Analytical calculation of the solid angle subtended by a circular disc detector at a point cosine source

We derive analytical expressions for the solid angle subtended by a circular disc at a point source with cosine angular distribution (f(μ)=μ/π) under the sole condition that the disc lies in the half-space illuminated by the source (μ⩾0). The expressions are given with reference to two alternative coordinate systems (S and S′), S being such that the z-axis is parallel to the symmetry axis of the disc and S′ such that the z′-axis is aligned with the source direction. Sample plots of the expressions are presented.