The Opposition Effect: Laboratory Studies Compared to Theoretical Models R

Lunar and Planetary Science XXXIII (2002) 1816.pdf

THE OPPOSITION EFFECT: LABORATORY STUDIES COMPARED TO THEORETICAL MODELS R. M. Nelson1. B. W. Hapke2, W. D. Smythe1, A. S. Hale1, J. L. Piatek2, 1 Jet Propulsion Labotatory, MS 183-501, 4800 Oak Grove Drive, Pasadena CA 91109, [email protected], 2Department of Geology and Planetary Science, 321 OEH, University of Pittsburgh, Pittsburgh PA 15260.

Introduction: A pronounced non-linear intensity in- 0.68, 0.57 and 0.07 for the Al2O3, diamond, SiC and crease in the reflectance phase curve with decreasing B4C respectively. A detailed description of the ex- phase angle, θ, has long been observed in solar system perimental procedure is found in our earlier publica- bodies and in laboratory investigations of the angular tions [12]. The only change from our earlier procedures scattering properties of particulate media[1]. The size was that a ½ wave plate was used to rotate the linear and shape of the phase curve, and the change in linear polarization of the incident beam rather than polarizing polarization with θ, have been related to the physical material. This increased the intensity of the incident properties of planetary regolith scattering materials beam. The samples were presented with light that was [e.g. 2,3]. This ‘opposition surge’ in is attributed to polarized in and perpendicular to the scattering plane. two distinct processes. One is the elimination of shad- A quarter wave plate was inserted into the optical train ows mutually cast between the regolith grains as the at appropriate places to permit the samples to be pre- phase angle decreases. This is called the shadow hiding sented with both senses of circular polarization. The opposition effect (SHOE)[4]. The other is coherent scattered beam was analyzed in both senses of linear constructive interference between rays of light travel- and circular polarization. In this study we combined the ing along identical but opposite paths in multiply scat- data from all of the polarization configurations. We tering media. This is called the coherent backscattering show these as integrated phase curves. opposition effect (CBOE). [5,6,7,8]. The Results: The integrated phase curves are shown Measurements of the angular scattering properties of in Figure 1. The phase curves (normalized at 5o) all planetary regolith materials and particulate ensembles exhibit an increase in reflectance as phase angle de- simulating planetary regoliths provide useful tests of creases. Of particular relevance to this research is the the theoretical models [9,10,11,12]. These investigations of regolith simulants form a very important link with laboratory studies of CBOE involving particles in liquid suspension which are often done by researchers in non-astronomical disciplines for model development and verification [e.g. 13,14, 15]. We report the results of an investigation into the opposition surge of particulate materials of the same par- ticle size and packing density but of differing reflectance. Some models suggest that as the materials become more absorbing the shape of the phase curve should become more rounded near 0o[ 13, 16]. For the materials studied we find that the phase curve exhibits increasing slope with decreasing phase angle down to the angular limit of our measurement. It becomes more Figure 1. The phase curves of Al2O3 ,SiC, B4C sharply peaked and does not become rounded. This is and diamond powders. All three continually in- true regardless of reflectance. crease as phase angle gets smaller. The Experiment: The measurements were made on change in the phase curve as θ approaches 0o. There- the long arm goniometer at NASA’s Jet Propulsion fore, we have calculated the slope (change between two Laboratory. The phase angle studied varied from 0.05 adjacent points) of the phase curves shown in Figure 1. to 5o. Four particulate samples of aluminum oxide, We show the result in Figure 2. diamond, silicon carbide, and boron carbide were pre- Discussion: The results shown above differ from angu- sented with linearly and circularly polarized coherent lar scattering investigations of polystyrene spheres in light from a laser of wavelength 0.633 µm. The sam- liquid suspension. The suspension cases show the ples differed widely in reflectance and were of similar phase curves to increase in slope as θ decreases near 0o diameter (22-24 µm). They were uncompressed (~75% for cases where the liquid suspending the spheres is void space). The reflectance of each sample measured transparent. However, these studies find that as the at 5o phase angle relative to Spectralon was 0.92, liquid suspending the polystyrene spheres becomes

Lunar and Planetary Science XXXIII (2002) 1816.pdf

COHERENT BACKSCATTER: EXPERIMENTS AND THEORY: R. M. Nelson et al.

