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: http://xmm.vilspa.esa.es/sas/8.0.0/doc/bkgfit/node3.html
Дата изменения: Wed Jul 2 12:49:36 2008 Дата индексирования: Fri Sep 5 17:52:53 2008 Кодировка: Поисковые слова: п п п п п |
Although the task is non-XMM specific, it is primarily intended to generate maps of the background in XMM EPIC images. The task does this by fitting a linear combination of background-model component images. The task takes three main inputs (see section 6 for details): (i) the Poissonian FITS image which is to be fitted; (ii) a list of model component FITS images; (iii) (optionally) a FITS mask image. The output is a single FITS image which represents the best-fit background model. The best-fit amplitudes
and the names of the component datasets are recorded in this output dataset in a binary table extension.
Clearly all the input images must have the same dimensions: call this pixels.
The fitting is done by minimizes the maximum-likelihood estimator defined as follows:
where is the vector of
component amplitudes, and the sums are understood to be over all unmasked image pixels. Suppressing the
subscript for the sake of brevity, the Poissonian probability
is given by
where the total background model is the linear combination of the
components
, viz
and represents the value at that pixel of the Poissonian image. Inserting equation 5 into 1 gives