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E-mail:
aschwanden@lmsal.com -
Markus J.Aschwanden (Lockheed Martin Solar & Astrophysics Lab.)
HESSI Tutorial on Forward-Fitting : III. Number of Source ComponentsThis tutorial is intended to demonstrate how the number of source components can be determined to obtain an optimum result with the forward-fitting algorithm. We simulate an image that contains 4 source components and apply forward-fitting with a smaller (than optimum) number of source components. A recommended strategy is to start with one single source, and then to increase the number incrementally in subsequent runs until a chi-square (or C-statistic) in the range of 0.95...1.05 is achieved. Here is the model map of the simulated data:
Without any a priori knowledge we would first attempt to fit the data with a
single gaussian component:
The average value of the C-statistic has a value of C=1.10, which is not too
bad, because the centroid of the 4 sources produce a similar modulation as the
sum of the 4 sources. However, the total flux (6117/s cts) deviates strongly
from the modelmap (2500 cts/s), which does not affect the C-value (in the
current renormalization). Because a value of C>1.05 is considered not as
best possible fit, we increase the number of sources to two:
The fit with two gaussians yields a C-statistic of C=1.16, and a disagreement
in the count rate of N=6117 cts/s instead of N=2500 cts/s. Because a value of
C<1.05 is expected for a best possible fit, we increase the number of sources
to three:
The fit with three gaussians yields a C-statistic of C=1.05.
We increase the number of sources to four:
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