International Journal of Mathematics and Mathematical Sciences
Volume 2010 (2010), Article ID 915958, 18 pages
Research Article

Geometric Sensitivity of a Pinhole Collimator

1Department of Mathematical Sciences, Rutgers University, Camden, NJ 08102, USA
2Department of Radiology, University of Pennsylvania, Philadelphia, PA 19104, USA

Received 25 August 2009; Revised 7 December 2009; Accepted 19 February 2010

Academic Editor: Harvinder S. Sidhu

Copyright © 2010 Howard Jacobowitz and Scott D. Metzler. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


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.