 509–511. Hapke, B., R. Nelson, and W. Smythe 1998. The opposition effect on the Moon: Coherent backscatter and shadow hiding. Icarus 133, 89–97. Helfenstein, P., J. Veverka, and J. Hillier 1997. The lunar opposition effect: A test of alternative models. Icarus 128, 2–14.
ACKNOWLEDGMENTS
Pieters, C., Y. Shkuratov, and D. Stankevich 1990. Character of the opposition effect and the negative polarization. Bull. Am. Astron. Soc. 22, 1033–1034.
This work was supported by PG&G Grant NAG5-4000 (MKS) and NAGW3870 to R.E.A. B. Hapke (University of Pittsburgh) graciously allowed us access to his goniometer for this work. We thank D. Kremser for rapidly acquiring the electron photomicrographs. B. Campbell provided helpful comments during the preparation of the manuscript, and excellent reviews were provided by B. Hapke, J. Goguen, and Y. Shkuratov.
Shepard, M. K., R. E. Arvidson, and E. A. Guinness 1993. Specular scattering on a terrestrial playa and implications for planetary surface studies. J. Geophys. Res. 98, 18707–18718.
REFERENCES Dahlgren, M., J. F. Lahulla, C.-I. Lagerkvist, J. Lagerrow, S. Mottola, A. Erikson, and M. Gonano-Beurer 1998. A study of Hilda asteroids. V. Lightcurves of 47 Hilda asteroids. Icarus 133, 247–285. Dollfus, A., and J. E. Geake 1977. Polarimetric and photometric studies of lunar samples. Phil. Trans. R. Soc. London 285, 397–402. Dollfus, A., J. E. Geake, J. C. Mandeville, and B. Zellner 1977. The nature of the asteroid surfaces, from optical polarimetry. In Comets, Asteroids, Meteorites (A. H. Delsemme, Ed.), pp. 243–261. Univ. of Toledo Press, Toledo.
McGurn, A. R. 1990. Enhanced retroreflectance effects in the reflection of light from randomly rough surfaces. Surf. Sci. Rep. 10, 357–410. Mishchenko, M. I. 1991. Polarization effects in weak localization of light: Calculation of the copolarized and depolarized backscattering enhancement. Phys. Rev. B. 44, 12597–12600. Muinonen, K. 1990. Light Scattering by Inhomogeneous Media: Backward Enhancement and Reversal of Linear Polarization. Ph.D. dissertation, University of Helsinki, Finland.
Shkuratov, Y. 1988. Diffractional model of the brightness surge of complex structure surfaces. Kin. Phys. Celest. Bodies 4, 33–39. Shkuratov, Y., and K. Muinonen 1992. Interpreting asteroid photometry and polarimetry using a model of shadowing and coherent backscattering. In Asteroids, Comets, Meteors (A. W. Harris and E. Bowell, Eds.), pp. 549– 552. LPI, Houston, TX. Trowbridge, T. 1978. Retroreflection from rough surfaces. J. Opt. Soc. Am. 68, 1225–1242. Zellner, B., M. Leake, T. Le Bertre, M. Duseaux, and A. Dollfus 1977a. The asteroid albedo scale. I. Laboratory polarimetry of meteorites. Proc. Lunar Sci. Conf. 8th, 1091–1100. Zellner, B., T. Le Bertre, and K. Day 1977b. The asteroid albedo scale. II. Laboratory polarimetry of dark carbon-bearing silicates. Proc. Lunar Sci. Conf. 8th, 1111–1117.
The Opposition Surge and Photopolarimetry of Fresh and Coated Basalts Michael K. Shepard Department of Geography and Earth Science, 400 East Second Street, Bloomsburg University, Bloomsburg, Pennsylvania 17815 E-mail: [email protected]
and Raymond E. Arvidson Department of Earth and Planetary Sciences, Campus Box 1169, One Brookings Drive, Washington University, St. Louis, Missouri 63130 Received July 30, 1998; revised February 9, 1999
We present polarization-phase curve measurements and analysis for three basalt samples: fresh, dark red varnished, and dark gray varnished. Each sample displays a prominent opposition surge, countering the widely held notion that only particulate surfaces, and not bare rock, will display this phenomenon. The most likely cause of the opposition surge is coherent backscattering, but the width of the surge suggests that other mechanisms may also contribute. The photopolarimetric properties of the samples, especially the negative branch parameters, are most comparable to those of C-class asteroids. °c 1999 Academic Press Key Words: photometry; polarimetry; surfaces, asteroids; regoliths; surfaces, planets.
