Hapke Parameters
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The Hapke parameters are a set of parameters for an
empirical model Empirical modelling refers to any kind of ( computer) modelling based on empirical observations rather than on mathematically describable relationships of the system modelled. Empirical Modelling Empirical Modelling as a variety of empirical m ...
that is commonly used to describe the directional reflectance properties of the airless
regolith Regolith () is a blanket of unconsolidated, loose, heterogeneous superficial deposits covering solid rock. It includes dust, broken rocks, and other related materials and is present on Earth, the Moon, Mars, some asteroids, and other terrestria ...
surfaces of bodies in the
Solar System The Solar SystemCapitalization of the name varies. The International Astronomical Union, the authoritative body regarding astronomical nomenclature, specifies capitalizing the names of all individual astronomical objects but uses mixed "Solar S ...
. The model has been developed by astronomer
Bruce Hapke Bruce William Hapke (born February 17, 1931) is a noted American planetary scientist, currently a professor emeritus at the University of Pittsburgh and a specialist in bidirectional reflectance spectroscopy. Career Born in Racine, Wisconsin, ...
at the
University of Pittsburgh The University of Pittsburgh (Pitt) is a public state-related research university in Pittsburgh, Pennsylvania. The university is composed of 17 undergraduate and graduate schools and colleges at its urban Pittsburgh campus, home to the universit ...
. The parameters are: #\bar_0
Single scattering albedo Single-scattering albedo is the ratio of scattering efficiency to total extinction efficiency (which is also termed "attenuance", a sum of scattering and absorption). Most often it is defined for small-particle scattering of electromagnetic waves. ...
. This is the ratio of scattering efficiency to total light extinction (which includes also absorption), for small-particle scattering of light. That is, K_s/(K_s+K_a), where K_s is the
scattering coefficient The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
, and K_a is the
absorption coefficient The linear attenuation coefficient, attenuation coefficient, or narrow-beam attenuation coefficient characterizes how easily a volume of material can be penetrated by a beam of light, sound, particles, or other energy or matter. A coefficient valu ...
Single Scattering Albedo
scienceworld.wolfram.com.
#h — The width of the
opposition surge The opposition surge (sometimes known as the opposition effect, opposition spike or Seeliger effect) is the brightening of a rough surface, or an object with many particles, when illuminated from directly behind the observer. The term is most wid ...
. #B_0 or S_0 — The strength of the opposition surge. #P_0 or ''g'' — The particle phase function parameter, also called the asymmetry factor. #\theta — The effective surface tilt, also called the macroscopic roughness angle. The Hapke parameters can be used to derive other albedo and scattering properties such as the
geometric albedo In astronomy, the geometric albedo of a celestial body is the ratio of its actual brightness as seen from the light source (i.e. at zero phase angle) to that of an ''idealized'' flat, fully reflecting, diffusively scattering ( Lambertian) disk w ...
, the phase integral, and the
Bond albedo The Bond albedo (or ''spheric albedo'' or ''planetary albedo'' or ''bolometric albedo''), named after the American astronomer George Phillips Bond (1825–1865), who originally proposed it, is the fraction of power in the total electromagnetic rad ...
.


See also

*
Albedo Albedo (; ) is the measure of the diffuse reflection of sunlight, solar radiation out of the total solar radiation and measured on a scale from 0, corresponding to a black body that absorbs all incident radiation, to 1, corresponding to a body ...
*
Geometric albedo In astronomy, the geometric albedo of a celestial body is the ratio of its actual brightness as seen from the light source (i.e. at zero phase angle) to that of an ''idealized'' flat, fully reflecting, diffusively scattering ( Lambertian) disk w ...
*
Bidirectional reflectance distribution function The bidirectional reflectance distribution function (BRDF; f_(\omega_,\, \omega_) ) is a function of four real variables that defines how light is reflected at an opaque surface. It is employed in the optics of real-world light, in compute ...


References

Radiometry Scattering, absorption and radiative transfer (optics) {{scattering-stub