Physics and Engineering of Radiation Detection

400 Chapter 6. Scintillation Detectors and Photodetectors

The overall signal-to-noise ratio from these measurements is then given by

S/N =

Ipe

σ^2 tot+σbg,d,amp^2

=

Ipe

σ^2 st+2

(

σ^2 bk+σ^2 d+σamp^2

)

=

Ipe

[2eμ^2 FB{Ipe+2Ibg+2Id}+8FampkBTB/Reqv]^1 /^2

. (6.5.37)

Except for the statistical fluctuations, all the noise sources described above are
instrumental in nature and therefore can be reduced by proper design and construc-
tion. for example decreasing the bandwidth of the readout circuitry improves the
signal-to-noise ratio. This can be done in practical system provided it does not affect
the dynamic range of the system.

Example:

Determine the fluctuations in the dark current of 1nAfrom a PMT having a

gain of 10^4. The PMT is built with 6 dynodes and the system bandwidth is

50 Hz. Assume that the PMT noise figure is unity.

Solution:

Substituting the given values in equation 6.5.29, we get

σd = μ

√

2 eIdFB

=10^4

[

(2)

(

1. 602 × 10 −^19

)(

10 −^9

)

(1)(30)

] 1 / 2

=9. 8 × 10 −^10 A

=0. 98 nA.

Apart from the signal-to-noise ratio, another parameter that is widely used to
characterize the noise level of PMTs is theequivalent noise inputorENI.Itrepre-
sents the amount of light necessary to produce a signal-to-noise ratio of unity.ENI
is mathematically defined as

ENI=

1

Sl,a

[2eIdμB]^1 /^2 , (6.5.38)

whereSl,ais the anode luminous sensitivity inA/lm,Idis the anode dark current
in amperes,μis the tube gain, andBis the bandwidth of the system. The dark
current can easily be determined by measuring the tube output without any light
input, not even the background light. For that the tube is generally kept in darkness
for some time (a few minutes wait normally suffices) before measuring the output
current.

A.18NoiseinDigitalMode

In digital mode the requirements on the noise are not as stringent as in analog mode.
The reason is that in this mode the number of output pulses are counted in contrast