INTRODUCTION
A photometric feature ubiquitous to nearly all Solar System objects is the opposition surge—the nonlinear brightening of an object as the phase angle of observation approaches 0◦ . The underlying physics of the phenomenon are not completely understood, and major hypotheses for its existence are (a) interparticle shadow hiding (cf. Hapke (1986) for a discussion and historical review), (b) coherent backscattering (Shkuratov 1988, Muinonen 1990, Hapke 1990, Mishchenko 1991), and (c) specular and/or retroreflections (two reflections) from crystalline or metallic phases (Trowbridge 1978). A combination of shadow hiding and coherent backscattering is currently favored to explain most or all opposition surge observations (Shkuratov and Muinonen 1992, Helfenstein et al. 1997, Hapke et al. 1998). In the models proposed, it is generally assumed that a particulate surface is required to generate an opposition surge, and the strength of the opposition surge is believed to be a function (in part) of regolith porosity. In the laboratory, porous low-density powders are observed to exhibit a stronger opposition effect than compacted powders, and it is widely believed that solid surfaces will not exhibit any significant opposition effect. For example, 172 0019-1035/99 $30.00 c 1999 by Academic Press Copyright ° All rights of reproduction in any form reserved.
the lack of an opposition surge on some darker asteroids, e.g., the Trojan asteroid 1173 Anchises (French 1987) and 3694 Sharon (Dahlgren et al. 1998), has led to suggestions that these objects may lack a regolith and instead consist of a coherent, solid surface (French et al. 1989), or alternatively that their surfaces are smoother than average (Dahlgren et al. 1998). Recently, we measured the polarization-phase curves of fresh and coated basalt in the laboratory. The original intent of those measurements was to investigate the general scattering characteristics, and in particular, the specular reflection characteristics of desert-varnished basalt for comparison with rocks at the Viking Lander sites (Guinness et al. 1997). Quite unexpectedly, these samples displayed prominent opposition effects. We have since learned that a similar observation was reported in the past (Pieters et al. 1990). Below, we report our observations with a brief analysis and discuss the implications for the geologic interpretation of asteroid photometry. 2. OBSERVATIONS
2.1. Samples All of the samples measured in this study consist of basalt from the Pisgah volcanic field in California. The samples are discussed at some length in Guinness et al. (1997), and we summarize here. There are three samples: one coated with a “typical” dark desert-varnish which we refer to here as “dark gray varnish” (DGV); one coated with oxidized clays formed by direct contact with eolian derived sediments, referred to here as “dark red varnish” (DRV); and one sample cut with a rock saw to expose fresh, unweathered basalt (FCB). In general, the samples are competent and contain minimal quantities of vesicles or visible pores (<10% by surface area). Each of the samples were cut into a convenient size for measurement, rinsed in water, and dried. No other preparation or modification of the surface took place. After their scattering characteristics were measured, each sample was sliced to obtain
173
OPPOSITION SURGE AND PHOTOPOLARIMETRY
thin sections for inspection and study of their respective coatings. Sketches of photomicrograph cross sections are shown in Fig. 1a for each sample. Scanning electron micrographs of the DGV and DRV surface coatings were also acquired (Figs. 1b and 1c). These were taken from the same rock samples (although not at the exact location of the thin sections) and were cleaned of surface debris using only compressed air. 2.2. Opposition Surge Figure 2 illustrates the photometric behavior of all three samples. The incidence angle (angle from nadir) for the source (a tungsten lamp) was set and maintained at 30◦ , while the emission angle was varied from +60◦ (forward) to −60◦ (back), in 10◦ intervals. All observations were made in the solar principal plane. From emission angles −25◦ to −35◦ (phase angles −5◦ to +5◦ ), the emission angle was varied in 1◦ intervals (no observation