For on-axis sources, some simple PSF core metrics are the centroid and its second moments, cuts through the centroid pixel, and fits to those cuts. The PSF wings can be characterized by the radial surface brightness and encircled energy, but these quantities yield no azimuthal information. The PSFs of off-axis sources lose the simple centrally-peaked geometry enjoyed by on-axis sources (see the MST Phase 1 report). Other, more complicated metrics must be employed here, such as width of the pincushion caustics and major and minor axes of the extended lobes. Again we must work closely with MST to characterize these features, generating a common set of metrics to facilitate comparison.
``Standard'' analysis products like radial histograms and encircled energies must be treated with care when the bulk of the PSF is contained in a single pixel. Most algorithms to calculate these quantities yield inaccurate results when the PSF is undersampled, as is the case with ACIS at XRCF. Since the point of this test was to explore the details of the PSF core, we will use comparitors that are more appropriate for this region.
The simplest and most obvious metric is an image. Figure 6.16
shows a greyscale image of the data PSF core and one of the simulation,
on the same scale. The number of events is the same (19428). The simulation
was tuned by moving the ``virtual FAM,'' i.e. by adjusting the subpixel
position of the entire rayfile. The offsets used here are (chipx, chipy)
= (+0.1, -0.3). Since the data are affected by pile-up but the simulation
is not, the number of events in the central pixel is not a good metric.
Instead, we used the number of events in the neighboring pixels, examining
all the neighbors in a 5 X 5 pixel region around the central pixel.
Figure 6.16: The left image
shows the data for test
H-IAI-CR-1.001; the right shows the simulation.
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By examining the difference image (Figure 6.17),
we can get a sense for the accuracy of the offsets, although we must keep
in mind the pile-up and other factors, such as the pointlike nature of
the current rayfile and the fact that we have not attempted to apply any
rotation. This difference image implies that the offsets might need further
adjusting - either a slight rotation or a smaller offset in CHIPX.
Figure 6.17: Difference image,
simulation - data. The image scaling is between the minimum and maximum
values in the difference image (black = -349 counts, white = +254 counts).
There are 19428 counts in each dataset. The PSF is centered on the
white pixel, where the simulation has more counts because it is unaffected
by pile-up.
Figure 6.18 illustrates another
way to view the 2-dimensional datasets, as lego plots. These help illustrate
the fact that the central pixel in the simulation has more events than
in the data (because of pile-up) and the neighboring pixel at (962,962)
has a similar number of extra events - a fact that will require further
investigation.
Figure 6.18: The left 2-dimensional histogram (``lego plot'') shows the data for test H-IAI-CR-1.001; the right shows the simulation.
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One-dimensional metrics are also useful, supplying a simpler means of comparing the datasets (with, of course, a corresponding loss of information over 2-dimensional methods). These are illustrated in Figure 6.19, showing vertical and horizontal cuts through the centroids of both the data and the simulation, and Figure 6.20, showing x and y marginal sums.
Figure 6.19: Horizontal and vertical cuts through the centroid of the PSF from the data (left) and the simulation (right).
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Figure 6.20: Marginal sums of
the PSF from the data (left)
and the simulation (right).
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