Physics and Engineering of Radiation Detection

3.8. Detector Efficiency 213

The signal-to-noise ratio will then be given by

SNRin =

Sin

√

Sin

=

√

Sin. (3.8.12)

Example:

A detector is exposed to a photon fluence of 10^5 cm−^2. If the detector’s

window has a radius of 3cm, calculate the input signal-to-noise ratio.

Solution:

The number of photons seen by the detector are

Sin =(Φ)

(

πr^2

)

=

(

105

)(

π 32

)

=2. 83 × 106 photons.

The expected noise from this signal is given by

Nin =

√

Sin

=

√

2. 83 × 108

=1. 68 × 103

The input singal-to-noise ratio is

SNRin =

Sin

Nin

=

2. 83 × 106

1. 68 × 103

= 1683.

The output signal-to-noise ratio is defined in a similar fashion but now the signal
represents the actual particles seen by the detector and the noise includes all the
sources of noise in the detector. If detetor’s quantum efficiency isQE, the output
signal is given by
Sout=(QE)(Sin). (3.8.13)
The output noise includes statistical noise inSoutas well as readout noise of the
system, that is

Nout =

[

σ^2 stat+σrout^2

] 1 / 2

(3.8.14)

=

[

Sout+σrout^2

] 1 / 2

=

[

(QE)(Sin)+σrout^2

] 1 / 2

. (3.8.15)

Note that here readout noise includes all the noise sources in the detector and not
just the electronics noise.