Analytical formulae to calculate the solid angle subtended at an arbitrarily positioned point source by an elliptical radiation detector

In this article, we introduce a direct analytical mathematical method for calculating the solid angle, Ω, subtended at a point by closed elliptical contours. The solid angle is required in many areas of optical and nuclear physics to estimate the flux of particle beam of radiation and to determine the activity of a radioactive source. The validity of the derived analytical expressions was successfully confirmed by the comparison with some published data (Numerical Method).