Cd-109 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 agree with the predicted rates.

Data sets examined:

Cd-109 coarse grid runs (from /local/data/gcn3c/array_cal/coarse_grid/dpi):

    1. arr_x_cd109_200_20_030627_1.fits
    2. arr_x_cd109_200_20_030627_2.fits
    3. arr_x_cd109_200_20_030627_3.fits
    4. arr_x_cd109_200_20_030627_4.fits
    5. arr_x_cd109_200_20_030627_5.fits
    6. arr_x_cd109_200_20_030627_6.fits
    7. arr_x_cd109_200_21_030630_71.fits
    8. arr_x_cd109_200_21_030630_72.fits

Cd-109 far field runs (from /local/data/gcn3a/array_cal/far_field/dpi):

    1. arr_x_cd109_200_21_0_0_030405_15.fits
    2. arr_x_cd109_200_21_0_0_030405_16.fits

I) Measured Count Rates:

For each of the above data sets:

    1. ran batgse2dpi with histmode=window and using a 31 keV window file in order to generate a dpi that only includes counts from the 88 keV line

      2. example command:

      batgse2dpi arr_x_cd109_200_20_030627_1.list arr_x_cd109_200_20_030627_1.dpi_window histmode=window windows=/home/lhea/derek/windows/31kev.window

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

      3. example command:

      bathotpix arr_x_cd109_200_20_030627_1.dpi_window arr_x_cd109_200_20_030627_1.mask2_window detmask=arr_x_cd109_200_20_030627_1.mask_thresh chatter=3

      arr_x_cd109_200_20_030627_1.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_cd109_200_20_030627_1.dpi_window arr_x_cd109_200_20_030627_1.dpi_window_clean arr_x_cd109_200_20_030627_1.src detmask=arr_x_cd109_200_20_030627_1.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):

S:

The number of 88 keV photons/s emitted by the source into 4π

Source used for both cg and ff runs: Cd-109-154
On 8/18/03, S = 5.7379 x 106 photons/s
(from Nadine’s calibration report calibhigh.xls)

On 6/27/03 (the first day of the coarse grid runs), the rate was a factor of (0.5)^(-52/462.6) = 1.08 higher.
On 6/30/03 (the second day of the coarse grid runs), the rate was a factor of (0.5)^(-49/462.6) = 1.08 higher.
On 4/5/03 (the day of the far field runs), the rate was a factor of (0.5)^(-135/462.6) = 1.22 higher.

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:

Effective area of the detector
=0.16 cm2 * efficiency * (Cosine Correction Factor)
efficiency = 0.91 for 88 keV photons
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)

fillum:

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

fatten:

the attenutation of 88 keV photons 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.

Cd-109 Coarse Grid:

arr_x_cd109_200_20_030627_1:

back-of-envelope calculation:

  • For a fully-illuminated detector directly below the source, the count rate would be
    ∑[S/(4πr2) * (0.16 cm2) * (efficiency) * (fatten)].
  • The source is at x=-19.0, y=-11.43, z=294.7 (all in cm), so for a detector directly belor the source, r=294.7 cm.
  • S=6.18×106 photons/s.
  • efficiency=0.909
  • fatten=0.895.
  • With all of these values, the count rate comes out to be 0.73 counts/s.
arr_x_cd109_200_20_030627_4:
arr_x_cd109_200_20_030627_2:
arr_x_cd109_200_20_030627_3:
arr_x_cd109_200_20_030627_5:
arr_x_cd109_200_21_030630_71:
arr_x_cd109_200_20_030627_6:
arr_x_cd109_200_21_030630_72:

Run ID

tan(θ)

Measured

Predicted

Ratio

1

0.075

0.75

0.74

1.01

4

0.119

0.75

0.74

1.01

2

0.122

0.74

0.74

1.00

3

0.151

0.75

0.74

1.01

5

0.327

0.66

0.63

1.05

71

0.368

0.59

0.56

1.05

6

0.529

0.45

0.42

1.07

72

0.563

0.36

0.33

1.09

The measured rates are all equal to the predicted rates to within the margin of error of the peak-finding method

Cd-109 Far Field:

arr_x_cd109_200_21_0_0_030405_15:

back-of-envelope calculation:

  • For a fully-illuminated detector directly below the source, the count rate would be
    ∑[S/(4πr2) * (0.16 cm2) * (efficiency) * (fatten)].
  • The source is at x=-23.3, y=-73.93, z=1926.7 (all in cm). This is not directly above the array, so there are no detectors directly below it. The closest detector to this position would be at x=-23.3, y=-36. At this position, r=√[(73.9-36)2+1926.72]=1927.1 cm (which is pretty close to z).
  • S=7.02×106 photons/s.
  • efficiency=0.909
  • fatten=0.638.
  • With all of these values, the count rate comes out to be 0.014 counts/s.
arr_x_cd109_200_21_0_0_030405_16:

Run ID

tan(θ)

Measured

Predicted

Ratio

15

0.040

0.0135

0.0140

0.0964

16

0.040

0.0135

0.0140

0.964

The measured rates are all equal to the predicted rates to within the margin of error of the peak-finding method

IV) Conclusions:

The predicted rate and the measured rate agree to within the precision of this analysis, which is good news!


Changes from 15 Apr 2004:

Changes from 2 Feb 2004:

Changes from 2 Dec 2003:


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