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Fig. 3.9.
Example of a spectrum
⎧
⎨
µ
j
X
i
0
−
Y
i
0
(
y
0
−
y
j
) f
Y
i
0
>ρ
;
Y
i
0
∆
y
0
=
=
i
⎩
0
otherwise
.
That initialization method appears to be very e
cient; convergence is
obtained in a few iterations (less than ten) [Pilato 1998].
3.5.6 Applied to Spectrometry
The application described below was performed in the Saclay Study Centre
[Pilato 1998]. It deals with the measurement of the concentration of radioac-
tive materials. The inspection of nuclear processing units (power plants, re-
processing factories) requires the measurement of concentrations of certain
radioactive materials. Concentration measurements are performed on solu-
tions from the water circuits of the plants. One of the techniques used is the
X-ray fluorescence, which enables fast, non-destructive analyses to be carried
out directly on sampling containers or pipes. X-ray fluorescence consists in
exciting the material of interest, and in analyzing the spectra of the photons
generated by deactivation.
Figure 3.9 shows an example of a spectrum obtained by X-ray fluores-
cence on a vessel containing Uranium 235 and Thorium. The peaks denote
the presence and concentration of those two elements. In our application, each
spectrum is quantized on 4096 energy values. Each value on the vertical axis
indicates to the number of photons counted for a given energy level.
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