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where $\sigma$ is the time resolution of a single scintillator detector. In cases where we use a known reference scintillator detector, the CTR is determined by subtraction in quadrature and a subsequent scaling such that  \begin{align}  \text{CTR} = 4\sqrt{\ln{2}}\sqrt{\sigma-\sigma_\textrm{ref}^2}  \label{eqn:ctrfromref}  \end{align}  where $\sigma_\text{ref}$ is the reference time resolution.