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<strong>MOPEX</strong> User’s <strong>Guide</strong><br />
the parameter Background_Fit is set to 1, then the fitting will also estimate the background,<br />
which is assumed to be constant within the fitting area. For the i-th input image the data in fitting<br />
area Wi around the potential point source position is used in the fitting. The local coordinates of<br />
the point sources Ri(n) in the i-th input image are in general a complicated function of the global<br />
coordinates R(n). The following quantity is minimized:<br />
χ 2 =<br />
N images<br />
∑<br />
j=1<br />
∑<br />
i∈W j<br />
⎛ NPS ⎞<br />
⎜ s j(i) −∑ f (n)PRF(i,R j(n)) − background ⎟<br />
⎝ n=1<br />
⎠<br />
2<br />
σ j (i)<br />
Basic Concepts in <strong>MOPEX</strong> 209<br />
P RF fitting in <strong>MOPEX</strong><br />
2<br />
Equation 8.23<br />
Here s is the input image, possibly background subtracted, and σ is the input uncertainty image.<br />
Fitting is performed simultaneously in Nimages images using NPS point source candidates. First, χ 2<br />
is minimized for NPS = 1. The success of the fitting is determined by the parameter Chi Threshold.<br />
If<br />
χ 2 / dof < Chi Threshold<br />
then the fitting is successful. The number of degrees of freedom, dof, is equal to the sum of all the<br />
good pixels in the fitting areas Wj in all the images minus the number of fitting parameters.<br />
If the fitting is not successful and the namelist parameter Max Number ps is greater than 1, then<br />
active de-blending can be performed. The same data are fit with more than one point source. The<br />
number of sources is incremented until it reaches the limit set by the Max Number ps parameter<br />
or the success condition (above) is satisfied, whichever comes first. Since active de-blending is<br />
not a well-defined process, a more stringent condition needs to be met in order to accept extra<br />
point sources:<br />
(χ 2 /dof ) new < Chi _Threshold + χ 2 /dof<br />
2⋅ Chi2_ Improvement<br />
.<br />
Equation 8.24<br />
This is meant to prevent the algorithm from splitting detections into several point sources, unless<br />
it has a really good reason to do so.<br />
If the BlendSize for a given cluster is greater than zero in the output of the Detect module, then<br />
passive de-blending is performed, and all the detections from one blend are fit simultaneously.<br />
That is, NPS is set to BlendSize, even if BlendSize is greater than Max Number ps. The fitting area
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