ICARUS 133, 89–97 (1998) ARTICLE NO. IS985907

The Opposition Effect of the : Coherent Backscatter and Shadow Hiding

Bruce Hapke Department of Geology and Planetary Science, University of Pittsburgh, Pittsburgh, Pennsylvania 15260 E-mail: [email protected]

and

Robert Nelson and William Smythe Jet Propulsion Laboratory, Pasadena, California 91109

Received July 23, 1997; revised January 22, 1998

opposition effect.) However, another process, coherent The electromagnetic scattering properties of backscatter, that causes an opposition effect has recently are commonly interpreted using the lunar as gained widespread attention in several scientific fields a prototype. Hence, a thorough understanding of the reflectance (Watson 1969; Kravtsov and Saichev 1982; Kuga and Ishi- of lunar soil is essential to remote sensing planetary studies. maru 1984; Van Albada and Lagendijk 1985). In this phe- We have measured the linearly and circularly polarized re- nomenon portions of waves traveling in opposite directions flectances of samples of lunar soil in order to better understand along multiply scattered paths within a nonuniform me- the nature of the lunar opposition effect. Several independent dium interfere constructively with each other to cause a observations show that the zero-phase peak is caused by both peak at zero phase. It has been suggested by several per- shadow hiding and coherent backscatter in roughly equal sons (including Kuga and Ishimaru 1984; Shkuratov 1988; amounts. Any radiative transfer model for planetary regoliths must take this dual nature into account. The transport mean Muinonen 1990; Hapke 1990; Mishchenko and Dlugach free path for photons in the lunar regolith is about 1 ␮m, which 1992) that this phenomenon may contribute to the opposi- is much smaller than the mean particle size.  1998 Academic Press tion effect of solar system bodies. Hapke et al. (1993) mea- sured the reflectances of Apollo lunar soil samples in circu- larly polarized light and showed that coherent backscatter INTRODUCTION is a major contributor to the lunar opposition effect. The opposition effect is an important tool in remote The opposition effect is the narrow peak in the intensity sensing and contains information about such quantities as of light scattered from a particulate medium directly back porosity and transport mean free path for photons in the in the direction toward the source. It is a nearly ubiquitous soil. Every solar system object whose surface can be seen phenomenon which is exhibited by media as diverse as and whose photometric function has been measured at soils, frosts, and vegetation canopies (Hapke et al. 1996). small phase angles exhibits the phenomenon. However, It has been known for over a century, having first been the moon is the only body (besides the ) for which observed in the light received from the rings of by we possess samples of regolith, and properties of the rego- Seeliger (1895), and was first observed for the moon by liths of other objects are commonly interpreted in terms Gehrels et al. (1964). The brightness of any area on the of a lunar model. Both shadow hiding and coherent back- lunar surface increases by nearly 40% between about one scatter are viable mechanisms for producing an opposition day before and the time of full moon. effect. Hence, it is important both for the interpretation During most of the time since its discovery the opposi- of planetary remote sensing measurements and for the tion effect has been interpreted as being caused by shadow construction of improved models of light scattering by hiding, in which particles of a medium cast shadows that planetary regoliths to understand whether or not both pro- are partly visible at all times except near astronomical cesses are operating and the role of each. opposition, when each particle hides its own shadow. (See Recently, Buratti et al. (1996) and Helfenstein et al. Hapke, 1986 for a recent treatment of the shadow hiding (1997) analyzed Clementine and telescopic lunar data. Bur-

89 0019-1035/98 $25.00 Copyright  1998 by Academic Press All rights of reproduction in any form reserved. 90 HAPKE, NELSON, AND SMYTHE

TABLE I The sample was illuminated vertically, and the detector Opposition Peak Angular Widths could be moved to view the sample from zenith angles of 1Њ to 65Њ for the short arm instrument and from 0.2Њ to 5Њ Sample Normal Reverse-helicity Same-helicity number albedoa HWHM (Њ) HWHM (Њ) for the long arm. In this configuration, the g is equal to the viewing angle e. Background noise was 10084 0.078 4.3 1.4 minimized by placing a narrow band transmission filter in 15041 0.094 8.3 2.7 front of the detector and also by chopping the incident 15271 0.128 5.2 1.7 beam and measuring the signal with a synchronous de- 15601 0.102 8.9 1.5 61221 0.375 12.1 3.0 tector. 65701 0.153 7.4 2.3 Linear polarizers and quarter wave plates could be 75121 0.083 4.1 1.5 placed between the source and sample and between the 79221 0.084 14.4 3.6 sample and detector, allowing the sample to be illuminated Averages 8.1 2.2 and viewed with orthogonal senses of both linearly and circularly polarized light. The observing procedure used a In red light (633 nm). was to fix the detector position and measure the intensity in all eight configurations of polarizers and quarter wave plates before moving on to the next detector angle. atti et al. concluded that shadow hiding was the dominant A fixed area about 3 mm in diameter was illuminated mechanism; however, the data cited to support this conclu- on the sample surface, while the detector viewed a sion can be interpreted in other ways. In particular, the much larger area. The surface was horizontal, while the photometric differences between the highland and maria scattering plane was tilted by a fraction of a degree from support coherent backscatter. Helfenstein et al. concluded the vertical to insure that no specularly reflected light that both processes contribute to the opposition effect of reached the detector. When a stationary sample was the moon. However, this conclusion does not have as illuminated the usual laser speckle pattern due to con- strong an observational basis as one would like because it structive and destructive interference of light scattered rests rather critically on one data point. In this paper we along different paths within the material was observed report further results of laboratory measurements on lunar (Kaveh et al. 1986). Hence, the sample was continuously samples that greatly strengthen and illuminate the conclu- rotated about its central vertical axis in order to average sion of Helfenstein et al. out this speckle pattern. The main source of noise in the instrument is random laser drift of about Ϯ2% on DESCRIPTION OF SAMPLES AND INSTRUMENTS a time scale of minutes.

