deletions | additions       diff --git a/Method 2.tex b/Method 2.tex  index 4e935a8..a5761e3 100644  --- a/Method 2.tex  +++ b/Method 2.tex 
...
\subsection{Processing Data}  There are two principal sources of systematic error to correct for in $\gamma\gamma$ data collected The positron emission  from timing coincidence measurements. Firstly low-energy ($\lesssim$1MeV) the Na22 source will generate two 0.511MeV  gamma ray photonsmay interact with matter  in two ways. We wish to select opposition correlated in time. By selecting for  events which interact solely by the photoelectric effect to we  ensure collected events that the incident gamma ray photon has interacted with matter only once. Therefore if two gamma ray photons  are unambiguously correlated detected  in time. Electronic collimation opposition within a small time window, it is highly likely they are from the same electron-positron annhilation. It is this 'electronic collimination' timing property which  ensures 'true' we only record  eventswere excited  from within the confinement region. This is shown in figure \ref{fig:doi-ctr}.     $\gamma$ These  events falling are found by selecting the subset of interactions which fall  within $2\sigma$ of the photopeak centroid of their respective energy spectra are selected. spectra.  This narrow range is chosen to drastically reduce the contribution of overlapping Compton interactions despite losing some photoelectric events. Events matching these criteria interactions. When two gamma ray photons  are grouped to produce detected within their respective photopeak energy ranges, within  a subset nanosecond  of data solely due to $\gamma\gamma$ correlations. The each other, the relative time delay between the two is recorded. For many such true events the relative  difference in arrival timebetween $\gamma\gamma$ pairs  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_\textrm{measured} 
...
where $\sigma_\text{ref}$ is the (known) reference time resolution. All CTR values in this paper are given in picoseconds.  \subsection{Analysis of Data}  The parameters describing the location and scale of the Gaussian distributions (the photopeaks and delay peak per measurement) were found by weighted least-squared fit. The error per bin was assumed Poissonian and taken as the square root of the number of measurements per bin. The standard error in the fit parameters were determined by the bootstrap method  \cite{degroot2012probability}. The full code used to perform the peak detection, peak fitting, parameter error determination and image \& table generation can be found at \href{https://github.com/marksbrown/ProcessingCTRData}{https://github.com/marksbrown/ProcessingCTRData}. An online version of this paper can be found at \cite{Brown2014}.