Ba-133 Count Rates:
Measured vs. Predicted

Derek Hullinger
29 Jul 2004

Bottom Line First:

The measured rates are 6-8% lower than the predicted rates.

Data sets examined:

    1. cg_x_ba133_030304_3.fits
    2. cg_x_ba133_030304_4.fits
    3. cg17_x_ba133_030304_19.fits
    4. cg18_x_ba133_030304_20.fits
    5. cg25_x_ba133_030304_27.fits
    6. cg33_x_ba133_030304_35.fits
    7. cg34_x_ba133_030304_36.fits

    8. arr_x_ba133_200_20_030701_82.fits
    9. arr_x_ba133_200_20_030701_87.fits
    10. arr_x_ba133_200_20_030701_88.fits

    (1 thru 7 from /local/data/gcn3a/array_cal/coarse_grid/)
    (8 thru 10 from /local/data/gcn3c/array_cal/coarse_grid/)

I) Measured Count Rates (from ground software (gsw) tools):

For each of the above data sets:

    1. ran batgse2dpi with histmode="window" and only including counts between 17 to 90 keV

      2. example command:

      batgse2dpi cg17_x_ba133_030304_19.list cg17_x_ba133_030304_19.dpi_window histmode="window" windows="/home/lhea/derek/windows/ba_133.window"

    2. ran bathotpix to generate a "good map" file for the windowed dpi

      3. example command:

      bathotpix cg17_x_ba133_030304_19.dpi_window cg17_x_ba133_030304_19.mask2_window chatter=2

    3. ran batfftimage to produce a "sky" image

      4. example command:

      batfftimage cg17_x_ba133_030304_19.dpi_window cg17_x_ba133_030304_19.img_window attitude=NONE detmask=cg17_x_ba133_030304_19.mask2_window bat_z=305.370972

      (bat_z comes from Jay Cummings' analysis)

    4. ran batcelldetect to find source position

      5. example command:

      batcelldetect cg17_x_ba133_030304_19.img_window cg17_x_ba133_030304_19.src_window 6.0

    5. ran batclean to remove background from the windowed dpi

      6. example command:

      batclean cg17_x_ba133_030304_19.dpi_window cg17_x_ba133_030304_19.dpi_window_clean cg17_x_ba133_030304_19.src detmask=cg17_x_ba133_030304_19.mask2_window srcclean=YES outversion="bkgcleaned"

      By default, counts in the dpi are dead-time corrected (that is, they are multiplied by exposure/live-time).

Measured Count Rate (For Each Detector):

C: dead-time corrected counts from windowed dpi (counts*exposure/live_time)

t:   exposure time for the data set

(See the IDL routine used to generate the measured count rate for each detector)

I examined the measured count rates in two ways:
  1. I plotted a histogram of the count rates and picked out the "peak" rate
  2. I flat-fielded and summed the rates using the mask-weighting factors

II) Predicted Count Rates:

Predicted Count Rate (For Each Detector):

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):

S31 = 2.96 x 107 photons/s (on 6/27/03)
on 3/4/03, this rate would have been higher by a factor of (1/2)^(-115/3839) (=1.02), making it 3.02 x 107 photons/s
on 7/1/03, this rate would have been lower by a factor of (1/2)^(4/3839) (=0.999), making it 2.96 x 107 photons/s

S35 = 6.53 x 106 photons/s (on 6/27/03)
on 3/4/03, this rate would have been higher by a factor of (1/2)^(-115/3839) (=1.02), making it 6.66 x 106 photons/s
on 7/1/03, this rate would have been lower by a factor of (1/2)^(4/3839) (=0.999), making it 6.52 x 106 photons/s

S53 = 5.53 x 105 photons/s (on 6/27/03)
on 3/4/03, this rate would have been higher by a factor of (1/2)^(-115/3839) (=1.02), making it 5.65 x 105 photons/s
on 7/1/03, this rate would have been lower by a factor of (1/2)^(4/3839) (=0.999), making it 5.53 x 105 photons/s

S80 = 9.85 x 106 photons/s (on 6/27/03)
on 3/4/03, this rate would have been higher by a factor of (1/2)^(-115/3839) (=1.02), making it 1.01 x 107 photons/s
on 7/1/03, this rate would have been lower by a factor of (1/2)^(4/3839) (=0.999), making it 9.84 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 photons that are transmitted through the mask

for fully illuminated detectors, this is 1
for fully masked detectors, this is the tranmission 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 * (Cosine Correction Factor) * QE * (fraction of depositions above 17 keV)

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

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)

 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)

As with the measured count rates, I examined the predicted count rates in two ways:
  1. I plotted a histogram of the count rates and picked out the "peak" rate
  2. I flat-fielded and summed the rates using the mask-weighting factors

I then compared the results of the measured rates with the predicted rates.

