Physics and Engineering of Radiation Detection

402 Chapter 6. Scintillation Detectors and Photodetectors

separate the data into the three components. What is done instead is to perform the
measurements in two steps. In the first step the counts without any light source are
accumulated for a certain period of time. This gives the counts due to background
light and dark current only. That is

Nbg,d=Nbg+Nd. (6.5.44)

In the second step, the PMT is illuminated with light and the counts are recorded
for the same period of time. This gives the total counts due to all the noise sources
and the incident light, that is

Ntotal=Nst+Nbg+Nd. (6.5.45)

The counts due only to the incident light can then be obtained by subtractingNbg,d
fromNtotal.
Nst=Ntotal−Nbg,d (6.5.46)

Now, the two measurements performed have their own noise levels given respectively
by

σbg,d =

√

σbg^2 +σ^2 d

=

√

Nbg+Nd and (6.5.47)

σtotal =

√

σst^2 +σ^2 bg+σ^2 d

=

√

Nst+Nbg+Nd. (6.5.48)

The signal-to-noise ratio for the measurements will then be given by

S/N =

Nst

√

σ^2 tota+σ^2 bg,d

=

Nst

√

Nst+Nbg+Nd+Nbg+Nd

=

Nst

√

Nst+2(Nbg+Nd)

. (6.5.49)

Example:

A PMT working in the digital records dark and background counts of 5× 104

and 1. 5 × 102 respectively. Compute the total fluctuations due to these two

noise sources.

Solution:

The shot noise due to the dark counts is

σd =

√

Nd

=

√

5 × 104

= 223. 6.