more absorbing, the phase curves becomes less peaked We note that the Akkermans model assumes perfectly (or more rounded) [14,15]. Theoretical models of reflecting spheres but the authors of the model suggest CBOE predict that the phase curves will become more that the peak is expected to be more rounded as the rounded as the medium becomes more absorb- medium becomes more absorbing. Our results with ing[13,14,15,16,17]. This is inconsistent with our re- B4C, which has very low normal reflectance, find that sults (see Figs 1 and 2). this is not the case. Furthermore, we have previously published phase curves of eight lunar soils of low reflectance and these do not show rounding near 0o[19]. We note furthermore that the Shkuratov and Helfen- stein model predicts that the strength of the CBOE in- duced enhancedment decreases with decreaseing parti-

cle single scattering albedo ϖo.This is not observed in this study because SiC and diamond both have lower

reflectence (and hence lower ϖo) than A2O3 yet they have stronger opposition surges. We suggest that parti- cle shape may have significance along with reflectance on the contribution of CBOE to the reflectance phase curve. Lastly, we suggest that spherical particles in liquid suspension are not good analogues for planetary regoliths. Conclusion: Our measurements of powdered materials, including lunar regolith samples, do not agree with current models of coherent backscatter, which predict a rounding and truncation of the opposition effect peak near zero phase. This lack of rounding is consistent Figure 2. The slope of the phase curves in Figure with the hypothesis that very long light paths contribute 1. The slope of the phase curves for all three mate- to the CBOE of particulate materials including plane- rials continues to increase as phase angle gets tary rgoliths. smaller. Each is displaced by 0.01 on y axis Acknowledgement: This work was performed at NASA’s JPL under a grant from NASA’s Planetary Theoretical models of the CBOE and SHOE opposition Geology and Geophysics program. surges model the intensity as a function of θ. Shkura- References: [1] T. Gehrels, Astrrophys. J. 123, 331-338 tov and Helfenstein model CBOE with an expression in (1956). [2] B. W. Hapke, J. Geophys Res. 68, 4571-4586 terms of 1/(1+z2)1/2 [18] where z= kθ; Akkermans and (1963). [3] J. E. Geake. M. Geake, and B. Zellner, Mon. Not. coworkers use an expression of the form (1+((1-e- R. Astron. Soc. 210, 89-112 (1984). [4] B. W. Hapke, J. z)/z))/2(1+z2). These are plotted for the case k=1 in Geophys, Res. 86, 3039-3054 (1981). [5] Yu. Shkuratov, Soviet Astron. 27, 581-583 (1983). [6] B. W. Hapke, Icarus Figure 3. For comparison we show Hapke’s SHOE 88, 407-417 (1990).[7] K. Muinonen PhD. Thesis, Univer- expression which is of the form 1/(1+z). sity of Helsinki (1990). [8] M. I. Mishchenko, Astrophys. Space Sci. 194, 327-333 (1992). [9] B. W. Hapke, R. M. Nelson and W. D. Smythe, Science 260, 509-511 (1993). [10] R. M. Nelson, B. W. Hapke, W. D. Smythe and L. J. Horn, Icarus 131, 223-230 (1998). [11] Yu. G. Shkuratov, D. G. Stankevich, A. A. Ovcharenko, and V. V. Korokhin, Solar System Res., 31, 50-63 (1997). [12]R. M. Nelson, B. W. Hapke, W. D. Smythe, and L. J. Spilker, Icarus 147, 545-558 (2000). [13] E. Akkermans, P. E. Wolf, and R. Maynard, Phys. Rev. Let 56, 1471-1474 (1986). [14] M. P. van Al-

bada, M. B. van der Mark, and Ad Lagendijk, Phys. Rev. Let. 58, 361-364 (1987) [15] P. E. Wolf, G. Maret, E. Ak- kermans and R. Maynard, J. Phys. France 49, 63-75 (1988). [16] Yu. Shkuratov and A. A. Ovcharenko, “Solar System Res. 12, 315-326 (1998). [17] V. D. Ozrin, Physics Let A 162, 341-345 (1992). [18] Yu. Shkuratov and P. Helfenstein, Figure 3. Theoretical models which have been used to Icarus, 152,96-116(2001), [19] B. W. Hapke, Robert M. interpret the reflectance phase curve. We do not ob- Nelson and William D. Smythe, Icarus, 133, 89-97 (1998). serve a rounding of the phase curve near zero degrees in our laboratory measurements.