Am-241 Count Rates:
Measured vs. Predicted

Derek Hullinger
9 Jun 2004

In order to keep this analysis as simple as possible (so that mistakes would be less likely to creep in), I didn't use sum_spectra or any rebinning process. I also did not apply the mask-weighting map directly to the measured data--I only used it to find the illumination fractions that were needed to create a set of predicted data. I then compared the entire set of predicted rates (in the form of a histogram) with the entire set of measured rates, so that the results wouldn't depend on whether the source position was precisely correct.

Bottom Line First:

The measured rates are 60-70% lower than the predicted rates.

Data sets examined:

Am-241 coarse grid runs (from /local/data/gcn3c/array_cal/coarse_grid/dpi):

    1. arr_x_am241_200_20_030701_97.fits
    2. arr_x_am241_200_20_030701_98.fits
    3. arr_x_am241_200_20_030702_101.fits
    4. arr_x_am241_200_20_030702_104.fits (partially coded FOV)
    5. arr_x_am241_200_20_030702_108.fits (partially coded FOV)
    6. arr_x_am241_200_20_030702_110.fits (partially coded FOV)

I) Measured Count Rates:

For each of the above data sets:

    1. ran batgse2dpi with histmode=window and using a 29-keV window file in order to generate a dpi that only includes counts above 29 keV

      2. example command:

      batgse2dpi arr_x_am241_200_20_030701_97.list arr_x_am241_200_20_030701_97.dpi_window histmode=window windows=/home/lhea/derek/windows/29kev.window

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

      3. example command:

      bathotpix arr_x_am241_200_20_030701_97.dpi_window arr_x_am241_200_20_030701_97.mask2_window detmask=arr_x_am241_200_20_030701_97.mask_thresh chatter=3

      arr_x_am241_200_20_030701_97.mask_thresh is a detector map that excludes all detectors with fewer than 30 counts

    3. ran batclean to remove background from the windowed dpi

      4. example command:

      batclean arr_x_am241_200_20_030701_97.dpi_window arr_x_am241_200_20_030701_97.dpi_window_clean arr_x_am241_200_20_030701_97.src detmask=arr_x_am241_200_20_030701_97.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 generate the measured count rate for each detector)

II) Predicted Count Rates:

Predicted Count Rate (For Each Detector):

SE:     The number of photons/s emitted at energy E by the source into 4π

E is 33 keV, and 60 keV,

Source: Am-241-605

S33 = (1.39 x 10-2 Ci)*(3.7x1010 Bq/Ci)*(0.00126) = 6.53 x 105 photons/s
S60 = (1.39 x 10-2 Ci)*(3.7x1010 Bq/Ci)*(0.359) = 1.86 x 108 photons/s

(from BAT_Cal_Sources.xls prepared by Ann)

     r:           distance from the source to the detector

    Photons/s/cm2 incident on a fully-illuminated detector at a distance r from the source.

Aeff,E:            Effective area of the detector

0.16 cm2 * efficiency * (Cosine Correction Factor)
efficiency ≅ 1 for both lines
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))

where x, y, and z are the x-,y-, and z-distances from the source to the detector

this factor works well for non-leading-edge detectors. For that reason, only center detectors are used in the comparison)

 In the case of the 33 keV Am-241 line, the escape peaks are below the threshold, so these escape counts were not counted in the calculation. This effect was small.

fillum:          fraction of the detector that is illuminated through the mask (a number between 0 and 1)

fatten,E:       the attenutation of photons of energy E through all passive materials between the source and the detectors, including air (which turns out to be a significant attenuator). This attenuation was calculated for the on-axis case, then it was adjusted for each detector to include the cosine effect.

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

III) Results:

These are histograms of the measured 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

You'll notice that the measured rates are all systematically lower than the predicted rates. After the the plots, there are tables that attempt to quantify this.

Am-241 Coarse Grid:

arr_x_am241_200_20_030701_97:

back-of-envelope calculation:

  • For a fully-illuminated detector directly below the source, the count rate would be ∑[SE/(4πr2) * (0.16 cm2) * (fatten,E)].
  • The source is at x=-16.7, y=-0.18, z=286.6 (all in cm), so for a detector directly belor the source, r=286.6 cm.
  • S33=6.53×105 photons/s and S60=1.86×108 photons/s.
  • fatten,33=0.827 and fatten,60=0.883.
  • 20.5% of the counts resulting from 33 keV photons lie in the escape peak. Because this peak lies below the threshold, only 79.5% of the counts from this energy should be counted.
  • With all of these values, the count rate comes out to be 25.5 counts/s.
arr_x_am241_200_20_030701_98:
arr_x_am241_200_20_030702_101:
arr_x_am241_200_20_030702_104:
arr_x_am241_200_20_030702_108:
arr_x_am241_200_20_030702_110:

This table shows the count rates that correspond to the "peak" rates in the histograms. This isn't a perfect way to quantify how much lower the measured rates are, but it's not bad.

"Measured" is the peak rate in the histogram of measured rates
"Predicted" is the peak rate in the histogram of predicted rates
"Ratio" is the ratio between the two

Run ID

tan(θ)

Measured

Predicted

Ratio

97

0.058

10.0

25.6

0.39

98

0.120

9.2

25.6

0.36

101

0.351

8.1

24.3

0.33

104

0.581

4.2

11.2

0.38

108

0.687

2.4

7.2

0.33

110

0.688

2.3

8.1

0.28

Overall, the measured rates are 30-40% as large as the predicted rates for this set of runs. There is a large spread, but it is probably partly due to the method of picking out the peaks.

IV) Source Orientation:

One reason that was proposed for the 30-40% discrepancy is the possibility that the source was placed upside down during the calibration runs. If this were the case, photons would have been attenuated by the stainless steel shielding of the source. To test whether this was a plausible explanation, we placed the source above the detector array in both orientations (correct and backward) and measured the total count rate in the array. It was found that, after subtracting the background rate, the backward orientation yielded 33.11% (+/- 0.12%) as many counts as the correct orientation. This is consistent with the discrepancy between measurement and prediction seen in the data above.

V) Conclusions:

The most likely explanation for the discrepancy between measured rates and predicted rates is that the source was improperly oriented.

Things I double checked:


Changes from 15 Apr 2004:

Changes from 2 Feb 2004:


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