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As an imaging x-ray telescope, AXAF focuses a point source onto the CCD. Since the point response function FWHM is comparable to the size of one pixel, pileup from a strong point source is a particular problem.

All pileup cross sections presented so far are evaluated in terms of
detected x-rays per quadrant per frame. However, it is often useful to
describe pileup in units of x-rays per pixel per frame. The factors
are translated multiplying by . Thus, if *R*_{no pileup}=incident x-ray rate per pixel
per frame for a monochromatic beam, then to first approximation the
detected rate *R*_{no pileup} is given by the transcendental equation

(26) |

From another viewpoint, pileup in a single pixel with a monochromatic source is easily understood as a simple Poisson process. That is, if the probability for an x-ray to interact with a pixel during one exposure is , then the probability that N x-rays interact during one exposure is

Consider an entire observation of *N*_{frames} frames. If there was no
pileup, the total incident flux of x-rays would be
detected. The effect of pileup is manifest as several (or many)
x-rays which add during one exposure. Let

number of frames with no interaction.

Combining these two equations yields,

For example, if out of 1000 frames, x-rays from a point source are present in 100 frames, then

Thus, pileup accounted for an apparent reduction in the incident flux of 5%.

This method differs from the first method developed in this chapter by
treating every incident x-ray as a valid event, including the
coincidence of two or many x-rays. This method has use in high pileup
situations where Eqn. 4.13
presents ambiguity. For example, the shape of
the graphs in Fig. 4.11
show that for a given value of the detected flux,
there are *two* possibilities for the incident flux. Without
additional information it is impossible to discriminate between the
low and high flux solution. Although most astrophysical point sources
should not be so strong, the ambiguity of strong sources can be
resolved by application of the method described above.

11/20/1997