Analytic treatment of resolution precision in electronically collimated SPECT imaging involving multiple-interaction gamma rays.

The widely applied single-interaction analytic expression characterizing the energy resolution component of the angular resolution precision for an electronically collimated point source is extended to include multiple-interaction Compton scatter sequences as well as sequences terminated by photoelectric absorption. The analytic formulation is developed using the statistical variance of the mean for components comprising composite, multivariate resolution precision estimators. It is demonstrated that enhanced resolution precision in the incident interaction scatter angle is attained when use is made of information from multiple interactions. An improvement in the resolution precision of up to approximately 40% is observed for triple Compton scatter. Comparison of the analytic estimates with Monte Carlo/chi-square results shows good agreement.