Re: Linearity of SiPM's (fwd from George)

[Eugene Chudakov <gen@jlab.org>]

Sure, I used 58000 for the full number of pixels. 
The number 5480 is the number of the pixels fired by 32000 photons, 
or, one may say, by 5760 photoelectrons.

Eugene

On Fri, 17 Jul 2009, George Lolos wrote:

> Hi Eugene:
>
> The number of pixels in the 16-cell A35 SensL array is 58, 240 NOT 5480! 
> That's a huge difference!
>
> George
>
> On 16-Jul-09, at 6:04 PM, Eugene Chudakov wrote:
>
>> Hi,
>> I would like to discuss the numbers again. George wrote:
>>> 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.
>> 
>> The maximum photon energy the BCAL can see in GlueX is 2 GeV, released
>> in the most downstream part. Let us take the Elton's normalization of
>> 1e4 photons/side/1.GeV for showers at the BCAL center. Such a shower
>> at the downstream end will make 2e4 photons/side/1.GeV.  From the
>> Irina's calculations I see that for 0.2 GeV photons at 20 degrees, the
>> maximum energy per a calorimeter cell (the fibers only) is 20 MeV.
>> The full energy for the cell is 20MeV/0.12=160MeV. So, there are cases
>> when nealy all the energy of the shower is absorbed in one cell. For
>> 10 deg photons, the maximum energy might be a factor of 2 higher. On
>> the other hand a 2 GeV shower is deeper, so I assume that for a 2 GeV
>> shower at 10 deg the maximum energy is 160MeV*2000MeV/200MeV=1600MeV.
>> The number of photons is 1600MeV/1000MeV*2e4=32000 (about 3 times
>> higher than the George's upper limit) . The PDE*packing_factor is
>> about 0.18 (Hamamatsu).  This makes 5760 photoelectrons. The
>> number of pixels fired is 5480 (see the formula in the George's
>> mail). The non-linearity correction is 5760/5480=1.05. Let us assume
>> that the detector is calibrated at 500MeV. The appropriate correction
>> is 1.2%. So, we will have a 4% shift at 2 GeV. At 2 GeV one expects a
>> resolution of about 4%. So, the shift is not negligible. It can be
>> corrected well, unless we combine several SiPMs to one ADC. One should
>> point out that at 8 GeV the correction would be about 15%. In general,
>> such a limitation is annoying, since the calorimeter itself can cover
>> a much wider energy range.  Still it seems to be good enough for
>> GlueX.
>> 
>> Eugene
>> 
>> ------------------------------------------------------
>> Eugene Chudakov
>> http://www.jlab.org/~gen
>> phone (757) 269 5352  fax (757) 269 5703
>> Thomas Jefferson National Accelerator Facility
>> 12000 Jefferson Ave, Suite #4
>> Newport News, VA 23606 USA
>> 
>> On Thu, 16 Jul 2009, Elton Smith wrote:
>> 
>>> 
>>> 
>>> ---------- 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
>>> 
>