Re: pileup in ACIS

On Tue, 15 May 2001 15:42:12 -0400 (EDT), Philip Kaaret <kaaret_at_email.domain.hidden>Concerning psffrac, for the example in the ISIS user's manual, you
>state that psffrac should be set to 0.95 which is the fraction of
>energy within the extraction region which falls within the central 3x3
>pixel.  Is the general definition of psffrac that it should be set to
>the fraction of energy within the extraction region which falls within
>the central 3x3 pixel?  Just to check my understanding, if one were to

  Yes.
  
>use a larger extraction region for an on-axis source should psffrac be
>lower?  Also, if one were to analyze an off-axis source for which the

  Yes.  However, as you increase the region size, the amount of
  background will go up.  For this reason, I would keep it as small as
  possible.

>psf is less concentrated, should psffrac be set to the fraction of
>energy which falls within the brighest 3x3 pixel?

  That is a tough call.  If you feel that the pileup is occuring in
  only one 3x3 region, then yes.

>Concerning nregions, I can't find any description of this parameter.

It is basically a first crack at implemented the more general equation
described in the extended source portion of the paper.  The parameters
work like this: The pileup kernel computes the expected number of
counts in a pha channel as the sum of 2 terms: one from pileup from a
central 3x3 region, and an unpiled contribution from the surrounding
area. Hence:

   C(h) = F_1(f*s) + F_2((1-f)*s)

where f is psffrac, and s is the incident source flux.  Here, F_1
represents the pileup equation, and F_2 represents the standard
equation.  Now, let n be nregions.  Then the formula used is:

   C(h) = n*F_1(f*s/n) + F_2((1-f)*s)

In other words, the incident flux f*s is considered to be distributed
_equally_ over n pileup regions, which is reflected by the use of
f*s/n in the above equation.  Since the regions are equal, they
contribute the same number of counts; hence the multiplication by n.

>In particular, should psffrac be the fraction of energy within the
>extraction region which falls within the number of 3x3 pixel fields
>given by nregions?

Yes.  (1-f) represents the fraction of the flux which is non-piled.

I hope this helps.

--John
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