Ba-133 Count Rates Taken with FSW:
Measured vs. Predicted
Derek Hullinger
6 Aug 2004
Bottom Line First:
For the 31 and 35 keV lines together, the measured rates are about 37%
lower than the predicted rates.
For the 53 and 80 keV lines together, the measured rates are about 11%
lower than the predicted rates.
For all four lines together, the measured rates are about 30%
lower than the predicted rates.
Data sets examined:
- fg_1_10_40.dpi and fg_1_40_90.dpi
- fg_2_10_40.dpi and fg_2_40_90.dpi
- fg_3_10_40.dpi and fg_3_40_90.dpi
- fg_4_10_40.dpi and fg_4_40_90.dpi
- fg_5_10_40.dpi and fg_5_40_90.dpi
- fg_6_10_40.dpi and fg_6_40_90.dpi
- fg_7_10_40.dpi and fg_7_40_90.dpi
- fg_8_10_40.dpi and fg_8_40_90.dpi
- fg_10_10_40.dpi and fg_10_40_90.dpi
- fg_11_10_40.dpi and fg_11_40_90.dpi
- fg_12_10_40.dpi and fg_12_40_90.dpi
- fg_13_10_40.dpi and fg_13_40_90.dpi
- fg_14_10_40.dpi and fg_14_40_90.dpi
- fg_15_10_40.dpi and fg_15_40_90.dpi
- fg_16_10_40.dpi and fg_16_40_90.dpi
- fg_17_10_40.dpi and fg_17_40_90.dpi
- fg_18_10_40.dpi and fg_18_40_90.dpi
- fg_19_10_40.dpi and fg_19_40_90.dpi
- fg_20_10_40.dpi and fg_20_40_90.dpi
- fg_21_10_40.dpi and fg_21_40_90.dpi
- fg_22_10_40.dpi and fg_22_40_90.dpi
- fg_23_10_40.dpi and fg_23_40_90.dpi
- fg_24_10_40.dpi and fg_24_40_90.dpi
(from /local/data/gcn5a/jayc/fg_031130/)
Each dpi was created from survey data accumulated with a Ba-133
source placed on the ceiling of the clean tent
(at a height of 474.9 cm above the detector plane). The first file in
each row includes counts between 10 and 40 keV, and the second file
includes counts between 40 and 90 keV. The exposure times range from
600 s to 1000 s for each dpi.
I) Procedure (Measurement):
For each of the above data sets:
- ran bathotpix to generate a "good map" file for each dpi
example command:
bathotpix fg_1_10_40.dpi fg_1_10_40.mask2 chatter=2
- combined the "good map" file from the low-energy dpi with the "good map"
file from the high-energy dpi using combine_goodmaps
example command:
combine_goodmaps fg_1.mask2 fg_1_10_40.mask2 fg_1_40_90.mask2
- ran batfftimage to produce a "sky" image for each dpi
example command:
batfftimage fg_1_10_40.dpi fg_1_10_40.img attitude=NONE
detmask=fg_1.mask2 bat_z=474.9
- ran batcelldetect to find source position
example command:
batcelldetect fg_1_10_40.img fg_1_10_40.src 6.0
- ran batclean to remove background from each dpi
example command:
batclean fg_1_10_40.dpi fg_1_10_40.dpi_clean fg_1_10_40.src
detmask=fg_1.mask2 srcclean=YES outversion=bkgcleaned
Measured Count Rate (For Each Detector):
C: counts from the "cleaned" dpi (*.dpi_clean)
t: exposure time for the data set
The average deadtime per sandwich was only about 1.4% of the exposure time,
so I neglected the deadtime correction.
The exposure time was obtained by summing up the gti intervals from the
dph used to generate each dpi.
When comparing the the count rates for all four lines, I added together
the background-subtracted (i.e., "cleaned") low-energy dpi and high-energy
dpi.
(See the IDL routine for details)
II) Procedure (Calculated):
Predicted Count Rate (For Each Detector):
Low-energy Lines:
High-energy Lines:
S: The number of photons/s emitted
by the source into 4π
Source used: Ba-133-037
According to Nadine’s calibration report (calibhigh.xls), on 6/27/03
these rates were:
S31 = 2.96 x 107 photons/s
S35 = 6.53 x 106 photons/s
S53 = 5.53 x 105 photons/s
S80 = 9.85 x 106 photons/s
on 11/30/03, these rates would have been lower by a factor of
(1/2)^(156/3839) (=0.972), making them:
S31 = 2.88 x 107 photons/s
S35 = 6.35 x 106 photons/s
S53 = 5.38 x 105 photons/s
S80 = 9.58 x 106 photons/s
r:
distance from the source to the detector
Photons/s/cm2 incident on a fully-illuminated detector at a distance r from the source.
fatten:
fraction of photons that are transmitted through the passive materials
between the source and the detectors (not including the lead tiles)
fillum:
fraction of the photons that are transmitted through the mask
for fully illuminated detectors, this is 1
for fully masked detectors, this is the transmission of the photons
through the lead tile
for a partially-illuminated detector, it is a number between the two
The cleaning process removes un-modulated counts, so the prediction must do
that, too. This is done by subtracting from each illumination fraction
the transmission of photons through a lead tile onto the center of the array.
