E-mail: aschwanden@lmsal.com - Markus J.Aschwanden (Lockheed Martin Solar & Astrophysics Lab.)

HESSI Tutorial on Forward-Fitting : III. Number of Source Components

This 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:

o = hsi_image()
o -> set,image_algorithm='forwardfit'
o -> set,n_gaussians=1
o -> set,image_dim=[64,64]
o -> set,pixel_size=[2,2]
o -> set,det_index_mask=byte([0,1,1,1,1,1,1,1,1])
im = o -> getdata()
o -> plot

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:

o -> set,n_gaussians=2
o -> set,det_index_mask=byte([0,1,1,1,1,1,1,1,1])
im = o -> getdata()
o -> plot

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:

o -> set,n_gaussians=3
o -> set,det_index_mask=byte([0,1,1,1,1,1,1,1,1])
im = o -> getdata()
o -> plot

The fit with three gaussians yields a C-statistic of C=1.05. We increase the number of sources to four: