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

摘要

We derive analytical expressions for the solid angle subtended by a circulardisc at a point source with cosine angular distribution ($f(\mu)=\mu/\pi$)underthe sole condition that the disc lies in the half-space illuminated by thesource ($\mu \geq 0$). The expressions are given with reference to twoalternative coordinate systems (S and S'), S being such that the z axis isparallel to the symmetry axis of the disc and S' such that the $z'$ axis isaligned with the source direction. Sample plots of the expressions arepresented.