The same eight lunar soil samples described in our previ- THEORETICAL REMARKS ous paper (Hapke et al. 1993) were used in this study (Table I). They include mature and immature soils from the maria As an aid to understanding the results of the tests carried and highlands. The samples were prepared for measure- out on the lunar samples, the processes that occur in light ment by gently pouring them from a height of about one scattering by a particulate medium will be reviewed. The cm into a circular cup about 2.5 cm in diameter by 0.5 cm reflectance is made up of the sum of light that has been deep. If necessary, a sample was gently shaken to even out scattered only once by a particle and light scattered be- its thickness but, in order to mimic its natural condition tween two or more particles. In a low material on the lunar surface as closely as practical, its surface was the reflectance is dominated by single scattering, while not pressed or scraped in any way. multiple scattering becomes progressively more important The samples were studied using two instruments, a short as the albedo increases. The shadow hiding opposition arm and a long arm goniometric photopolarimeter, both effect (SHOE) is caused almost entirely by radiation scat- housed in the Goniometric Laboratory at the Jet Propul- tered once, multiply scattered light serving only to fill in sion Laboratory. The light source on the short arm instru- the particle shadows. However, the coherent backscatter ment was either a Cd laser at 442 nm (blue) or a He–Ne opposition effect (CBOE) is due to the multiply scat- laser at 633 nm (red); only the He–Ne laser was used on tered component. the long arm instrument. The detector was a solid state The opposition effect is concerned with light scattered photodiode with sensitive surface about 1 mm in diameter. backwards in the general direction of the source. If the On the short arm instrument the source and detector were particles of the medium are comparable or smaller than 33 cm from the sample, so that the detector subtended an the wavelength, they scatter approximately like polarizable angle of 0.17Њ from the sample. On the long arm instrument dipoles. If linearly polarized light is incident on a medium the corresponding length was 228 cm and the angle 0.025Њ. of such particles, a single backscattering event tends to LUNAR OPPOSITION EFFECT 91 preserve the direction of polarization, but multiple scatter- where ␭ is the wavelength, b is a constant whose empirical ings randomize, or depolarize, this direction. If the incident value is 0.36, and L is the transport mean free path for light is circularly polarized, the handedness, or helicity, of photons in the medium. The usual equation for L in the the incident light is reversed upon being backscattered radiative transfer literature is once, but is preserved if the light is scattered into the Ϫ1 Ϫ1 forward hemisphere. L ϭ [n␴Qs(1 Ϫ ͗cos ␪͘)] ϭ [n␴wQE(1 Ϫ ͗cos ␪͘)] , (2) If the particles of the medium are larger than the wave- length a single backscattering occurs either by specular where n is the number of particles per unit volume, ␴ is reflection from the first surface of the particle, or by specu- the mean particle geometrical cross section, Qs is the mean lar internal reflection from the far surface, or by scattering scattering efficiency, QE is the mean extinction efficiency, from internal imperfections. All three processes tend to w ϭ Qs/QE is the mean single scattering albedo and ͗cos preserve the direction of incident linear polarization, but ␪͘ is the average cosine of the scattering angle. It should reverse the helicity of incident circular polarization. Light be noted that w may vary with wavelength. is forward scattered by either refraction and transmission If a medium is illuminated and observed in linearly po- through the particle or by diffraction around it, both of larized light whose electric vector is parallel to the scatter- which tend to preserve the direction of incident linear ing plane, the resulting CBOE peak is wider than if the polarization and the helicity of incident circular polariza- electric vector is perpendicular to the scattering plane (Van tion. Multiple scatterings tend to randomize the senses of Albada et al. 1987). Thus, if the incident irradiance is unpo- linear and circular polarization. However, the randomiza- larized, CBOE will be accompanied by a narrow branch tion takes place by rotation of the electric vector, to which of negative polarization (Shkuratov 1989; Muinonen 1990; the linearly polarized light is much more sensitive than the Mishchenko 1993), which is sometimes referred to as the circularly polarized. Hence, the randomization takes many ‘‘polarization opposition effect.’’ Detailed discussions of more scatterings for circularly polarized light than for lin- the phenomen