Physics and Engineering of Radiation Detection

6.5. Photodetectors 401

with analog mode where actual pulse heights are measured. In digital mode one
generally uses a discriminator at an early stage of the electronics, with the purpose
of deciding which pulses are to be blocked. The discriminator generally has a lower
and an upper threshold. The lower threshold is set to discriminate the noise pulses
from the rest while the upper threshold has the purpose of eliminating spurious large
pulses. The working principle is quite simple: only the pulses with heights within
the lower and upper thresholds are allowed to pass through and get counted. All
other pulses are simply rejected. In this waymostof the noise is simply rejected at
an early stage no matter what its origin is andmostof thegoodpulses are allowed
to pass through and counted. The reason why not all noise can be rejected in this
manner lies in the uncertainty associated with the noise level. Complete rejection
of noise would require the lower discriminator threshold to be set too high and
upper discriminator threshold to be set too low, which would result in rejection of
significant number of good pulses too. The settings of the discriminator are therefore
based on a compromise between the acceptable signal-to-noise ratio and the count
rate.
Except for the Johnson’s noise, all the other noise components we discussed earlier
for the analog mode can be defined for the digital mode as well. However now the
shot noise values can be determined by simpler relations due to the digital nature
of the readout.

Statistical Fluctuations:Due to the statistical nature of photoelectric and

electron multiplication processes, there is always some uncertainty in the num-

ber of counts detected. The shot noise attributable to this uncertainty can be

obtained by noting that the process is Poisson in nature. Hence, the statistical

noise counts are given by

σst=

√

Nst, (6.5.39)

whereNstrepresents the number of counts due to incident light only.


Background Light: IfNbgrepresents the counts due to background light

only, the shot noise component due the uncertainty associated with it can be

obtained from

σbg=

√

Nbg. (6.5.40)

Dark Counts:The shot noise component due to dark countsNdis given by

σd=

√

Nd. (6.5.41)

The total shot noise due to all sources in digital mode is then given by

σt =

√

σ^2 st+σbg^2 +σd^2

=

√

Nst+Nbg+Nd. (6.5.42)

And the signal-to-noise ratio will be

S/N=

Nst

√

Nst+Nbg+Nd

. (6.5.43)

Though this is a simple relation, however using it requires one to know the counts
due to all the three noise sources individually. Practically, it is extremely difficult to