The Opposition Effect of the Moon: The Contribution of Coherent Backscatter

Hapke, Bruce; Nelson, Robert M.; Smythe, W. D.

doi:10.1126/science.260.5107.509

Cited by 190 publications

(161 citation statements)

References 27 publications

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“…The very few measurements of the relative importance of shadow hiding and coherent backscatter for terrestrial vegetated surfaces suggest that while shadow hiding dominates for most plants and clumpy moist soils, coherent backscatter can dominate for finely structured plants such as moss and for fine dry soils [Hapke et al, 1996]. Laboratory studies indicate that coherent backscatter generates a peak of width less than 0.5°varying proportionally to wavelength [Hapke et al, 1993]. The present paper reports half widths larger than 1°and roughly spectrally neutral, which do support the idea that shadow hiding mechanism is prevalent on terrestrial surfaces.…”

Section: Coherent Backscattermentioning

confidence: 99%

“…However, processes at all scales from a wave-length to a pixel can potentially influence an angular reflectance signature. Coherent backscatter is a wavelength-scale hot spot mechanism that is important for lunar soil and other barren solar system surfaces [Hapke et al, 1993]. The very few measurements of the relative importance of shadow hiding and coherent backscatter for terrestrial vegetated surfaces suggest that while shadow hiding dominates for most plants and clumpy moist soils, coherent backscatter can dominate for finely structured plants such as moss and for fine dry soils [Hapke et al, 1996].…”

Section: Coherent Backscattermentioning

confidence: 99%

“…Those shadows are visible at large phase angles (the angle between the Sun and view directions), but at zero phase angle they are hidden by the particles that cast them. Coherent backscatter is another physical cause of enhancement of reflectance in the hot spot direction [Kuga and Ishimaru, 1984;Hapke et al, 1993]. It is based on the fact that portions of wave fronts that are multiply scattered within a nonuniform medium and follow the same path, but in opposite directions, combine constructively at zero phase angle.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of hot spot directional signatures measured from space

Bréon

2002

J. Geophys. Res.

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[1] Reflectance measurements from the spaceborne Polarization and Directionality of Earth Reflectances (POLDER) instrument are used to analyze the so-called hot spot directional signature in the backscattering direction. The hot spot is measured with an angular resolution better than half a degree using the directional capabilities of the radiometer, with some assumptions on the spatial homogeneity of the surface. The analysis yields the first quantitative observation of the hot spot signature of vegetated surfaces, with such angular resolution. The measurements show that the hot spot reflectance is a function of the phase angle x rather than a function of a parameter Á, often used in hot spot modeling, that quantifies the horizontal distance between Sun and view directions. The observed directional signature is very accurately fitted by a linear ratio of the phase angle, as predicted by a simple theory of radiative transfer within the canopy foliage. Most of the measured hot spot half widths are between 1°and 2°. Some dispersion occurs for the cases belonging to the forest and desert International Geosphere-Biosphere Program (IGBP) classes, in the range 1°to 5°. Theory predicts that the width is independent of wavelength. Our measurements indicate that the widths at 670 and 865 nm are very close, but with a significant scatter in regards to the rather small variability. The distribution of the width as a function of the IGBP surface classification shows a variability within the classes that is larger than between the classes, except for the ''evergreen broadleaf'' class. The hot spot reflectance amplitude is generally on the order of 0.10-0.20 at 865 nm and 0.03-0.18 at 670 nm, although the full range of values is wider. For thick canopies, it may be interpreted in terms of foliage element (leaf ) reflectance. Retrieved values are on the order of 0.4 in the near infrared and in the range 0.05-0.20 at 670 nm. At 440 nm, the amplitude of the signature is very small, as is expected from the small surface reflectance. This confirms that the atmospheric contribution to the reflectance increase at the backscattering direction is negligible.

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Section: Coherent Backscattermentioning

confidence: 99%

Section: Coherent Backscattermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Analysis of hot spot directional signatures measured from space

Bréon

2002

J. Geophys. Res.

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“…Most important for determining (λ, a) are the albedo and polarization measurements for the reflection from several Apollo lunar soil samples by Hapke et al (1993Hapke et al ( , 1998. They illuminated eight samples under an inclination of five degrees (to avoid specular reflection) with 100% polarized blue and red light and measured the ratio of I ⊥ /I for phase angles 1…”

Section: A Correction For the Depolarization Due To Backscattering Atmentioning

confidence: 99%

Measurement of the earthshine polarization in theB, V, R, andIbands as function of phase

