Analytical calculation of the solid angle subtended by a circular disc detector at a point cosine source
Abstract
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 halfspace 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 zaxis 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.
 Publication:

Nuclear Instruments and Methods in Physics Research A
 Pub Date:
 April 2004
 DOI:
 10.1016/j.nima.2003.10.098
 arXiv:
 arXiv:mathph/0305034
 Bibcode:
 2004NIMPA.521..576P
 Keywords:

 Mathematical Physics;
 Physics  Instrumentation and Detectors
 EPrint:
 12 pages, 10 figures, LaTex12 pages, 10 figures, LaTex. Minor changes from previous version: references added, english reshaping, the phrase "If beta=0.." (pag. 5 near eq. 20 in the old version) was corrected to "If beta=pi/2.."