Chemistry Reference
In-Depth Information
than 10 percent. That means the term R
m
t should be less than 0.1. The counting loss
DR is then given by
R
2
m
t
1 R
m
t
DR ¼ R R
m
¼
ð4
:
8Þ
The percentage counting loss is given by
D
R
R
¼ R
m
t
ð4
:
9Þ
A detector can be categorized as having either nonparalyzable dead time or
paralyzable dead time. The counting curve C represents the behavior of a detector
with nonparalyzable dead time. That means that the detector is dead for a fixed time
after each count, but not influenced by the counts occurring during the dead time.
The counting loss increases with increasing count rate, but the true count rate of a
detector with nonparalyzable dead time can always be estimated by Eq. (4.7) until the
true count rate reaches infinity, when the maximum observed count rate is equal to the
inverse of the dead time. In a paralyzable detector, as is shown by counting curve D,
a second count after each observed count will not be collected unless after an time
interval at least equal to the dead time. Any event that occurs during the elapsed
time will extend the dead time further for an additional dead time. With increasing
count rate, the counting loss increases so dramatically that the detector will reach
a maximum count rate (saturation point) where it will be incapable of collecting
any counts at all. At this saturation point, the true count rate reaches the inverse of the
dead time
1
t
R ¼
ð4
:
10Þ
The observed count rate at the saturation point based on Poisson distribution is
then given by
1
et
R
m
¼
ð4
:
11Þ
The counting curve E represents the behavior of a detector with semiparalyzable
dead time. When the count rate approaches saturation, the observed count rate
decreases with increasing incoming flux. In practice, the maximum count rate of a
detector may be defined as the count rate at a specified counting loss, for instance,
5 percent.
4.3.4 Energy Resolution
The energy resolution of a detector is its ability to resolve X-ray photons of different
energy (or wavelength). The transducer and the electronics as well as its specific
setting in a detector can be considered as having an energy window or multiple energy
windows if a multichannel analyzer (MCA) is used. The energy window allows only
the signals generated fromX-ray photons within a specific energy range to be counted.
The energy resolution of a detector can be expressed in many formats with a variety
