Analytic variance estimates of Swank and Fano factors

Abstract

Purpose: Variance estimates for detector energy resolution metrics can be used as stopping criteria in Monte Carlo simulations for the purpose of ensuring a small uncertainty of those metrics and for the design of variance reduction techniques.

Methods: The authors derive an estimate for the variance of two energy resolution metrics, the Swank factor and the Fano factor, in terms of statistical moments that can be accumulated without significant computational overhead. The authors examine the accuracy of these two estimators and demonstrate how the estimates of the coefficient of variation of the Swank and Fano factors behave with data from a Monte Carlo simulation of an indirect x-ray imaging detector.

Results: The authors' analyses suggest that the accuracy of their variance estimators is appropriate for estimating the actual variances of the Swank and Fano factors for a variety of distributions of detector outputs.

Conclusions: The variance estimators derived in this work provide a computationally convenient way to estimate the error or coefficient of variation of the Swank and Fano factors during Monte Carlo simulations of radiation imaging systems.