Comparison of Simulation Data
with Calibration Data
Derek Hullinger
6 Feb 2004
I. Bottom Line:
The number of counts in the calibration data is about 42% higher than
the number of counts in the simulated data.
However, the predicted number of counts (from calculation) agrees with the
simulation to within 3%.
(The values and histogram plots given below were generated with this
IDL routine.)
II. Comparison of Spectra:
- Both data sets were processed using sum_spectra (and, for
comparison, using IDL to do the same thing).
- For both data sets, the following detectors were excluded:
- "bad" detectors (i.e., hot or
disabled detectors)
- edge (i.e., non-center) detectors
- detectors for which good linearity correction
factors are not known
- detectors for which μτ values are not known
- Before comparing the two, the calibration data was divided by a factor of 200
(to compensate for
the fact that the simulation source was 200 times weaker).
Results:
Calibration Data
Calibration Data (Scaled to 122 keV peak of Sim Data)
Simulation Data
At the 122 keV peak, the calibration data is about 50% higher than
the simulation data.
III. Comparison of Total Counts (above 20 keV)
- For the simulation and the calibration data, the total counts were found by
multiplying by the exposure time (1073 s) and adding up the counts in all bins
corresponding to energies greater than 20 keV.
- The total calibration data counts was divided by a factor of 200 (see above).
- The predicted counts above 20 keV was calculated for each detector as:
I122 / (4πr2) *
fPb,122 * fatten,122 *
Cos(θ) * A * CZT122 +
I136 / (4πr2) *
fPb,136 * fatten,135 *
Cos(θ) * A * CZT122
where
I122 is the number of 122 keV photons/s emitted by the source
in 4π
fPb,122 is the fraction of 122 keV photons that pass through any
lead tile that may be between the source and the detector.
fatten,122 is the fraction of 122 keV photons that pass through other
attenuating materials between the source and the detector (air is excluded).
CZT122 is the fraction of 122 keV photons that are absorbed in
a CZT detector.
Each value was then multiplied by the appropriate mask-weighting factor and
all values were added together (excluding those detectors that were excluded
during the processing of the simulation and calibration data).
The result was then divided by the sum of the squares of the
mask-weighting factors. These are the same steps that sum_spectra follows.
Results:
- Total Counts from Simulation (above 20 keV):
- 77.2 counts
- Total Counts from Calibration Data (above 20 keV):
- 109.4 counts
- Total Counts from Calculation (above 20 keV):
- 79.4 counts
The total counts from the calibration data is 42% higher than the total counts
from the simulation. This is pretty consistent with what is seen in the plot.
The total calculated counts is within 3% of the total simulation counts.
IV. Back-of-Envelope Calculation:
The source is located at x=-7.778, y=4.129, and z=294.4 (all in cm).
A fully illuminated detector directly below the source would be at r=294.4 cm.
The absorption efficiency in CZT of 122 keV photons is 0.61, and the absorption
efficiency in CZT of 136 keV photons is 0.49. The attenuation due to all of
the other passive materials (except air) for 122 keV photons is 0.955, and for
136 keV photons is 0.956.
Using a source photon rate of 8.25 x 105 122 keV photons/s and
1.045 x 105 136 keV photons/s,
the predicted counts is:
[(8.25 x 105)*/(4*π*294.4*294.4)*(0.955)*(0.16)*(0.61)+
(1.045 x 105)*/(4*π*294.4*294.4)*(0.956)*(0.16)*(0.49)]
*1073
=83.5 counts.
This agrees fairly very well with the predicted total counts above.
V. Comparison of Histograms:
Simulation Data
Calibration Data
Predicted Data
The peak positions in these background-subtracted histograms match the
totals above very well.
VI. Conclusions:
The difference between the simulation and the calibration data is large, but the
simulation matches the prediction very well—within 3%.
Since all background (i.e., scattered) photons were removed by the background
subtraction, the only reasons that the measurement would be higher than
the simulation (that I have thought of so far) are:
- In the actual experiment, there are materials present in the
immediate vicinity of the detectors and/or in the immediate vicinity of the source
which significantly contribute to the count rate but that are not included
in the simulation (these would not be removed by the background subtraction)
- The source activity is not what we think it is
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