\section{Appendix}
Figure~\ref{YZcomparison} shows the expected distribution of photons on the PMT plane for charged pions intersecting the DIRC at various locations. The \gx~design greatly reduces the overlap in the patterns.
There are still side reflections for hits in the bars that are farthest from the beam line. These reflections could be removed by instrumenting an additional 300~mm along the length of the FOB with PMTs; however, the cost of this extra instrumentation outweighs the benefits as it is unlikely to get particles near the limits of $\pi/K$ separation in this region.
\begin{figure*}[!h]
\includegraphics[height=5.2cm]{figures/YZ_barLastBar.pdf}\quad
\includegraphics[height=5.2cm]{figures/YZ_LastBar.pdf} \\
\includegraphics[height=5cm]{figures/YZ_barcentrale.pdf}\quad
\includegraphics[height=4.8cm]{figures/YZ_MiddleBar.pdf} \\
\includegraphics[height=5cm]{figures/YZ_bar1ere.pdf}\quad
\includegraphics[height=5cm]{figures/YZ_1stBar.pdf} \\
\caption{Comparison of the (right) original SLAC design to the (left) adapted version of the camera for \gx. The figures correspond to the following: (top) a hit in the bar the far from the beam line; (middle) a hit in the central part of a box; and (bottom) a hit in the bar closest to the beam line.}
\label{YZcomparison}
\end{figure*}