Determination
of photoelectron yield 
The pulse height distribution from a photomultiplier tube (PMT) observing
light pulses from a scintillator has its qualitative features determined
by:
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quantum limitations imposed by the light output from the scintillator and
the quantum efficiency of the PMT. In general, these limitations
result in a Poisson distribution of photoelectrons (p.e.) emitted by the
photocathode of the PMT.
-
the PMT response, specifying the pulse height distribution when M p.e.
are emitted by the photocathode of the PMT. In general, the pulse
height distribution for a specific number of p.e. is Gaussian.
The resulting pulse height distribution from the PMT can be described by
a convolution of a Poisson distribution, specifying the number of p.e.
produced in a single event, and a Gaussian distribution, specifying the
PMT response to M p.e.. It is assumed for the latter that the normalization
of the Gaussian distribution is given by Poisson statistics, the centroid
of the Mth p.e. peak is given as M C1 (where C1
is the centroid of the single p.e. peak), and the squared sigma of the
Mth p.e. peak is given as M S12 (where
S1 is the sigma of the single p.e. peak).
Although there are potentially many effects (electronic non-linearities,
etc.) that can impact this simple description, we have found that pulse
height distributions from PMT recording small light yields from scintillators
can be quantitatively described as a convolution of a Poisson distribution
with Gaussian distributions specifying the PMT response. Hence, the
measured pulse height distribution can be analyzed to yield the following
parameters:
-
the normalization of the Poisson distribution (N).
-
the mean value of the Poisson distribution (mu), specifying the average
number of p.e. produced.
-
the centroid of the single p.e. peak (C1), specifying the gain
of the PMT.
-
the sigma of the single p.e. peak (S1), specifying the resolution
of the PMT.
This quantitative description has been used to ascertain the yield of p.e.
from scintillator tiles and strips for the STAR endcap electromagnetic
calorimeter (EEMC) project. An example of such an analysis is shown
below. In this case, the goal is to determine the transverse
uniformity of the light output from a 5-mm thick SCSN-81 scintillator
tile comprising one layer of an EEMC tower. The tile is excited by
energy deposited by electrons emitted from a collimated 90Sr source fixed
at one position relative to the scintillator tile. Scintillation
light from the tile is collected by a 0.83 mm diameter wave-length shifting
(WLS) optical fiber, produced by Kuraray. The WLS fiber is inserted
in a sigma groove within the scintillator tile. The end of the fiber
within the sigma groove is mirrored, and the free end is attached to a
Burle 83101 PMT. The PMT current is integrated when the trigger scintillator
produces a current pulse above threshold.
The pulse height distribution from the trigger scintillator is shown
in the bottom right pixel of the figure. The distribution reflects
the continuous energy spectrum of electrons emitted in the beta decay of
90Sr. The remaining three pixels show the pulse height distribution
from the scintillator tile, for each of three trigger pulse height intervals.
Visible in each pixel is a peak at low pulse height, corresponding to the
PMT response to a single p.e.. The ADC pedestal peak (having a width
less than a single channel) is off scale to the left in each pixel.
A single fit is performed simultaneously to the three distributions so
that they are described by common Gaussian parameters specifying the single
p.e. response. Each distribution is fitted by independent Poisson
distributions described by the parameters (N, the normalization, and mu,
the p.e. yield). As determined by the goodness of fit parameter,
a quantitative description of the distributions is obtained. Similar
results are found for all data obtained from the transverse uniformity
scan of the scintillator tile.
Last Updated 26 June 2000
by LCB