BAT Field of View

BAT Cal Memo 2004-08-12

12 Aug 2004

C. Markwardt

Estimated Solid Angle Coverage of the BAT

Summary

I provide estimates of the BAT field of view as a function of partial
coding.  At 95%, 50% and 5% partial coding fractions, the BAT solid
angle coverage is 0.34, 1.18 and 2.29 sr respectively, including
corrections to the projected detector area such as the cosine effect.

Details

The BAT is a wide field instrument with a non-trivially shaped field
of view.  Also, the field of view depends on the minimum partial
coding fraction demanded.  For example, the fully coded field of view,
where sources must illuminate the entire array, is much smaller than
the half- or zero-coded field of view, where only fractional
illumination is required.

The BAT field of view was computed using a combination of standard BAT
tools and a specialized script.  The batfftimage tool calculates the
partial coding map as a function of image position.  In principle this
depends on the number of detectors enabled, but for this computation,
all detectors were assumed to be enabled. (See Appendix: Analysis for details)

An IDL script was used to sum the solid angle, for different partial
coding fraction thresholds.  A differential solid angle element in BAT
image coordinates is:

  d(OHMEGA) = dIMX * dIMY / (1 + IMX^2 + IMY^2)^1.5

where IMX and IMY are the tangent plane coordinates (BAT_X/BAT_Z and
BAT_Y/BAT_Z respectively).  The solid angle computation is a simple
matter of numerically summing the solid angle elements for which the
partial coding threshold is exceeded.

Results

The resulting solid area curves are shown in the Figure.  The values
are also available in a data file.



Figure. BAT partial coding vs. solid angle.  The black curve is
the unadjusted partial coding, representing 2 times the fraction of
illuminated area, divided by the total nominal detector area (top
detector faces only).  The red curve is the same curve, adjusted for
off-axis projection effects.

Projection Effects

The figure shows two curves.  The red curve is adjusted for projection
effects such as the cosine effect.  In fact, the correction profile is
the "Tueller/Hullinger" flat-fielding model.  Close to on-axis, the
effective area actually increases above nominal because of significant
illumination of the detector sides.


Appendix: Data File

  pcodevssolid.dat - partial coding vs. solid angle (ASCII table)

; Columns:
;    (1) "partial coding" (= 2 x illuminated detector area / total area)
;    (2) solid angle [sr] (no projection corrections)
;    (3) solid angle [sr] (w/ projection corrections)
  
Appendix: Analysis techniques

Commands used:

For flat-fielding adjusted partial coding map:
  batfftimage events.dpi pcodemap.img NONE pcodemap=yes

For pure partial coding map (no adjustments):
  batfftimage events.dpi pcodemap_noflat.img NONE pcodemap=yes corrections=autocollim

Analysis script:

  pcodevssolid.pro - for image IMG with FITS header HH, compute the solid angle as a function of partial coding.