was made at −30◦ ). All observations were made in red light (0.69 µm) and in linear polarizations both perpendicular and parallel to the scattering plane. Radiance factors for all observations were made by normalizing to a spectrahalon sample illuminated at 0◦ and observed at 5◦ . Errors in the measurements were estimated to be 5% relative and 15% absolute. We made a number of measurements at different incidence angles, and these display the same trends and behaviors observed in Fig. 2. Two major photometric features of these samples are worth noting. First, there is a strong specular (quasi-specular for DGV) reflection from two of the three samples (FCB and DGV), evident from the ratio of the reflectance observed in perpendicular polarization to that observed in parallel polarization (the FCB sample had a strong specular component because portions of the surface were polished when cut by the rock saw). This feature was discussed at some length in Guinness et al. (1997). Additionally, there is a significant opposition surge observed from each sample. Guinness et al. (1997) fit the average reflectance (radiance factor) of each sample to a combined Hapke (1981, 1984, 1986) and Fresnel reflection model (Shepard et al. 1993). Their best estimates of the single scattering albedo, w, and opposition surge height, B0 , and width, h, are given in Table I. 2.3. Photopolarimetry To investigate the opposition surge further, we utilized the data collected to generate polarization-phase curves for each sample,
seen in Fig. 3. The polarization, P, was calculated from ¶ rperp − rparallel . P = 100 rperp − rparallel µ
(1)
Where duplicate phase angles were available (e.g., 5◦ on either side of opposition), we averaged the radiance factors prior to calculating the polarization. We are unaware of any systematic polarization (sometimes referred to as parasitic polarization) in the instrument which might lead to errors in the radiance factors, r . However, any systematic errors that might exist in r should be significantly reduced in P by the division in Eq. (1). Figure 4 illustrates the common characteristics of polarization-phase curves: (1) the negative branch which displays a minimum, Pmin at phase angle gmin ; (2) a cross-over or inversion phase angle, g0 , where P goes from negative to positive; (3) a maximum polarization, Pmax , at gmax ; and (4) the ascending slope of the positive branch of polarization, s. (Unfortunately, the commonly used symbol for polarization slope, h, is the same symbol as used by Hapke (1986) for the opposition surge width. We therefore use s here to differentiate between the two parameters.) The polarization-phase parameters (except Pmax and gmax ) for our samples are listed in Table I. Although a general theory of polarization-phase behavior is lacking, numerous laboratory studies have empirically demonstrated that these parameters are related to surface albedo and texture (Dollfus and Geake 1977, Zellner et al. 1977a,b, Geake et al. 1984). For example, it has been observed that there is an inverse correlation between the surface albedo and slope in laboratory samples. This is one of the more valuable relationships discovered and is widely used to estimate the absolute albedos of asteroids and, from these, their diameters (cf., Dollfus et al. 1989). 3. DISCUSSION
3.1. Opposition Surge Based on the observations illustrated in Fig. 2, the widely held notion that only regoliths or very porous substances display an opposition surge must be questioned. As evident from Fig. 1, these surfaces are solid and coherent rock surfaces or essentially solid, amorphous coatings. The electron micrographs reveal
TABLE I Opposition and Surge Polarization Parameters of Our Samples Sample
w
B0
h
Pmin (%)
gmin
g0
s (%/◦ )
DGV DRV FCB
0.42 ± 0.01 0.56 ± 0.01 0.40 ± 0.01
1.36 ± 0.12 0.75 ± 0.10 1.41 ± 0.13
0.04 ± 0.01 0.03 ± 0.01 0.04 ± 0.01
−1.7 ± 0.02 −1.7 ± 0.02 −2.1 ± 0.02
7 ± 2◦ 3 ± 1◦ 7 ± 3◦
20 ± 2◦ 18 ± 2◦ 21 ± 2◦
0.7 ± 0.05 0.2 ± 0.05 0.7 ± 0.05
Note. Values and uncertainties of w, B0 , and h are from Guinness et al. (1997). Uncertainties in Pmin are propagated errors assuming a 5% (relative) uncertainty in radiance factor. All other polarization uncertainties are estimates of the most likely range.
FIG. 1. (a) Cross-section sketches of photomicrographs for dark gray varnish (DGV), dark red varnish (DRV), and fresh cut basalt (FCB). The dark and light stippled areas are varnish coatings on two of the samples. Note lithic and mineral fragments in the varnish (after Guinness et al. 1997). (b) Electron photomicrograph of DGV, bar scale is 5 µm. Note the evidence of defoliation and micrometer scale fragments. (c) Electron photomicrograph of DRV, bar scale is 5 µm. Note the rugged nature of the surface (compare with 1a). 174
OPPOSITION SURGE AND PHOTOPOLARIMETRY
175
rugged landscapes at the micrometer scale and there is evidence of defoliation on the DGV. However, these surfaces are clearly not regoliths. It is also evident that smooth surfaces may exhibit an opposition surge—two of these surfaces (FCB and DGV) were smooth enough to display specular or quasi-specular behavior. This contrasts with the observations of Pieters et al. (1990), who observed an opposition surge from a roughened basalt sample, but none from a smooth basalt sample and none from roughened or smooth obsidian samples. Below we briefly discuss the possible mechanisms for the observed behavior. 3.1.1. Specular or retro-reflections. Because at least two samples (FCB and DGV) have significant specular or quasispecular reflections, we cannot rule out the possibility that these might contribute to the observed opposition surge. Indeed, the micrometer-scale foliation on DGV may favor the development of corner or retroreflectors. However, near opposition we expect Fresnel reflectance coefficients of only ∼0.04 if we use the indices of refraction deduced by Guinness et al. (1997). Additionally, if the “facets” contributing to the surge are distributed (as expected) with a preference to slopes clustered about a horizontal mean, we would expect a weaker opposition surge at large incidence angles than at small incidence angles (fewer facets to contribute when i = 60◦ than when i = 30◦ ). Although we have not illustrated the data acquired at other incidence angles in this paper, such a dependence is not observed in our data. Therefore, we conclude that retro-reflections are, at best, only a weak possible contributor to the observed opposition surge in our samples.
FIG. 2. Radiance factor versus emission angle for each sample. Samples were illuminated at an incidence angle of −30◦ (negative emission angles indicate backscatter geometry, positive emission angles indicate forward scattering.) Circles are measurements made in perpendicular polarization, squares are parallel polarization, and the solid line is the average radiance factor. Note the strong opposition surge seen in each sample. Also note the strong quasi-specular and specular lobes in DGV and FCB, respectively, as evident from the large perpendicular to parallel polarization ratio.
3.1.2. Interparticle shadow hiding. Shadow hiding requires the existence of structure much larger than the scale of the wavelength to cast shadows. As opposition is approached, the shadows of such structures become hidden by the structures themselves, and the surface brightens nonlinearly. Inspection of the fresh basalt (FCB) under a stereomicroscope revealed numerous microscopic pores that may have been responsible for some of the opposition surge in that sample. However, in the other two samples, the coatings on the surface filled in these pores. The photomicrographs of DGV and especially DRV (Fig. 1) show rough surface structure at the 1- to 100-µm scale which may contribute to a shadow hiding surge. However, photometric models which include roughness effects [such as Hapke 1984] reveal that surface roughness alone is not sufficient to create sharp shadow hiding surges, even at unrealistically high roughness values. In addition, the presence of strong specular and quasispecular peaks from DGV and FCB argue against significant surface roughness at scales larger than a few tens of micrometers. Electron photomicrographs of DGV at scales of tens to hundreds of micrometers confirm this. Despite the arguments outlined above, the width of the opposition surge and negative branch (∼20◦ to 30◦ ) are more consistent with a shadow-hiding mechanism than coherent backscatter (Hapke et al. 1998). Therefore, if shadow-hiding is responsible for any of the observed opposition surge, then it must be
176
SHEPARD AND ARVIDSON
FIG. 3. Polarization-phase curve for dark gray varnish, dark red varnish, and fresh cut basalt (top to bottom). Plots on the right are enlargements of those on the left to highlight the negative polarization branch.
OPPOSITION SURGE AND PHOTOPOLARIMETRY
FIG. 4. Illustration of “typical” polarization-phase curve behavior and associated parameters commonly measured and reported.
