International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 915958, 18 pages
doi:10.1155/2010/915958
Geometric sensitivity of a pinhole collimator
Howard Jacobowitz1
and Scott D. Metzler2
1Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA
2Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA
Abstract
Geometric sensitivity for single photon emission computerized tomography (SPECT) is given by a double integral over the detection plane. It would be useful to be able to explicitly evaluate this quantity. This paper shows that the inner integral can be evaluated in the situation where there is no gamma ray penetration of the material surrounding the pinhole aperture. This is done by converting the integral to an integral in the complex plane and using Cauchy's theorem to replace it by one which can be evaluated in terms of elliptic functions.