deletions | additions       diff --git a/Depth of Interaction.tex b/Depth of Interaction.tex  index 6d98aaf..e718894 100644  --- a/Depth of Interaction.tex  +++ b/Depth of Interaction.tex 
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\subsection{Overview}  The standard coincidence apparatus, as shown in figure \ref{fig:doi-ctr}(a) is altered in two key respects. Firstly the right photodetector is placed within a 3D-printed clamp designed to hold the scintillator crystal which is held vertically with respect to the reference detector. Secondly the $^{22}$Na source is placed much closer to the vertically aligned scintillator detector than the reference. As in the standard apparatus both scintillator crystals are coupled to their respective photodetectors, Hamamatsu MPPC S10931-050P SiPMs, using Rhodorsil 47V optical grease.   The size of the confinement region is primarily determined by the separation distances between scintillator detectors and the $^{22}$Na source. The source is placed 5mm from the scintillator crystal under investigation. The reference scintillator detector is a further 40mm 40 mm  on the opposite side from the source, unless otherwise stated. As the $^{22}$Na cylinder is not a point source, its finite size of 1 mm$^3$ gives a minimum to the confinement region. For a source much closer to the scintillator detector under interest than to the reference detector, the confinement region will tend to the width of the source. To determine the size of the confinement region we can exploit the fact that the scintillator detector will detect a fixed number of events per unit time if the volume of scintillator crystal does not change. Therefore for the same measurement and same confinement region we can assume a uniform number of events, regardless of DOI. Furthermore if the confinement region passes outside the scintillator crystal, the number of $\gamma\gamma$ events will drop until electronic collimation prevents any correlations from being detected. In this we assume good alignment of the scintillator crystal with respect to the central axis of the coincidence apparatus. We represent this described behaviour as a convolution between a uniform distribution and a Gaussian distribution. The uniform distribution has a width corresponding to the scintillator crystal length and an amplitude corresponding to the mean number of detected $\gamma\gamma$ events. The FWHM of the normal distribution corresponds to the confinement region; In this case taken as 1mm. 1 mm.  As shown in figures \ref{fig:confinement} and \ref{fig:confinement-20} as a black-dotted line this is a valid assumption for our apparatus on the provision the scintillator crystal is properly aligned. diff --git a/Method 2.tex b/Method 2.tex  index c7993a1..7bc543d 100644  --- a/Method 2.tex  +++ b/Method 2.tex 
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\subsection{Processing Data}  The positron emission from the Na22 source will generate two 0.511MeV 0.511 MeV  gamma ray photons in opposition correlated in time. By selecting for events which interact solely by the photoelectric effect we ensure that the incident gamma ray photon has interacted with matter only once. Therefore if two gamma ray photons are detected in opposition within a small time window, it is highly likely they are from the same electron-positron annihilation. It is this `electronic collimation' timing property which ensures we only record events from within the confinement region. These events are found by selecting the subset of interactions which fall within $2\sigma$ of the photopeak centroid of their respective energy spectra. This narrow range is chosen to drastically reduce the contribution of overlapping Compton interactions. When two gamma ray photons are detected within their respective photopeak energy ranges, within a nanosecond of each other, the relative time delay between the two is recorded. For many such true events the relative difference in arrival time is histogrammed to produce a Gaussian distribution. This will be referred to as the (relative) delay peak. For two identical photodetectors the FWHM of the delay peak is defined as the coincidence time resolution (CTR), such that \begin{align}  \text{CTR} &= 2\sqrt{2\ln{2}}\sigma_\text{measured}\\  diff --git a/ctrdiscussion.tex b/ctrdiscussion.tex  index 7a5aafd..525cdc1 100644  --- a/ctrdiscussion.tex  +++ b/ctrdiscussion.tex 