occurring interior to the surface. The dense basalt and coatings examined here consist of discrete mineral grains, voids, and other discontinuities interspersed in a matrix. Each component has different optical properties, and the matrix may be viewed as an analog to the interstitial vacuum of a regolith. Therefore, it may be possible for some variant on the traditional shadow hiding mechanism to occur in these samples. 3.1.3. Coherent backscatter. Coherent backscatter is essentially a multiple scattering phenomenon, in which two photons take exactly the same path, but in opposite directions, from source to receiver. Their mutual constructive interference near opposition is responsible for the observed nonlinear brightening. Any medium interspersed with refractive index discontinuities, such as our samples, should display the phenomenon. It is therefore likely that coherent backscatter plays a major role in these samples. Coherent backscattering is frequently associated with volume scattering; however, it is also possible for micrometer-scale structures on the surface to cause this effect (McGurn 1990). This latter mechanism is especially feasible for DGV because of its numerous micrometer scale surface structures. The only significant argument against coherent backscatter in these samples is that the width of the opposition surge (∼20◦ to 30◦ ) is much larger than expected and typically observed. Although widths of this size do not preclude coherent backscattering, they suggest that another mechanism is also present, e.g., shadow-hiding. (Hapke et al. 1998). 3.2. Polarimetric Behavior The results of the polarimetric analysis are intriguing. Figure 5, a standard Pmin versus g0 plot, compares our samples to samples measured in a laboratory and to observed asteroids. Area I on the plot encompasses the parameter range observed
177
from bare siliceous rocks, Area II encompasses observations of fine-grained regoliths and powders displaying “fairy castle” structures, and Area III is where most asteroids, dust covered lunar rocks, and coarsely crushed rock samples are observed (Dollfus et al. 1989). All of our samples lie in Area III, not in Area I where they might be expected, and are most comparable in polarimetric attributes to C-class asteroids despite their relatively high single scattering albedos (all samples are significantly brighter in red light than perceived by the eye). Interestingly, the fresh basalt has the most negative value of Pmin in our sample set, and is comparable to the most negative values ever measured. If confirmed, these observations suggest some interesting implications for studies of asteroid regoliths. It is frequently argued that the presence of most asteroids in Area III is evidence for a coarse-grained regolith, i.e., an absence of fines and associated fairy castle structures observed on the Moon, or for bare rock lightly coated with dust (cf. Dollfus et al. 1977, 1989). In our samples, however, we see evidence that fresh or coated rock may mimic these behaviors. While we are not suggesting that these are possible analog surficial materials for asteroids, we do suggest that surface textures other than a coarse-grained regolith, or bare rock covered by a thin layer of fines may be possible. There are several points of caution to note, however. A possible contributor to the strong negative branch is volume scattering. It has been demonstrated that light escaping from an optically smooth surface will be negatively polarized near opposition because of the preference for parallel polarized light to be transmitted out of the surface (cf. Hapke 1993). It is also
FIG. 5. Plot of Pmin versus g0 (cross-over polarization). Areas I, II, and III are where solid rocks, fines, and asteroids tend to plot, respectively. The cross-hatched region, labeled “S-class,” demarcates the approximate boundary for most S-class asteroids, and the hatched region, labeled “C-class,” covers the approximate boundary for C-class asteroids. Our samples are labeled F (FCB), G (DGV), and R (DRV) and fall within Area III and the C-class asteroid region (after Dollfus et al. 1989).
178
SHEPARD AND ARVIDSON
possible that a slight (but unobserved) tilt of the samples caused a shift in both Pmin and g0 (Shkuratov, pers. commun.). Both volume scattering and an unaccounted surface tilt would also lead to nonzero polarization when extrapolated to zero phase— something observed in DRV and FCB. Another feature of interest is the magnitude of Pmax approached in our data (Fig. 3). Both DGV and FCB show extremely high values of P at large phase angles (40–50%), a factor of four or more times larger than expected from particulate surfaces (∼10%). This is likely caused by the strong component of specular reflection observed from these surfaces. This hypothesis could be tested by repeating the measurements out of the principal plane, where specular reflections are of less importance (this was not possible on the instrument used for these measurements). The DRV sample, which did not display a significant specular component, approaches a Pmax value more comparable to particulate surfaces. 4. CONCLUSIONS
Dollfus, A., M. Wolff, J. E. Geake, D. F. Lupishko, and L. M. Dougherty 1989. Photopolarimetry of asteroids. In Asteroids II (R. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 594–616. Univ. of Arizona Press, Tucson. French, L. M. 1987. Rotational properties of four L5 Trojan asteroids from CCD photometry. Icarus 72, 325–341. French, L. M., F. Vilas, W. K. Hartmann, and D. J. Tholen 1989. Distant asteroids and Chiron. In Asteroids II (R. Binzel, T. Gehrels, and M. S. Matthews, Eds.), pp. 468–486. Univ. of Arizona Press, Tucson. Geake, J. E., M. Geake, and B. Zellner 1984. Experiments to test theoretical models of the polarization of light by rough surfaces. Mon. Not. R. Astron. Soc. 210, 89–112. Guinness, E. A., R. E. Arvidson, I. H. D. Clark, and M. K. Shepard 1997. Optical scattering properties of terrestrial varnished basalts compared with rocks and soils at the Viking Lander Sites. J. Geophys. Res. 102, 28687–28703. Hapke, B. 1981. Bidirectional reflectance spectroscopy. 1. Theory. J. Geophys. Res. 86, 3039–3054. Hapke, B. 1984. Bidirectional reflectance spectroscopy. 3. Correction for macroscopic roughness. Icarus 59, 41–59. Hapke, B. 1986. Bidirectional reflectance spectroscopy. 4. The extinction coefficient and the opposition effect. Icarus 67, 264–280. Hapke, B. 1993. Theory of Reflectance and Emittance Spectroscopy. Cambridge Univ. Press, Cambridge, UK.
