A Classic Thesis Style - Johannes Gutenberg-Universität Mainz

100 prototyping and efficiency measurements
Accidental coincidence rate (Hz)
6
10
5
10
4 10
3
10
2 10
Eff. > 90%
Eff. > 94%
Eff. > 98%
0.8 1 1.2 1.4 1.6 1.8 2
Fiber thickness (mm)
Figure 64: Numerical calculation of the accidental coincidence rate vs. fiber
thickness, for matching detector area, when a detection efficiency
larger than 90 % (full line), 94 % (dashed-dotted line), and 98 %
(dashed line) is demanded. A quadratic increase in the rate proportional
to the active area of the SiPM can be observed before a light
level is reached where the threshold can be increased by one unit
(single pixel amplitude) reducing abruptly the noise rate. For a
given detection efficiency a minimum fiber thickness is necessary.
zero pixel cross-talk probability, P(0) = exp(−λ), was calculated by
considering the number of events in the pedestal. This value was
compatible with the one measured with a square fiber of 4 mm 2 crosssection.
It is important to stress that in general the number of fired
pixels does not follow a Poisson distribution due to optical cross-talk
and after-pulsing. Nevertheless, the mean number of detected photons
is correctly calculated with this expression as these effects only appear
when at least one pixel has been fired.
Fig. 64 shows the calculated accidental coincidence rate as a function
of fiber thickness assuming a matching area for the SiPM when a
detection efficiency higher than 90 %, 94 %, and 98 % is required. It is
seen that after each sharp drop of the noise level, when an increase of
one unit in the threshold is achieved, there is a region in which the rate
increases quadratically as the SiPM area does. Despite the fast increase
in the accidental coincidence rate it is apparent that an adequate fiber
thickness will result in an almost silent detector. A similar behavior
appears when the bias voltage is increased: the PDE increases linearly
while the dark count rate shows an exponential dependency, compare
to Figs. 58 and 62 for an experimental measurement of these quantities.
In addition, the optical cross-talk probability also will rise linearly. The
steps are consequently less pronounced. One should conclude, that
when signal pile-up can be neglected higher voltages are preferred for
high efficiencies.
One needs to consider that path length dispersion and the decay
time of the emitted photons reduce the effective pulse height and will
have an effect on the efficiency for a detector based on long scintillating
fibers. The spread of propagation times is given for a fiber of
length L and refractive index n by ∆tprop = (Ln/c)(1/ cos θmax − 1)