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Physics LibreTexts

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)=2π010fr(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.

Table I. Properties of Surfaces
Lambertian Lommel-Seeliger
fr ϖ0 ϖ04π1μ0+μ
ρ ϖ0 ϖ02[1μ0ln(1+1/μ0)]
pn ϖ0 ϖ08

This page titled 2.7: Surfaces - Hemispherical Albedo is shared under a CC BY-NC 4.0 license and was authored, remixed, and/or curated by Max Fairbairn & Jeremy Tatum via source content that was edited to the style and standards of the LibreTexts platform.

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