Time Shift Function

The function used to fit the pedestal data is an empirically determined function which combines a second order polynomial and a exponential tail:

$$\Delta t = (Ax = Bx^2)e^{-Cx}$$

This function is implemented in the FORTRAN function tsp_func_tslh.for, which begins by obtaining the parameters ($A$,$B$,$C$) for the fit from the TTSP titles bank. If all three parameters are zero, the original fit to the pedestal data either failed or the data did not exist, and in this case the parameters are replaced with those for Crate 0, Card 8, Channel 15, which was chosen to be a `typical' channel.

The function then checks to see if the TSLH passed to it is within the domain (taken here as 16 ns) over which the original pedestal delays ranged. If so, then the function obtains the time shift from the parameters it obtained from the titles bank (for either the true channel or the `typical' one).

If the TSLH is greater than 16 ns, then TSLH needs to extrapolate beyond this to get the time shift. The extrapolation is based on an exponential fit from (0,0) to (16 ns,$y$), where $y$ is the value of the fit to the data at 16 ns. The form of the exponential is such that the largest offset it will ever have is 17 ns.

In some cases, however, the value $y$ at 16 ns is positive, not negative, indicating that at the 16 ns end of the pedestal data there was still no real time shift. In this case, the time shift is set to 0 for all TSLH's beyond 16 ns.

Lastly, at least for now, the conversion between counts and ns is gotten by a hardwired slope of 10 counts/ns.