
Measurement Principle
Gamma-Ray Absorption
Radiometric level measurement relies on
the fact that gamma rays are absorbed
as they penetrate a material. The
attenuation of the radiation is dependent
upon the density ρ, the thickness d of
the material as well as the linear
absorption factor µ. This in turn is
dependent on the material and gamma
source. The attenuation is calculated
from the formula
Fs= e µ . ρ . d
The radiation also decreases with the
square of the distance between source
and detector.
Limit Detection
For limit detection µ, and d are
constants and the detected radiation
level depends upon the presence or not
of the penetrated material:
•The countrate is at a maximum when
the path to the detector is completely
free and
•at a minimum when all the radiation
has to travel through the material and
is attenuated.
The maximum and minimum countrates
Nmax and Nmin are obtained when the
transmitter is calibrated, whereby their
dependency is given by:
Nmin = Nmax e−µ . ρ . d
The switch points can be set anywhere
within these two countrates, which are
normalised to produce the end values 0
and 100.
Radiation Statistics
The emission of gamma rays by a
radioactive source is governed by the
laws of statistics. For this reason the
measurement precision of gamma
systems is dependent on the statistical
variation in countrate. The variance, i.e.
the degree of variation between
measurements, depends upon the time
interval chosen. The precision of the
measurement depends on the chosen
confidence level - 1σ, 2σor 3σ. For a
countrate of N pulses per second:
•σ=N;±68.28 % confidence
level
•2= 2N;σ± 95.48 % confidence level
•3= 3N;σ± 99.74 % confidence level
Normally, a confidence level of 2σis
used. The statistical variation can be
reduced by increasing the sampling or
integration time τ:
Statistical variation =2N±
τ
For limit switching the integration time
corresponds to the response time of the
relay.
Background Functions
The Gammapilot FTG 671 is equipped
with a number of background functions
which ensure accurate and reliable limit
switching. Thus, for example, the
statistical fluctuations in countrate and
decay of the gamma source described
above are accounted for without any
action on the part of the operator.
After calibration, the FTG automatically
sets the switch points to preset values. It
warns the operator if incorrect limits are
entered, and when the activity of the
source is no longer sufficient for reliable
switching.
3
Statistical fluctuation
in countrate
Change in countrate
as product moves
through barrier
Countrate due to residual
and background
radiation
time
Countrate
Nmax
Nmin
1000
Principle limit detection
by gamma radiography