One table gives the distribution of the mean number of photoelectrons expected as a function of the position and orientation of an OM relative to a muon track, and the other gives the time delay distribution of photoelectrons as a function of the same variables. Once the tables are compiled, events can be simulated quickly by locating the OM relative to any input particle and looking up the expected number and time distribution of photoelectrons in the tables. In an ideal medium without scattering, and with gaussian timing errors, one could in principle reconstruct the path of a muon by a minimization process. Because there is residual scattering in the ice, the distribution of arrival times of photoelectrons seen by an OM from a muon is not gaussian, but has a long tail on the high side. The correct method to use with nongaussian timing errors is likelihood analysis, which is more robust and much less sensitive to outliers.
Reconstruction proceeds by a multistep process.
First, a 0th order guess is made by a simple line fit. Finally, quality criteria are used to reject badly fit events. The most important quality criterion is , the number of OMs that are hit within 20 nsec of the time expected for unscattered Cerenkov photons from the fitted track. The requirement that provides our single strongest cut for elimination of misreconstructed downgoing muons.