Definition of BAT Count Units and Corrections
The default mask-weighted count units are defined as, "background subtracted counts per fully illuminated detector for an equivalent on-axis source." The meaning of this phrase, and a discussion of the mask weighting technique is provided. Conversion to counts per unit area are also straightforward.
Read this thread if you want to:
Know how BAT count and rate units are defined.
Last update: 2007-01-26
Because the BAT is a coded mask experiment, the correspondence between "counts" and actual source flux must be carefully defined. The coded mask imaging system clearly modifies the amount of photon flux that reaches the detector plane, but the nature of the imaging system also creates other effects which must be accounted for.
3. Definition of BAT Mask-Weighted Counts
BAT counts derived from mask weighting procedures or sky imaging -- batmaskwtevt, batmaskwtimg or batfftimage -- and using the default corrections are defined in the following way:
Background subtracted counts per fully illuminated detector for an equivalent on-axis source
Rate is defined similarly, per unit time.
Let us examine what each of these words means. Next to each phrase is the corresponding correction that can be used in the analysis tasks. These corrections apply to both the mask weighting programs and the sky imaging programs (which fundamentally apply the same technique).
Background subtracted counts...
The units are counts, not photons, which customary for X- and gamma-ray instruments. To convert to photon fluxes, one must generally fit the spectrum to an a priori model. However, the mask weighting technique provides automatic background subtraction.
Also the 'background' that is subtracted includes the effects of flux that passes through the lead mask cells without scattering. Both foreground and background include counts from photons that scatter off the lead mask cells and other parts of the BAT and Swift structure.
... per ... detector (correction 'ndets')
The counts are normalized to the number of enabled BAT detectors. This compensates for the possibility that some, or many, BAT detectors are disabled for a given observation.
... per ... *illuminated* detector ... (correction 'pcode')
The 'pcode' correction normalizes the counts by the number of illuminated detectors. Since the BAT is a wide-field instrument it is possible, indeed likely, that sources will be at the edge of the field of view. This means that only a fraction of the detector array is illuminated by through mask, i.e. the source is partially coded, and thus will produce fewer counts. This correction normalizes the partial coding fraction to unity for all sources.
... per *fully illuminated* detector ... (correction 'maskwt')
Even when detectors are illuminated by a source, most detectors are not 100% illuminated. In general, there is a distribution of detector illumination fractions, ranging from 0% (fully shadowed by the mask) to 100% (fully illuminated by the mask). The mask weighting technique used by the BAT software combines all events to produce background-subtracted counts in a "mean" fractionally illuminated detector. The 'maskwt' correction renormalizes the counts to be those received in a fully illuminated detector. This accounts for both the open fraction of the mask (50% for the BAT), plus the per-detector partial illumination.
The 'maskwt' correction should be distinguished from the partial coding correction. The partial coding correction adjusts for the fractional number of detectors that a source could illuminate through the mask, regardless of which mask cells are blocked or open. The 'maskwt' correction adjusts for the partial illumination of each individual detector.
... for an equivalent on-axis source* (correction 'flatfield')
Off-axis sources have a different count rate because the projected area of the BAT detectors is changed by projection effects. Generally, the effective area is reduced off-axis because of the "cosine effect." However, the effective area increases slightly for mild off-axis angles because detector sides are illuminated. The 'flatfield' correction adjusts for these effects, to create a count rate for an effective on-axis source. In this manner, it will be more practical to compare detections of the same source at different positions in the field of view.
It should be noted that this correction is primarily due to geometric effects. It is also understood that off-axis illumination changes the detector response in non-subtle ways, which is not corrected for by the 'flatfield' correction.
4. Converting to a counts per area
The area of a single BAT detector is 0.16 cm2. Thus, the conversion between "per unit area" and "per fully illuminated detector" is:
counts_cm2 = counts_fully_illuminated_det / 0.16
5. General Background: What is Mask Weighting?
The BAT software supports the method of "mask weighting" to estimate source fluxes. Mask weighting involves assigning each event a weight according to the illumination fraction of the detector it was detected in. At its crudest level, the weight is computed as:
w_i = 2*f_i - 1
where f_i is the illumination fraction of detector i, based on the mask shadow pattern. Note that this weight is source position dependent, since for a different position in the BAT field of view, the mask shadow pattern on the detector array is different.
The source flux is estimated by simply summing the weights over the desired time and energy interval. The count variance is computed as the sum of the squared weights.
Additional corrections are applied to the wi weights, according to the descriptions above, to make the derived counts useful. It is worth noting that the corrections apply to both the source flux estimate and its uncertainty. For example, a far off-axis source will have a small partial coding fraction, and the raw counts will also be reduced by projection effects. When compensating for these effects, the derived count rate will increase by a factor, but the uncertainties will increase by the same factor, so the significance of detection is the same.
2005-12-04 - first revision
2006-04-12 - formatting changes
2006-04-15 - correct formatting of superscript
2006-07-04 - clarify the "per unit area" formula
2007-01-08 - correct a spelling error
2007-01-25 - correct a spelling error