Aeff: Effective area of the detector
0.16 cm2 * QE * (Cosine Correction Factor) * (fraction of
depositions above 17 keV)
QE = the quantum efficiency of a detector at a particular photon energy and
at a particular angle
At 31 keV: QE = 1-exp(-107*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1
(for the on-axis case)
At 35 keV: QE = 1-exp(-152*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1
(for the on-axis case)
At 53 keV: QE = 1-exp(-50.6*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 1
(for the on-axis case)
At 80 keV: QE = 1-exp(-16.4*0.2/cos(atan(sqrt(x*x+y*y)/z))) ≅ 0.96
(for the on-axis case)
The Cosine Correction Factor is:
cos(atan(sqrt(x*x+y*y)/z))+
min(0.15,0.05*abs(z/x))*cos(atan(sqrt(y*y+z*z)/x))+
min(0.15,0.05*abs(z/y))*cos(atan(sqrt(x*x+z*z)/y))
The edge model included in this factor only applies to
non-leading-edge detectors. For
that reason, only center detectors are used in the
comparison.
x, y, and z are the x-,y-, and
z-distances from the source to the detector
Fraction of Depositions above 17 keV:
At 31 keV, the escape peaks are at 4 keV and 8 keV.
At 35 keV, the escape peaks are at 8 keV and 12 keV.
In both cases, the escape peaks lie below the 17 keV cutoff in the data,
so they should not be included in the calculation.
Based on monte carlo simulations, it turns out that at 31 keV, 13.5% of all
photo-electric energy depositions
result in escape peaks, and at 35 keV, about 21% result in escape peaks.
(See the IDL routine used to generate
the predicted count rate for each detector)
III) Results:
Plotted here are histograms from 3 of the 23 runs.
They show the measured count rates
and predicted count rates from all
of the "good" detectors in each run. Only center detectors
are included in the histograms.
black: histogram of predicted rates
red: histogram of measured rates
The predicted rates are all systematically higher than
the measured rates. After the plots, there is a table that compares these
peak rates.
fg_1:
back-of-envelope calculation:
- According to the fg_1_10_40.src file, the source is at
x=47.26, y=71.14, z=474.9 (all in cm).
- A fully-illuminated detector as close as possible to the source would be
at x=47.26, y=36.33, z=0, making r=476.2 cm.
- Also, for a detector at that position, the cosine
correction factor is 1.008.
- The quantum efficiency is very close
to 1 for the lower three lines. For the 80 keV line, the quantum efficiency
is about 0.96 for the nearest detector.
- The attenuation due to all the passive materials except for air is:
- 0.91 (31 keV)
- 0.92 (35 keV)
- 0.94 (53 keV)
- 0.95 (80 keV)
- The attenuation due to the presence of air is:
- 0.84 (31 keV)
- 0.86 (35 keV)
- 0.89 (53 keV)
- 0.91 (80 keV)
- The modulated-counts-corrected illumination fraction is:
- 1 (31 keV)
- 1 (35 keV)
- 1 (53 keV)
- 0.91 (80 keV)
- For 31 keV photons, 13.5% of interactions result in escape peaks which lie
below the 10 keV threshold, so only 86.5% contribute to the measurement.
- For 35 keV photons, 20.9% of interactions result in escape peaks which lie
below the 10 keV threshold, so only 79.1% contribute to the measurement.
These values yield count rates of:
Low-energy lines:
31 keV:
2.88 × 107
/ (4*π*476.2*476.2) * (0.16) * (1.008) * (0.91) * (0.84) * (0.865)
= 1.08 counts/s
35 keV:
6.35 × 106
/ (4*π*476.2*476.2) * (0.16) * (1.008) * (0.92) * (0.86) = (0.791)
0.22 counts/s
31 keV + 35 keV:
1.08 + 0.22 = 1.30 counts/s
High-energy lines:
53 keV:
5.38 × 105
/ (4*π*476.2*476.2) * (0.16) * (1.008) * (0.94) * (0.89) = 0.03 counts/s
80 keV:
9.58 × 106
/ (4*π*476.2*476.2) * (0.16) * (1.008) * (0.95) * (0.91) * (0.91)
= 0.43 counts/s
53 keV + 80 keV:
0.03 + 0.43 = 0.46 counts/s
All lines:
1.30 + 0.46 = 1.76 counts/s
fg_12:
fg_24:
The "Max Measured Rate" and the "Max Predicted Rate" columns in
this table show the
count rates that correspond to the maximum of the high-rate peak
in the histograms.
"Ratio" is the ratio between "Max Measured Rate" and "Max Predicted
Rate"
|
Run
|
Low-E Lines
Max Measured
Rate
|
Max Predicted
Rate
|
Ratio
|
High-E Lines
Max Measured
Rate
|
Max Predicted
Rate
|
Ratio
|
All Lines
Max Measured
Rate
|
Max Predicted
Rate
|
Ratio
|
|
fg_1
|
0.79
|
1.24
|
0.64
|
0.37
|
0.42
|
0.88
|
1.18
|
1.66
|
0.71
|
|
fg_2
|
0.81
|
1.28
|
0.63
|
0.36
|
0.42
|
0.86
|
1.20
|
1.71
|
0.70
|
|
fg_3
|
0.84
|
1.28
|
0.66
|
0.39
|
0.42
|
0.93
|
1.24
|
1.71
|
0.73
|
|
fg_4
|
0.82
|
1.29
|
0.64
|
0.37
|
0.42
|
0.88
|
1.20
|
1.72
|
0.70
|
|
fg_5
|
0.80
|
1.29
|
0.62
|
0.37
|
0.42
|
0.88
|
1.18
|
1.72
|
0.69
|
|
fg_6
|
0.78
|
1.29
|
0.60
|
0.36
|
0.42
|
0.86
|
1.16
|
1.72
|
0.67
|
|
fg_7
|
0.79
|
1.29
|
0.61
|
0.37
|
0.42
|
0.88
|
1.18
|
1.72
|
0.69
|
|
fg_8
|
0.78
|
1.24
|
0.63
|
0.37
|
0.41
|
0.90
|
1.15
|
1.66
|
0.69
|
|
fg_10
|
0.80
|
1.26
|
0.63
|
0.37
|
0.42
|
0.88
|
1.19
|
1.71
|
0.70
|
|
fg_11
|
0.84
|
1.28
|
0.66
|
0.38
|
0.42
|
0.90
|
1.23
|
1.71
|
0.72
|
|
fg_12
|
0.83
|
1.29
|
0.64
|
0.37
|
0.42
|
0.88
|
1.23
|
1.72
|
0.72
|
|
fg_13
|
0.79
|
1.29
|
0.61
|
0.37
|
0.42
|
0.88
|
1.17
|
1.71
|
0.68
|
|
fg_14
|
0.78
|
1.29
|
0.60
|
0.36
|
0.42
|
0.86
|
1.18
|
1.72
|
0.69
|
|
fg_15
|
0.78
|
1.29
|
0.60
|
0.38
|
0.42
|
0.90
|
1.17
|
1.72
|
0.68
|
|
fg_16
|
0.80
|
1.29
|
0.62
|
0.38
|
0.42
|
0.90
|
1.15
|
1.72
|
0.67
|
|
fg_17
|
0.79
|
1.25
|
0.63
|
0.37
|
0.42
|
0.88
|
1.17
|
1.67
|
0.70
|
|
fg_18
|
0.77
|
1.28
|
0.60
|
0.36
|
0.42
|
0.86
|
1.18
|
1.71
|
0.69
|
|
fg_19
|
0.83
|
1.26
|
0.66
|
0.38
|
0.42
|
0.90
|
1.18
|
1.69
|
0.70
|
|
fg_20
|
0.86
|
1.29
|
0.67
|
0.39
|
0.42
|
0.93
|
1.24
|
1.68
|
0.74
|
|
fg_21
|
0.80
|
1.29
|
0.62
|
0.37
|
0.42
|
0.88
|
1.22
|
1.72
|
0.71
|
|
fg_22
|
0.77
|
1.28
|
0.60
|
0.38
|
0.42
|
0.90
|
1.15
|
1.71
|
0.67
|
|
fg_23
|
0.78
|
1.29
|
0.60
|
0.38
|
0.42
|
0.90
|
1.16
|
1.72
|
0.67
|
|
fg_24
|
0.79
|
1.29
|
0.61
|
0.37
|
0.42
|
0.88
|
1.20
|
1.73
|
0.69
|
For the low-energy lines, the measured rates are lower than the predicted
rates by 37% on average (standard deviation: 2%).
For the high-energy lines, the measured rates are lower than the predicted
rates by 11% on average (standard deviation: 2%).
For all four lines, the measured rates are lower than the predicted
rates by 30% on average (standard deviation: 2%).
IV) Conclusions:
As was the case in the array calibration data,
the 133Ba runs produce lower rates than expected.
The discrepancy is larger than with the array calibration data set,
especially with the lower lines.
The escape peak from the 53 keV photons ended up in the low energy
measurement. This effect was not included in the prediction, but it is
a small effect.
Changes from 21 Jul 2004:
- Removed modulated counts from the prediction (significantly reduced
for the higher energy lines prediction)
Changes from 19 Jan 2004:
- Added attenuation due to passive materials (reduced prediction)
- Added effect of 31 and 35 keV escape peaks being below threshold
(reduced prediction for low energy lines)
- Added effect of transparency of lead tiles (reduced prediction)
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