Based on these observations, the existence of a strong opposition surge is not sufficient evidence to infer the presence of a regolith. Conversely, the absence of a surge (as for 1173 Anchises or 3694 Sharon) should not be used to infer the absence of a regolith, and other mechanisms for this phenomenon need to be explored (cf. French et al. (1989) for a discussion of some other possibilities). Coherent backscatter is the most likely cause of the observed opposition surge; however, we suggest that some variant on the traditional shadow-hiding mechanism may also contribute. Finally, a preliminary analysis suggests that the polarimetric negative branch and associated parameters of our samples are similar to those of C-class asteroids.
Hapke, B., R. Nelson, and W. Smythe 1993. The opposition effect on the Moon: The contribution of coherent backscatter. Science 260, 509–511. Hapke, B., R. Nelson, and W. Smythe 1998. The opposition effect on the Moon: Coherent backscatter and shadow hiding. Icarus 133, 89–97. Helfenstein, P., J. Veverka, and J. Hillier 1997. The lunar opposition effect: A test of alternative models. Icarus 128, 2–14.
ACKNOWLEDGMENTS
Pieters, C., Y. Shkuratov, and D. Stankevich 1990. Character of the opposition effect and the negative polarization. Bull. Am. Astron. Soc. 22, 1033–1034.
This work was supported by PG&G Grant NAG5-4000 (MKS) and NAGW3870 to R.E.A. B. Hapke (University of Pittsburgh) graciously allowed us access to his goniometer for this work. We thank D. Kremser for rapidly acquiring the electron photomicrographs. B. Campbell provided helpful comments during the preparation of the manuscript, and excellent reviews were provided by B. Hapke, J. Goguen, and Y. Shkuratov.
Shepard, M. K., R. E. Arvidson, and E. A. Guinness 1993. Specular scattering on a terrestrial playa and implications for planetary surface studies. J. Geophys. Res. 98, 18707–18718.
REFERENCES Dahlgren, M., J. F. Lahulla, C.-I. Lagerkvist, J. Lagerrow, S. Mottola, A. Erikson, and M. Gonano-Beurer 1998. A study of Hilda asteroids. V. Lightcurves of 47 Hilda asteroids. Icarus 133, 247–285. Dollfus, A., and J. E. Geake 1977. Polarimetric and photometric studies of lunar samples. Phil. Trans. R. Soc. London 285, 397–402. Dollfus, A., J. E. Geake, J. C. Mandeville, and B. Zellner 1977. The nature of the asteroid surfaces, from optical polarimetry. In Comets, Asteroids, Meteorites (A. H. Delsemme, Ed.), pp. 243–261. Univ. of Toledo Press, Toledo.
McGurn, A. R. 1990. Enhanced retroreflectance effects in the reflection of light from randomly rough surfaces. Surf. Sci. Rep. 10, 357–410. Mishchenko, M. I. 1991. Polarization effects in weak localization of light: Calculation of the copolarized and depolarized backscattering enhancement. Phys. Rev. B. 44, 12597–12600. Muinonen, K. 1990. Light Scattering by Inhomogeneous Media: Backward Enhancement and Reversal of Linear Polarization. Ph.D. dissertation, University of Helsinki, Finland.
Shkuratov, Y. 1988. Diffractional model of the brightness surge of complex structure surfaces. Kin. Phys. Celest. Bodies 4, 33–39. Shkuratov, Y., and K. Muinonen 1992. Interpreting asteroid photometry and polarimetry using a model of shadowing and coherent backscattering. In Asteroids, Comets, Meteors (A. W. Harris and E. Bowell, Eds.), pp. 549– 552. LPI, Houston, TX. Trowbridge, T. 1978. Retroreflection from rough surfaces. J. Opt. Soc. Am. 68, 1225–1242. Zellner, B., M. Leake, T. Le Bertre, M. Duseaux, and A. Dollfus 1977a. The asteroid albedo scale. I. Laboratory polarimetry of meteorites. Proc. Lunar Sci. Conf. 8th, 1091–1100. Zellner, B., T. Le Bertre, and K. Day 1977b. The asteroid albedo scale. II. Laboratory polarimetry of dark carbon-bearing silicates. Proc. Lunar Sci. Conf. 8th, 1111–1117.