2.7: Surfaces - Hemispherical Albedo
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Also known as the directional hemispherical reflectance, the hemispherical albedo ρ refers to a point on a reflecting surface, and is defined as the ratio of the exitance M to the irradiance E, so that
ρ(μ0,φ0)=ME(μ0,φ0),
and in terms of the BRDF, we have
ρ(μ0,φ0)=∫2π0∫10fr(μ,φ;μ0,φ0)μdμdφ.
Unlike the single scattering albedo, ρ and the other albedos that we will encounter do not necessarily have in principle a maximum possible value of unity. (See A Brief History of the Lommel-Seeliger Law). The scattering properties of the surfaces that we have studied so far are summarised in Table I, from which, for the Lommel-Seeliger law, it can be seen that the maximum possible value for ρ is ½ and 0.125 for the normal albedo.
Lambertian | Lommel-Seeliger | |
---|---|---|
fr | ϖ0/π | ϖ04π1μ0+μ |
ρ | ϖ0 | ϖ02[1−μ0ln(1+1/μ0)] |
pn | ϖ0 | ϖ08 |