Bidirectional Reflectance Spectroscopy

Hapke, Bruce

doi:10.1006/icar.2002.6853

Cited by 451 publications

(267 citation statements)

References 22 publications

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“…However, this argument is invalid and results from confusion about the meaning of multiple scattering [Hapke, 2002]. In the radiative transfer equation and its solutions, multiple scattering refers to scattering between particles of the medium.…”

Section: Discussionmentioning

confidence: 99%

“…[16] Data Set S2 was analyzed quantitatively by fitting a simplified version of the bidirectional reflectance model of Hapke [1993], as subsequently modified by Hapke [2002Hapke [ , 2008see also Hapke, 2012]. Unfortunately, a similar analysis could not be done for Data Set S1 because the range of …”

Section: Reflectance Equationsmentioning

confidence: 99%

“…[17] Hapke [1993Hapke [ , 2002Hapke [ , 2008Hapke [ , 2012 should be consulted for the derivation and detailed discussions of the quantities in equation (2). In this equation, K is the porosity factor and is a monotonically increasing function of the filling factor f; w is the volume average single scattering albedo; i e and e e are effective angles of incidence and emission, respectively, and are functions of the mean subpixel slope angle q; p(g) is the average single particle scattering function, which is assumed to be described by the three-parameter double Henyey-Greenstein function,…”

Section: Hapke Et Al: Wavelength-dependent Lunar Phase Curve E00h15 mentioning

confidence: 99%

“…Equation (6) is based on the model derived by Akkermans et al [1986] using diffusion theory (which is closely related to scalar radiative transfer theory). This model was adopted and slightly modified by Hapke [2002].…”

Section: Hapke Et Al: Wavelength-dependent Lunar Phase Curve E00h15 mentioning

confidence: 99%

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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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Section: Discussionmentioning

confidence: 99%

Section: Reflectance Equationsmentioning

confidence: 99%

Section: Hapke Et Al: Wavelength-dependent Lunar Phase Curve E00h15 mentioning

confidence: 99%

Section: Hapke Et Al: Wavelength-dependent Lunar Phase Curve E00h15 mentioning

confidence: 99%

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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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“…The single-particle phase function is modeled by the Henyey-Greenstein (H-G) functions (Hapke, 2002). The functions are single-term or double-term, depending on the kind of grain is being represented.…”

Section: Hapke-parameters Resolved Mapmentioning

confidence: 99%

Asteroid (21) Lutetia: Disk-resolved photometric analysis of Baetica region

Hasselmann

Fornasier

Leyrat

et al. 2016

Icarus

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ABSTRACT. (21) Lutetia has been visited by Rosetta mission on July 2010 and observed with a phase angle ranging from 0.15 to 156.8 degrees. The Baetica region, located at the north pole has been extensively observed by OSIRIS cameras system. Baetica encompass a region called North Pole Crater Cluster (NPCC), shows a cluster of superposed craters which presents signs of variegation at the small phase angle images. For studying the location, we used 187 images distributed throughout 14 filter recorded by the NAC (Narrow Angle Camera) and WAC (Wide Angle Camera) of the OSIRIS system on-board Rosetta taken during the fly-by. Then, we photometrically modeled the region using Minnaert diskfunction and Akimov phase function to obtain a resolved spectral slope map at phase angles of 5 • and 20 • . We observed a dicothomy between Gallicum and Danuvius-Sarnus Labes in the NPCC, but no significant phase reddening (−0.04 ± 0.045% · microns −1 deg −1 ). In the next step, we applied the Hapke (2008Hapke ( ,2012 model for the NAC F82+F22 (649.2 nm), WAC F13 (375 nm) and WAC F17 (631.6 nm) and we obtained normal albedo maps and Hapke parameter maps for NAC F82+F22. On Baetica, at 649.2 nm, the geometric albedo is 0.205 ± 0.005, the average single-scattering albedo is 0.181 ± 0.005, the average asymmetric factor is −0.342 ± 0.003, the average shadow-hiding opposition effect amplitude and width are 0.824 ± 0.002 and 0.040 ± 0.0007, the average roughness slope is 11.45 • ± 3 • and the average porosity is 0.85 ± 0.002. We are unable to confirm the presence of coherent-backscattering mechanism. In the NPCC, the normal albedo variegation among the craters walls reach 8% brighter for Gallicum Labes and 2% fainter for Danuvius Labes. The Hapke parameter maps also show a dicothomy at the opposition effect coefficients, single-scattering albedo and asymmetric factor, that may be attributed to the maturation degree of the regolith or to compositonal variation. In addition, we compared the Hapke (2008Hapke ( , 2012 and Hapke (1993) parameters with laboratory samples and other small-solar system bodies visited by space missions.

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Ilmenite mapping of the lunar regolith over Mare Australe and Mare Ingenii regions: An optimized multisource approach based on Hapke radiative transfer theory

et al. 2013

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[1] We model lunar ilmenite abundances over Mare Australe and Mare Ingenii regions using a new approach; we integrate Lunar Reconnaissance Orbiter Wide Angle Camera (WAC) and Clementine UV-visible/near-infrared (UVVIS/NIR) data to obtain a 14-band mosaic (320-2000 nm). We use Hapke's radiative transfer equations to compute spectra for various mixtures of orthopyroxene, clinopyroxene, plagioclase, olivine, and ilmenite, with varying grain size, chemistry, and degree of maturity, and find the closest match between the modeled spectra and the spectra of the less mature pixels (optical maturity ≥ 0.2) in the 14-band mosaic. We calculate a "maximum stoichiometrically possible ilmenite content", using Clementine-derived TiO 2 abundances and the amount of TiO 2 in stoichiometric ilmenite, and use it as a constraint in our model. We validate our methodology with lunar soil spectra of known composition. Our results show that the integrated WAC-UVVIS/ NIR data and the UVVIS/NIR data overestimate ilmenite abundances by 8.80 wt % and 7.97 wt %, respectively, when a fixed maximum of 20 wt % ilmenite is used. When the maximum stoichiometrically possible ilmenite content is used as a constraint, the integrated WAC-UVVIS/NIR data give slightly more accurate ilmenite abundance estimation (±2.87 wt %) than when using only UVVIS/NIR data (± 3.04 wt %). We find ilmenite concentrations of 0À11 wt % in Mare Australe and 0À6 wt % in Mare Ingenii region. Ilmenite abundances between 4 and 7 wt % are exposed in Mare Australe, whereas ilmenite abundances between 7 and 11 wt % are found on the walls of 0.6-11.8 km diameter craters within Mare Australe.

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Bidirectional Reflectance Spectroscopy

Cited by 451 publications

References 22 publications

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

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

Asteroid (21) Lutetia: Disk-resolved photometric analysis of Baetica region

Ilmenite mapping of the lunar regolith over Mare Australe and Mare Ingenii regions: An optimized multisource approach based on Hapke radiative transfer theory

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