The depression of the spot's central surface brightness relative to the wings with increasing fluence is one of the most obvious pileup signatures in the spatial domain. This effect is shown in Figure 13, where we have plotted the radial surface brightness profiles, normalized at 6 pixels radius, of four on-axis, focussed Al-Ka (1.486 keV) images with fluences ranging from 0.29-5.6 counts per frame. Table 3 lists the XRCF tests, pileup fractions, and fluence for each image. The central surface brightness decreases by more than a factor of four over a factor of 19 in fluence, while the degree of event pileup ranges between 8-60%. Event pileup fractions are defined as the ratio of the sum of photons in the n = 2-3 or n = 2-4 spectral pileup peaks to the total number of photons in the main (n=1) peak plus the pileup peaks calculated as
where An is the area under the main peak or pileup peak.
The surface brightness depression is strongest in the central pixel where the event density is maximal, but the effects migrate to a radius of ~4 pixels when the fluence reaches 5.6 cpf. The central depression reflects a deficit of detected events in the core relative to the wings. Because two or more coincident events are counted by the instrument as a single, higher energy event, the number density of counts in the core is reduced with respect to the wings.