[Halld-cal] Linearity requirements / dynamic range

[Elton Smith]

HI George,

I agree with your discussion below. But here are a few more comments:

1. fraction of energy deposited in various segments. Plots can be found in
Andrei's GlueX-doc-1474. Also useful discussion/information can be found
in the meeting notes from the cal working group meeting of May 27
http://www.jlab.org/Hall-D/software/wiki/index.php/May_27%2C_2010_Calorimetry.

These show that to cover extremes, a single SiPM can receive 60-80% of the
entire shower energy, although typically it is less.

2. Non-linearity at higher energies. You indicate the non-linearity of
about 3% at 1 GeV. This is at the center of the module. For asymmetric
detection at forward angles, numbers are larger. Also, there is also
potential physics interest in, e.g. J/Psi physics, which can produce 5 GeV
electrons in the Bcal. The non-linearity then grows to about 15% or more.

Clearly relevant questions are whether a) this requires calibration b)
to what accuracy can the calibration be performed, especially relative to
simple calculation of the corrections. These certainly need to be
considered and discussed quantitatively.

Cheers, Elton.




On Mon, 13 Dec 2010, George Lolos wrote:

> Hi guys:
>
> I have been thinking again about the perceived need for linearity
> measurements capability in the calibration system.  Let's look at the
> numbers a bit more carefully and, please, correct me if I am wrong:
>
> Nocc = M x [1-exp(-PDE x Nph/M)]
>
> Where:   Nocc is the number of pixels occupied by processing incident
> photons
>
>                  M is the number of pixels in the array
>
>                  Nph is the number of incident photons
>
> The ratio, then, of Nocc/M is the degree of non-linearity.   For
> example, if M= 56,000 pixels, PDE is 0.20 and Nph ~ 50,000 per side
> per GeV, we get Nocc/M ~ 8.5%, assuming that ~20,000 photons go into
> only one array.  So, the number of ~10% non-linearity that Elton often
> quotes is in the right ball park.  So, the calculations are correct
> but is the input correct?
>
> Let's start with the 56,000 ph/side/GeV.  This number comes out of
> Andrei's calculations based on the number of p.e.'s we get from the
> fibers using the Sr90 source and Irina's simulations of the energy
> deposition in the matrix.  However, these numbers were obtained with
> naked fibers, where the full effect of the outer cladding comes into
> play.  In the BCAL, the fibers trap the light in the region between
> the core and the first to second cladding volume, so the trapping
> efficiency will be reduced.  We will know the number of effective
> photons trapped in the BCAL when we get the cosmic ray measurements
> done.  In any case, the number will be less.
>
> Now come the really significant assumptions:
>
> Even at oblique angles (less than 20 degrees) is it reasonable to
> expect that all the photons on one side will go into a volume confined
> in two dimensions within 2 cm x 2 cm?  I have a difficult time
> accepting this and perhaps a real simulation of the shower generated
> by 1 GeV photon randomly distributed across the 2 cm width of a read-
> out cell will give us better answers.  The Moliere radius alone is
> over 3 cm so spill over will occur even if the photon was incident
> dead center on a read-out cell.  So, how many photons will be
> generated in a read-out cell as a fraction of the total energy
> deposited in the BCAL?  We need a better result to draw conclusions on
> this.
>
> Even if we take the 56,000 photons per side per GeV, this number
> corresponds to the number of photons arriving at the interface of the
> BCAL with the light guide.  Here one has to start counting losses:
> losses crossing the glued interface from fibers to light guide.  Then,
> and this is a significant number, losses from end of light guide to
> the SiPM.  Unless I recall wrong, our measurements here between
> physical contact with Si grease between light guide and PMT, on one
> hand, and air gap on the other, the latter was around 50% of the
> former.  In other words, just by the air gap we lose about 50% of the
> light.   So, the realistic maximum number of photons reaching
> photosensors per side per GeV is much closer to 20,000 than to
> 56,000.  If half of them are confined within the volume of one read-
> out cell (one SiPM), then Nocc/M  is ~ 3.5%.
>
> Is such non-linearity an issue to try and monitor if it means more
> complicated calibration system?
>
> George
>
>