\section{Standard Coincidence}
\label{sec:standardctr}
Prior to the DOI experiment, standard coincidence measurements are made of Proteus LYSO:Ce scintillator crystals with a cross section of $2\times2$ mm$^2$ wrapped in PTFE tape for lengths, $L$, of 5, 10, 15, 20 and 30 mm. Two identical crystals, which are referred to as $L\text{A}$ and $L\text{B}$, of each length are placed into opposing, identical, scintillator detectors. The CTR is then determined as the FWHM of the delay peak directly. Furthermore electronic collimation ensures the confinement region is the same in both scintillator crystals. In figure \ref{fig:standardctr} we see the expected degradation of the CTR with increasing crystal length \cite{r_Paganoni_Pauwels_et_al__2011}\cite{Wiener_Kaul_Surti_Karp_2010}\cite{Choong_2009}\cite{Gola_Piemonte_Tarolli_2013}\cite{o_Pro_Serra_Tarolli_Zorzi_2011}. The full set of results are given in table \ref{tab:standardctr}. In these measurements the wrapping was reapplied by a second individual and the measurement retaken. These will referred to as `wrap 1' and `wrap 2'. For 5 mm and 30 mm the measurement is repeated by the same person. We see that the `quality' of the wrapping leads to a large systematic variation that must be carefully taken into account for measurements to be validly compared between scintillator crystals. Given that we also see a shift in the delay peak centroid between these measurements, we would conclude correct alignment upon the SiPM is also vital. 

Also in table \ref{tab:standardctr} we see that the energy resolution (\%), for both left and right scintillator detectors, is poorer at higher scintillator crystal lengths. This is due to increased variance in the energy recorded and reduced light detected for a 0.511 MeV gamma ray photon; likely due to increased path length of photons through the scintillator crystal. Also note that each measurement was conducted for 15 minutes each. Thus the number of $\gamma\gamma$ events detected increases with the scintillator crystal lengths as expected  due to greater volume within the confinement region, leading to increased sensitivity.
