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\section{Discussion}
The most notable previous measurement of the CTR with DOI was conducted by Moses\cite{Moses1999}. In this paper the characteristic shift in the delay peak position with DOI was attributed to the time difference between the forward and backward modes approaching negligible levels thus the electronics will `see' a narrower, higher density pulse of photons compared to two individual pulses leading to an averaging effect related to the geometry of the scintillator crystal.
In this chapter the results shown in sections XX and XX show the lowest error per measurement, whilst demonstrating the clearest null \begin{enumerate}
\item Null relationship between
the CTR and DOI
\item Smaller ratio between unwrapped and
CTR. Of interest is the drop wrapped in
the mean CTR from $207\pm1$ to $199\pm1$ with the inclusion of PTFE tape wrapping. Whilst a drop is expected due to the increased DOI case than in standard. Indicates light
output with wrapping, this drop transport is
not as high as might expect due to the $\frac{1}{\sqrt{N}}$ dependency of the CTR. This implies large contribution and only
a small portion of
the generated photons
by the scintillator crystal are `useful' for timing purposes.
The results presented will subsequently be published, however the results are in direct contradiction with \cite{Yeom2013}. In this the CTR is shown to degrade with reduced DOI with range of 160 contribute to
190 ps over a $3\times3\times20$\mmc LYSO scintillator crystal. In \cite{Bircher2012} however no relationship between CTR and DOI is visible, on the provision that the scintillator crystal surface is smooth.
The second result the DOI results show, is a consistent shift the right photopeak position CTR.
\item Agreement with
DOI. This drop, typically between 4\% \cite{Bircher_Shao_2012} and
10\% over the length of the \cite{Moses_2001} for polished scintillator
crystal, indicates a loss mechanism with increasing DOI. A decrease crystals. Discuss conclusions drawn.
\item \cite{Yeom_Vinke_Levin_2013} figure 10 showing improvement in
the light output with scintillator crystal length\cite{sta_Mayhugh_Wolski_Flyckt_1997} is potentially the same effect. Also the mean photon path length\footnote{Investigate this via Monte Carlo} increases CTR with
DOI the chance of absorption within the scintillator crystal is increased. Another potential source of loss is due to imperfections in the surface of the scintillator crystal. For a small perturbation increasing distance from
specular, a situation that can be described adequately by the
Lobe reflection model\cite{Janecek_Moses_2008}, a small portion photodetector -> discuss.
\item Effective refractive index of
light can couple out of the scintillator. partially wrapped configuration.
\end{enumerate}