The solid angle subtended by a right circular cylinder at a point source located at an arbitrary position generally consists of a sum of two terms: that defined by the cylindrical surface (Ω cyl ) and the other by either of the end circles (Ω circ ). We derive an expression for Ω cyl in terms of elliptic integrals of the first and third kinds and give similar expressions for Ω circ using integrals of the first and second kinds. These latter can be used alternatively to an expression also in terms of elliptic integrals, due to Philip A. Macklin and included as a footnote in Masket (Rev. Sci. Instr., 28 (3), 191-197, 1957). The solid angle subtended by the whole cylinder when the source is located at an arbitrary location can then be calculated using elliptic integrals.

We derive analytical expressions for the solid angle subtended by a right circular cylinder at a point source with cosine angular distribution in the case where the source and the cylinder axes are mutually orthogonal.

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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.