Initial Calibration of Large Timing Arrays for the LHC

In preparation for HL-LHC operation a number of new detector systems are being constructed with timing precision on physics objects of <50 picoseconds. These time stamps will reduce the level of pileup induced backgrounds in this LHC phase where the number of interactions per crossing will reach of order 100-200. In the case of CMS, three new systems have initially to be corrected for the usual amplitude walk resulting from the effect of variations in signal size on leading edge timing. In these systems the resulting timing spread (ie walk) ranges from one to four nanoseconds. In the following note we advocate approaching this initial calibration for walk as a calculable correction given early calibration during commissioning -- rather than depending on special collider data to perform the calibration. We derive a simple analytic expression for the walk correction and confirm its effectiveness with lab data.