More on pileup

I've discussed the problem of pileup before, so I'd like to briefly discuss one method for getting rid of pileup in the analysis phase of an experiment.

In the first, if the hardware has sufficient time resolution to reliably separate two events with a time separation of $n$ nanoseconds, one form of analysis, called shadowing, creates a 'window' of $2n$ nanoseconds centered on the time at which the detector reached a maximum. The principle is that statistically, we are just as likely to see another event inside this window as in the $n$ nanoseconds on either side of the window (the "wings").

My attempt to create a schematic for the shadowing
method of pileup analysis.
Note: this isn't at all what any sort of detector pulse looks like. 

In the schematic above, the blue curve is the pulse shape received by the calorimeter (no, it's actually a terrible approximation in Mathematica). The maximum is fairly obvious. The window is the light green area, and the wings are the dark green area. As I understand it, the analysis looks at all of the calorimeter signals a certain length of time after time zero in each event. By looking at the number of pulses within the wings, analysts can get a good prediction for the number of pulses within the windows, which correspond to pileup that weren't separated by the temporal resolution. Repeat that analysis for many other times after time zero, and you have a profile of pileup over the course of each event.

This form of analysis may not tell you which events in particular experienced pileup, but it allows analysts to determine the overall energy profile of the particles detected, which is what they cared about in the first place. All in all, a success for physicists.