The Hapke parameters are a set of parameters for an empirical model that is commonly used to describe the directional reflectance properties of the airless regolith surfaces of bodies in the Solar System. The model has been developed by astronomer Bruce Hapke at the University of Pittsburgh.
The parameters are:
— Single scattering albedo. This is the ratio of scattering efficiency to total light extinction (which includes also absorption), for small-particle scattering of light. That is, , where is the scattering coefficient, and is the absorption coefficient
— The width of the opposition surge.
or — The strength of the opposition surge.
or g — The particle phase function parameter, also called the asymmetry factor.
— 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, the phase integral, and the Bond albedo.
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The bidirectional reflectance distribution function (BRDF; ) 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 computer graphics algorithms, and in computer vision algorithms. The function takes an incoming light direction, , and outgoing direction, (taken in a coordinate system where the surface normal lies along the z-axis), and returns the ratio of reflected radiance exiting along to the irradiance incident on the surface from direction .
Albedo (ælˈbiːdoʊ; ) is the fraction of sunlight that is diffusely reflected by a body. It is measured on a scale from 0 (corresponding to a black body that absorbs all incident radiation) to 1 (corresponding to a body that reflects all incident radiation). Surface albedo is defined as the ratio of radiosity Je to the irradiance Ee (flux per unit area) received by a surface. The proportion reflected is not only determined by properties of the surface itself, but also by the spectral and angular distribution of solar radiation reaching the Earth's surface.