Analytic Derivation and Monte Carlo Validation of a Sensitivity Formula for Slit-Slit Collimation With Penetration

A slit-slit collimator consists of two orthogonal slits and can be conceptualized as a generalized pinhole. Since the two slits are independent of each other, there can be independent axial and transaxial acceptance angles. A small axial acceptance angle may help mitigate axial blurring with circular orbits, allowing multiple copies axially. In addition, since the two slit planes can be placed at different distances with respect to the source, a better detector usage can be achieved, especially in the case of detectors and imaged objects with different aspect ratios. In this paper an analytical expression is derived for the sensitivity of slit-slit collimation including effective slit widths for photon penetration. An analytical expression for sensitivity is necessary in order to accurately model the system response. This expression could also be useful for comparing the slit-slit's sensitivity performance with others. When the effective slit width is used instead of the geometric slit width, the derived analytical expression accurately accounts for photon penetration of the aperture. The derived expression for the sensitivity was validated by Monte Carlo simulation for both geometric and penetrative cases.