A complete series expansion of Rubyʹs solid-angle formula

A full series expansion is presented of Rubyʹs formula (Nucl. Instr. and Meth. A 58 (1968) 345; Nucl. Instr. and Meth. A 337 (1994)) for the solid angle subtended by a disk-shaped detector for a coaxial, homogeneous, disk-shaped source. Its performance is compared with the fourth order expansion published by Tsoulfanidis (Ruby, Nucl. Instr. and Meth. A 337 (1994); Measurement and Detection of Radiation, Hemisphere, Washington, DC, 1983), the solid-angle formula of Blachman (Nucleonics 5 (1949) 28) and a numerical integration method (Nucl. Instr. and Meth. A 505 (2003) 286).