= Lambertian sphere at full phase
{c}
{title2=$F=\frac{2A}{3}F_\star(R/d)^2$}
A spherical body of <radius> R observed from distance $d\gg R$ is illuminated and viewed from the same direction, with incident <irradiance> $F_\star$. For uniform <Lambertian reflectance> A, a patch at angle $\theta$ has outgoing <radiance> $AF_\star\cos\theta/\pi$. The observer receives this radiance times projected area divided by $d^2$. Since $\int_{\mathrm{hemisphere}}\cos^2\theta\,dS=2\pi R^2/3$, integration proves the displayed full-phase <irradiance>. Its <geometric albedo> is $2A/3$. Total reflected power alone does not specify the brightness in one direction for a non-Lambertian surface.
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