Lookup Table Implementation

To implement a Look Up Table Reconstruction, use the same software as for the KDE.  Method used:

1) From middle, top of bar, simulate ~5M photons thrown uniformly in a 2pi half sphere

2) Store the initial direction of these photons indexed by the pixel they hit (~few 100MB).

3) Simulate a real event, and for each pixel hit, go through all directions that might have lead to this pixel.

4) For each possible direction store the angle it makes with each of the 8 reflected possibilities of the particle momentum vector in a histogram

5) The peak of this histogram is the estimated angle, while it's spread is the single photon resolution.

 

The histograms typically look like:

And the fit to the central peak looks like:

The sigma of this central peak is very angle dependent based on some quick checks, but varies between ~9mrad and 9.5mrad, with some angles reaching towards ~10.5mrad for single photon resolution.  These simulations were made with the GlueX expected geometry at 5 GeV (though the resolution shows little angular dependence).  For comparison,the KDE reconstruction method, has a single photon reolution of 7.8mrad (though it also includes timing information).  

Using the SLAC prototype fDIRC geometry gives a single photon resolution of ~11mrad.  The SLAC prototype (https://arxiv.org/ftp/arxiv/papers/1410/1410.0075.pdf) acheived 10.4 mrad resolution.  Given the high angular dependence, and distribution over which this was taken, 11mrad is consistent with this value. (The LUT was reported at the standard theta=4, phi=40 deg.  theta=3, phi=30 deg returns 12mrad as a resolution).  Of note is that when they make the chromatic correction and only consider forward or backward going photons, they acheive ~7.9mrad, which is closer to the KDE performance.

 

These plots do not include tracking uncertainty.