Biomedical Engineering Reference
In-Depth Information
Table 11.3
Comparison of Resolution of Typical Nal, Gas, and
Semiconductor Detectors for
137
Cs Photons
Average Energy
Per Entity
Detector
Collected (eV)
Resolution (%)
Nal
767
8.0
Gas
30
1.6
Semiconductor
3
0.50
By comparison, for a gas proportional counter
W
=
30 eV per ion pair (Table 10.1).
The average number of electrons produced by the absorption of a
137
Cs photon in
agasis
662000/30
22100
. The resolution of the total-energy peak (other sources
of fluctuations being negligible) with a gas counter is
R
=
2.35/(22100)
1/2
=
=
0.016
.
For germanium,
W
=
137
Cs photons is
3
eV per ion pair; and the resolution for
2.35/(221,000)
1/2
R
0.0050
. A comparison of spectra measured with Nal and
with Ge was shown in Fig. 10.33.
Resolution improves as the square root of the average number of entities col-
lected. The preceding comparisons are summarized in Table 11.3. Note that the
resolution defined by Eq. (11.89) depends on the energy of the photons being de-
tected through the average value
µ
.
=
=
Example
For the scintillator analyzed in the example given after Fig. 10.30, it was found that
the average energy needed to produce a photoelectron was 155 eV. (a) What is the
resolution for the total-energy peak for 450-keV photons? (b) What is the width of the
total-energy peak (FWHM) in keV? (c) What is the resolution for 1.2-MeV photons?
Solution
(a) The average number of photoelectrons produced by absorption of a 450-keV
photon is 450,000/155
=
2900. The resolution is therefore by Eq. (11.89),
R
=
2.35/(2900)
1/2
= 0.0436.
(b) For 450-keV photons, it follows that FWHM
19.6 keV.
(c) Equation (11.89) implies that the resolution decreases as the square root of the
photon energy. Thus, the resolution for 1.2-MeV photons is 0.0436 (0.450/1.2)
1/2
=
0.0436
×
450
=
=
0.0267.
The resolution achievable in gas and semiconductor detectors is considerably
better (by a factor of about 2 to 4) than the Poisson limit implied by Eq. (11.89). The
departure of ionization events from complete randomness is not surprising in view
of the energy-loss spectrum for charged particles discussed earlier (Section 5.3).
Some energy is spent in excitations, rather than ionizations, and in overcoming
electron binding energies. Also, a typical energy loss of several tens of eV gives
a secondary electron enough energy to produce several more ion pairs in clusters
along a track. The Fano factor has been introduced as a measure of the departure of
