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



Hi George,

I wanted to make sure that I understand the effect.

On Fri, 17 Jul 2009, George Lolos wrote:

> If a photon goes downstream at 10 deg it will miss the BCAL.  Realistically, 
> any photon at 12 deg or less will have a partial deposition in the BCAL.

I put an approximate value of 10 deg. Let it be 12 deg. I pointed out
that at 10 deg a BCAL cell is about twice thicker than at 20 deg.
The BCAL center is located at about 20 deg.

>
> The non-linearity is determined by the probability of a photon, out of the 
> 30k in your assumptions, to impinge on a pixel that has already detected one 
> photon and create a second avalanche within the "avalanche time" of the 
> first.  If 5480 pixels have fired what is now the probability that photons 
> will fire a fraction of the same pixels when another 50000 pixels occupy the 
> sensor area?   The occupancy of the pixels among 54000 available pixels is 
> 5480 and it's this ratio that dominates the non-linearity calculations.
>
> Am I missing something in the calculations?
>

I wanted to make three points. 
The first is that the maximum number of photons a shower can produce
per one SiPM detector in GlueX is about 32k.  This makes 5760
"photoelectrons", which fire 5480 pixels.

The second point is the impact of the non-linearity on GlueX.
The effect of non-linearity depends on the application. For example, for
small asymmetry measurements, the measured value is the true asymmetry
times a factor, which is a ratio of the relative increment of the response 
to the relative increment of the signal (which causes this increment of 
the response). In our case the factor would be 5760/5480*(1-5480/58000)=0.95
It is a 5% distortion of the asymmetry. At GlueX, the situation is slightly 
more complex, since we need to measure the energy of, say 2 GeV showers,
with a detector calibrated at, say, 0.5GeV. This leads to an energy
distortion of about 4%. It does not seem too bad, in particular since
the effect can be partially compensated off-line.

The third point is a trivial comment that these SiPMs have limitations
as a generic photodetector for calorimeters, in contrast with the PMTs
or even the APDs...

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 Fri, 17 Jul 2009, George Lolos wrote:

> Hi Eugene:
>
> I have some difficulty with your calculations and some of the assumptionsL
>
>
> 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.
>
> If a photon goes downstream at 10 deg it will miss the BCAL.  Realistically, 
> any photon at 12 deg or less will have a partial deposition in the BCAL.
>
>> 
>> 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.
>
> The non-linearity is determined by the probability of a photon, out of the 
> 30k in your assumptions, to impinge on a pixel that has already detected one 
> photon and create a second avalanche within the "avalanche time" of the 
> first.  If 5480 pixels have fired what is now the probability that photons 
> will fire a fraction of the same pixels when another 50000 pixels occupy the 
> sensor area?   The occupancy of the pixels among 54000 available pixels is 
> 5480 and it's this ratio that dominates the non-linearity calculations.
>
> Am I missing something in the calculations?
>
>> 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
>>> 
>