Bazzon

Schmid

Gisler

2013

A&A

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Context. Earth-like, extrasolar planets may soon become observable with upcoming high contrast polarimeters. Therefore, the characterization of the polarimetric properties of the planet Earth is important for interpreting expected observations and planning of future instruments. Aims. Benchmark values for the polarization signal of integrated light from the planet Earth in broad band filters are derived from new polarimetric observations of the earthshine backscattered from the Moon's dark side. Methods. The fractional polarization of the earthshine p es is measured in the B, V, R, and I filters for Earth-phase angles α between 30• and 110• with a new, specially designed wide field polarimeter. In the observations, the light from the bright lunar crescent is blocked with focal plane masks. Because the entire Moon is imaged, the earthshine observations can be corrected for the stray light from the bright lunar crescent and twilight. The phase dependence of p es is fitted by a function p es = q max sin 2 α. Depending on wavelength λ and the lunar surface albedo a, the polarization of the backscattered earthshine is significantly reduced. To determine the polarization of the planet Earth, we correct our earthshine measurements by a polarization efficiency function for the lunar surface (λ, a) derived from measurements of lunar samples from the literature. Results. The polarization of the earthshine decreases toward longer wavelengths and is about a factor 1.3 lower for the higher albedo highlands. For mare regions the measured maximum polarization is about q max,B = 13% for α = 90• (half moon) in the B band. The resulting fractional polarizations for the planet Earth derived from our earthshine measurements and corrected by (λ, a) are 24.6% for the B band, 19.1% for the V band, 13.5% for the R band, and 8.3% for the I band. Together with the literature values for the spectral reflectivity, we obtain a contrast C p between the polarized flux of the planet Earth and the (total) flux of the Sun with an uncertainty of less than 20%, and we find that the best phase for detecting an Earth twin is around α = 65• . Conclusions. The obtained results provide a multiwavelength and multiphase set of benchmark values that are useful for assessing different instrument and observing strategies for the future high contrast polarimetry of extrasolar planetary systems. Polarimetric models of Earth-like planets are in qualitative agreement with our results, but there are also significant differences that might guide more detailed computations.

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“…However, another effect that can cause a brightness surge near zero phase angle, coherent backscatter, was pointed out by Watson [1969] in connection with the scattering of radio waves by plasmas and later by Shkuratov [1988] for planetary regoliths. It was observed experimentally in colloidal suspensions of submicroscopic particles by Kuga and Ishimaru [1984], in planetary analog powders by Hapke and Blewett [1991], and in lunar soil samples by Hapke et al [1993]. In the coherent backscatter opposition effect (CBOE), two portions of a wave that travel the same, multiply scattered path through a regolith, but in opposite directions, combine randomly if the phase angle is large but interfere coherently and positively at near zero phase (see Hapke [1990] for a detailed explanation).…”

Section: Introductionmentioning

confidence: 99%

The wavelength dependence of the lunar phase curve as seen by the Lunar Reconnaissance Orbiter wide‐angle camera

et al. 2012

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[1] The Lunar Reconnaissance Orbiter wide-angle camera measured the bidirectional reflectances of two areas on the Moon at seven wavelengths between 321 and 689 nm and at phase angles between 0°and 120°. It is not possible to account for the phase curves unless both coherent backscatter and shadow hiding contribute to the opposition effect. For the analyzed highlands area, coherent backscatter contributes nearly 40% in the UV, increasing to over 60% in the red. This conclusion is supported by laboratory measurements of the circular polarization ratios of Apollo regolith samples, which also indicate that the Moon's opposition effect contains a large component of coherent backscatter. The angular width of the lunar opposition effect is almost independent of wavelength, contrary to theories of the coherent backscatter which, for the Moon, predict that the width should be proportional to the square of the wavelength. When added to the large body of other experimental evidence, this lack of wavelength dependence reinforces the argument that our current understanding of the coherent backscatter opposition effect is incomplete or perhaps incorrect. It is shown that phase reddening is caused by the increased contribution of interparticle multiple scattering as the wavelength and albedo increase. Hence, multiple scattering cannot be neglected in lunar photometric analyses. A simplified semiempirical bidirectional reflectance function is proposed for the Moon that contains four free parameters and that is mathematically simple and straightforward to invert. This function should be valid everywhere on the Moon for phase angles less than about 120°, except at large viewing and incidence angles close to the limb, terminator, and poles.Citation: Hapke, B., B. Denevi, H. Sato, S. Braden, and M. Robinson (2012), The wavelength dependence of the lunar phase curve as seen by the Lunar Reconnaissance Orbiter wide-angle camera,

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The Opposition Effect of the Moon: The Contribution of Coherent Backscatter

Cited by 190 publications

References 27 publications

Analysis of hot spot directional signatures measured from space

Analysis of hot spot directional signatures measured from space

Measurement of the earthshine polarization in theB, V, R, andIbands as function of phase

The wavelength dependence of the lunar phase curve as seen by the Lunar Reconnaissance Orbiter wide‐angle camera

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