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In figure \ref{fig:ctrvsdoi} the CTR (in ps) against DOI (in mm) per sample and configuration is given. In table \ref{tab:doictrresults} the values given for the timing and energy performance are averaged across the DOI. Firstly we note that no clear relationship between CTR and DOI is visible. The reduced chi-squared fit shows values close to unity for fitting to the weighted mean, indicating no relationship between CTR and DOI in both crystals and configurations. Secondly the CTR measurements from the wrapped configuration are consistently better than those from the unwrapped. The differences being 8$\pm$5ps 15$\pm$3 ps  and 18$\pm$6ps 25$\pm$6 ps  for 30A and 30B respectively. This difference is much smaller than that which we would expect in the standard CTR measurement. For instance it is seen in [Table IV]\cite{r_Paganoni_Pauwels_et_al__2011} that the difference in the CTR between wrapped and unwrapped configurations is approximately 33\%. The differences for 30A and 30B are 6$\pm$1\% and 10$\pm$2\%.  This implies that knowledge of the excitation position within the standard coincidence apparatus for an unwrapped scintillator crystal would reduce the measured CTR by at least 25\%. 23\%.  We would predict this behaviour is due to a reduction in the variance of the photon travel time to the photodetector across multiple gamma ray photon detections. With DOI information, and limited diffusion in a polished unwrapped scintillator crystal, the photon travel time variance will be low. diff --git a/introduction.tex b/introduction.tex  index 3d1851c..df9282b 100644  --- a/introduction.tex  +++ b/introduction.tex 
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In this work we investigate the relationship between the interaction position of 0.511 MeV gamma ray photons and the timing and energy performance of the scintillator detector. The depth of interaction (DOI), shown in figure \ref{fig:doi-ctr}, is the shortest distance to the photodetector from the gamma ray photon ($\gamma$) interaction position. The DOI is a potential source of degradation to the timing and energy performance of the scintillator detector due to photon time of flight and light loss from increased path lengths within the scintillator crystal. Furthermore determination of the DOI, of a given interaction, is of importance for PET to negate or reduce the contribution of parallax error upon the spatial resolution \cite{Moses_2001}\cite{Humm_Rosenfeld_Del_Guerra_2003}. If successful, longer scintillator crystals may be used leading to an improvement in the PET scanner's sensitivity and reduce overall scan times. Within monolithic scintillator detectors the same DOI information allows spatial confinement within the detector itself \cite{am_Borghi_Seifert_Schaart_2013}\cite{Maas_Bruyndonckx_Schaart_2012}, thus potentially allowing more novel\cite{Dendooven_Lohner_Beekman_2009}\cite{n_der_Lei_van_Dam_Schaart_2013} layouts and geometries.  In this paper we begin by describing the standard and DOI coincidence apparatus, along with the method utilised in both for analysing the raw data in section \ref{sec:method}. Using this method we characterise the $2\times2\times5$mm$^3$ $2\times2\times5$ mm$^3$  Agile Ca-co-doped LSO:Ce scintillator crystal used in the reference scintillator detector in section \ref{sec:reference}. Once this accomplished the time resolution with scintillator crystal length ($L$) is explored with the standard coincidence apparatus using two identical $2\times2\times L$mm$^3$ L$ mm$^3$  Proteus LYSO:Ce scintillator crystals in section \ref{sec:standardctr}. Measurements conducted using the DOI coincidence apparatus are split into two. Firstly for two identical $2\times2\times30$mm$^3$ $2\times2\times30$ mm$^3$  Proteus LYSO:Ce and secondly for a single $2\times2\times20$mm$^3$ $2\times2\times20$ mm$^3$  Agile Ca-co-doped LSO:Ce. These are covered in sections \ref{sec:30mm} and \ref{sec:20mm} respectively. In doing so we explore the contribution, if any, of scintillator crystal material, geometry and wrapping. All scintillator crystals are polished. PTFE (Teflon) tape is used as the wrapping material due its diffusive properties. Finally, we discuss the results in the discussion in section \ref{sec:discussion}. diff --git a/ref table.tex b/ref table.tex  index 6239bd7..2fa2ad3 100644  --- a/ref table.tex  +++ b/ref table.tex 
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\begin{table}  \caption{\label{tab:referencevals} Coincidence time resolution values for two identical polished $2\times2\times5$mm$^3$ $2\times2\times5$ mm$^3$  Ca-co-doped LSO:Ce wrapping in PTFE tape for standard and DOI measurements.} \begin{tabular}{cccccccc}  %\begin{tabular}{p{1.8cm}p{2.3cm}p{2.3cm}p{1.7cm}p{2.2cm}cc}  Coincidence Apparatus & Left Energy Resolution (\%) & Right Energy Resolution (\%) & Detected $\gamma\gamma$ Events & Valid $\gamma\gamma$ Events & Delay Peak Centroid (ps) & $\sigma_\textrm{ref}$ (ps) & CTR (ps)\\