Solid angle subtended by a cylindrical detector at a point source in terms of elliptic integrals

Abstract

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.

Reconstruction of a radiation point source’s radial location using goodness-of-fit test on spectra obtained from an HPGe detector

“…This is due to the fact that the solid angle subtended by the detector is greatest at the center of the front of the detector and the center of the side, as previously described in [9]. This difference was clearly visible without conducting statistical tests.…”

“…halfway down the side of the detector, the relative sum peak area was roughly five times greater than when the radiation source was placed behind the detector. This is due to the fact that the solid angle subtended by the detector is greatest at the center of the front of the detector and the center of the side, as previously described in [9]. This difference was clearly visible without conducting statistical tests.…”

Analytical calculation of the solid angle defined by a cylindrical detector and a point cosine source with parallel axes

“…The case of an isotropic point source has been treated to great extent (Jaffey (1954), Macklin (1957), Masket et al (1956), Masket (1957), Gillespie (1970), Gardner and Verghese (1971), Green et al (1974), Prata (2003b)). …”

“…In many situations in radiation physics the value of the solid angle subtended by a circular cylindrical detector at a point source is needed. The case of an isotropic point source has been treated to great extent (Jaffey (1954), Macklin (1957), Masket et al (1956), Masket (1957), Gillespie (1970), Gardner and Verghese (1971), Green et al (1974), Prata (2003b)).…”

Four Vignettes on Apparent Size

“…This problem was solved in [4] via a Fourier-Legendre series approximation for Ω. An exact formula, however, was mentioned by Maxwell [5] in 1873, explicitly given by Tallqvist [6] in 1931, and subsequently rediscovered several times [7,8,9,10,11,12,13,14,15,16,17,18]:…”