III) Results:

Plotted here are histograms of 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 measured rates
red: histogram of predicted rates

The predicted rates are all systematically higher than the measured rates. After the plots, there is a table that compares these peak rates along with the mask-weighted summed rates.

cg17_x_ba133_030304_19:

back-of-envelope calculation:

The source is at x=-121.18, y=3.84, z=304.8 (all in cm). A fully-illuminated detector as close as possible to the source would be at x=-59.85, y=3.84, z=304.8, making r=310.9 cm. The fraction of photons transmitted through all passive materials (when the source is on axis), including air is 0.813 (31 keV photons), 0.836 (35 keV photons), 0.877 (53 keV photons), and 0.893 (80 keV photons). Also, for a detector at that position, QE31 = QE35 = QE53 = 1, and QE80 = 0.98, and the cosine correction factor is approximately 1. fillum for 31, 35, and 53 keV photons is 1. For 80 keV photons, it's 0.948. For 31 keV photons, 86.5% of counts are above the 17 keV threshold. For 35 keV photons, 79.1% of counts are above the 17 keV threshold. Overall, this would give a count rate of:

(3.02 x 107)*/(4*π*310.9*310.9)*(0.813)*(0.16)*(1)*(0.865) = 2.79 counts/s from the 31 keV line,
(6.66 x 106)*/(4*π*310.9*310.9)*(0.836)*(0.16)*(1)*(0.791) = 0.58 counts/s from the 35 keV line,
(5.65 x 105)*/(4*π*310.9*310.9)*(0.877)*(0.16)*(1) = 0.07 counts/s from the 53 keV line, and
(1.01 x 107)*/(4*π*310.9*310.9)*(0.893)*(0.16)*(0.98)*(0.948) = 1.10 counts/s from the 80 keV line,
making a total of 4.54 counts/s.

cg18_x_ba133_030304_20:

cg25_x_ba133_030304_27:

cg33_x_ba133_030304_35:

cg34_x_ba133_030304_36:

cg_x_ba133_030304_3:

cg_x_ba133_030304_4:

arr_x_ba133_200_20_030701_82:

arr_x_ba133_200_20_030701_87:

arr_x_ba133_200_20_030701_88:

The "Max Measured Rate" and the "Max Predicted Rate" columns in this table show the count rates that correspond to the eyeball-middle of the high-rate peak in the histograms.


The runs are listed in order of increasing tan(θ)

Run ID

tan(θ)

Summed Rate
(from dpi)

Summed Rate
(from prediction)

Ratio

Max Measured
Rate

Max Predicted
Rate

Ratio

3

0.142

4.22

4.37

0.97

4.4

4.6

0.96

4

0.179

4.15

4.33

0.96

4.3

4.6

0.93

33

0.252

4.31

4.10

1.05

4.6

4.3

1.07

34

0.305

3.66

3.79

0.96

4.1

4.5

0.91

17

0.370

3.31

3.44

0.96

3.4

4.4

0.77

18

0.444

2.90

3.00

0.96

3.1

3.0

1.03

25

0.555

1.83

2.02

0.91

2.5

2.7

0.93

88

0.559

1.21

1.83

0.66

2.2

2.4

0.92

87

0.595

1.48

1.71

0.87

2.1

2.2

0.95

82

0.727

0.72

0.79

0.91

1.1

1.2

0.92

There is a lot of scatter in these measurements but,
The maximum measured rates are (on average) 6.1% lower than the maximum predicted rates.
The summed measured rates are (on average) 7.9% lower than the summed predicted rates.

IV) Conclusions:

The 133Ba runs produce slightly lower rates than expected.

It may be that some of the events from the dominant 31 keV line are partially cut off by the electronics threshold. An analysis of just the 80 keV and 53 keV lines, or (better yet) a fit of the 80 and 53 keV peaks to the response matrix would tell whether this was the case.


Changes from 11 Jun 2004:

Changes from 26 Feb 2004:

Changes from 5 Feb 2004:

Changes from 15 Dec 2003:


Return to main BAT response page
Return to Home Page of Derek Hullinger