Linearity of SiPM's (fwd from George)

[Elton Smith <elton@jlab.org>]

---------- Forwarded message ----------
Date: Tue, 14 Jul 2009 16:20:44 -0600
From: George Lolos <gjlolos@uregina.ca>
To: Hall-D Calorimetry <halld-cal@jlab.org>
Subject: Linearity of SiPM's

Hi all:

During yesterday's video conference on the preparations for the read
out review, the issue of SiPM non-linearity cane up.  The number of
occupied pixels, Nocc is given by the relationship:

Nocc = M x [1-exp(-PDE x Nph/M)]

where M = # pixels in the array (typically 58,240 for the 16 cell A35
type)
Nph =  number of photons incident
PDE = the array photo detection efficiency

Even in the completely unrealistic case of 10,000 photons incident on
a single SiPM array and an equally unrealistic case of 18% PDE, Nocc
= 1675.   Now, one has to compute the probability that two photons
are incident on the same pixel resulting in non-linearity.   The
number is well below 1%.

I hope this clarifies this issue.  One should also keep in mind that
the numbers are more likely Nph not more than 4,000 maximum and the
PDE something like 12%.

George