An Introduction to Exposure Maps. Houck, J. Technical Report
An Introduction to Exposure Maps [pdf]Paper  An Introduction to Exposure Maps [pdf]Website  abstract   bibtex   
The counts image of an extended X-ray source invariably contains instrumental artifacts which complicate surface brightness measurements. These artifacts are caused by imperfections in the mirror and the detector and are both energy and position dependent. Often, one would like to generate an image in physical units (e.g. photon sec−1 cm−2 arcsec−2), with these artifacts removed. A common approach is to divide the counts image by an exposure map to re-scale all parts of the image to the same relative exposure. Unfortunately, in the general case, no exposure map with this property exists. The reason is that, because the effective area is energy dependent, the number of counts produced in a given broad pulse-height band is not proportional to the incident flux in that band. Instead, an integral equation relates the total counts produced in a given pulse-height bin to the incident source spectrum; solution of this integral equation for point-source observations is the primary function of xspec and sherpa. The imaging case is further complicated by the need to account for the position-dependence of the effective area. As with point-sources, an integral equation describes the relationship between the counts image and the source surface-brightness distribution in a given energy band. In general, simply dividing the counts image by an exposure map does not constitute a solution to this integral equation and does not yield the true source surface brightness vs. position in the chosen band. However, when the effective area is roughly constant within a given energy band, the relevant integral equationsmay be greatly simplified, allowing one to divide by an exposuremap to effectively remove instrumental artifacts from a counts image within the specified band. 2.
@techreport{
 title = {An Introduction to Exposure Maps},
 type = {techreport},
 pages = {1-12},
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 websites = {http://space.mit.edu/ASC/docs/expmap_intro.pdf},
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 abstract = {The counts image of an extended X-ray source invariably contains instrumental artifacts which complicate surface brightness measurements. These artifacts are caused by imperfections in the mirror and the detector and are both energy and position dependent. Often, one would like to generate an image in physical units (e.g. photon sec−1 cm−2 arcsec−2), with these artifacts removed. A common approach is to divide the counts image by an exposure map to re-scale all parts of the image to the same relative exposure. Unfortunately, in the general case, no exposure map with this property exists. The reason is that, because the effective area is energy dependent, the number of counts produced in a given broad pulse-height band is not proportional to the incident flux in that band. Instead, an integral equation relates the total counts produced in a given pulse-height bin to the incident source spectrum; solution of this integral equation for point-source observations is the primary function of xspec and sherpa. The imaging case is further complicated by the need to account for the position-dependence of the effective area. As with point-sources, an integral equation describes the relationship between the counts image and the source surface-brightness distribution in a given energy band. In general, simply dividing the counts image by an exposure map does not constitute a solution to this integral equation and does not yield the true source surface brightness vs. position in the chosen band. However, when the effective area is roughly constant within a given energy band, the relevant integral equationsmay be greatly simplified, allowing one to divide by an exposuremap to effectively remove instrumental artifacts from a counts image within the specified band. 2.},
 bibtype = {techreport},
 author = {Houck, John}
}
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