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

[Elton Smith <elton@jlab.org>]

---------- Forwarded message ----------
Date: Fri, 17 Jul 2009 09:56:16 -0600
From: George Lolos <gjlolos@uregina.ca>
To: Eugene Chudakov <gen@jlab.org>
Cc: Hall-D Calorimetry <halld-cal@jlab.org>
Subject: Re: Linearity of SiPM's (fwd from George)

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
>>