The Timing of the Tile Calorimeter using laser events

The time reconstruction of the events in the Tile Calorimeter using a differential algorithm is discussed in this note. The laser pulses acquired during August 2001 and June 2002 test beam periods, have been used to extract the corrections due to the effect of the propagation of the TTC clock signal. The delay introduced by each digitizer board on the TTC clock propagation turns out to be about 2--3 ns, while the precision of the time reconstruction after the correction of the TTC clock propagation is about 0.5 ns. This timing algorithm is then applied to muon events. The comparison of the speed of a muon impinging on the barrel module at 90 degrees (the speed of the light) and the speed computed using the timing algorithm can be used as a check for the timing of all the channels of the barrel module. The computed speed of the muons turns out to be compatible with c.