Optimizing RHESSI XRay Imaging for Compact Sources

1
Optimizing RHESSI X-Ray Imaging for Compact
Sources
Brian R. Dennis,1 Chang Liu,2 Rick Pernak,1,3
Richard A. Schwartz,1,3 and A. Kimberley
Tolbert1,4 1 Goddard Space Flight Center,
Greenbelt, MD 20771 Brian.R.Dennis_at_nasa.gov 2 Big
Bear Solar Observatory, Big Bear City, CA 92314
cliu_at_bbso.njit.edu 3 The Catholic University of
America, Washington, DC 20064 Richard.L.Pernak.1_at_g
sfc.nasa.gov richard.a.schwartz.1_at_gsfc.nasa.gov 4
RSIS, Lanham, MD Anne.K.Tolbert.1_at_gsfc.nasa.gov
ABSTRACT RHESSI X-ray imaging is possible with
angular resolution as fine as 2 arcsec (FWHM) at
energies from as low as 3 keV to gt100 keV.
However, taking full advantage of this capability
has proven to be challenging given the
Fourier-transform imaging technique that is used.
In particular, it is difficult to image the
finest source structures at the few arcsecond
scale in the presence of Poisson noise and
artifacts of the image reconstruction techniques
that are available. In this poster, we show how
judicious choices of the various free parameters
of the CLEAN reconstruction procedure allow the
source morphology to be best determined down to
the most compact structures present. We
illustrate the process with RHESSI and TRACE
observations of the flare on 2005 May 13 reported
by Liu et al. (2007). By taking full advantage of
the RHESSI data from the finest grids, we can
show that the hard X-ray emission comes from an
extended range along the two ribbons seen with
TRACE. This is in contrast to the usual case in
which the hard X-rays are seen from only one or
two points in each ribbon. This same imaging
philosophy can be applied to other flares to
determine the source size distribution down into
the arcsecond range. Liu, C. and Lee, J. and
Gary, D. E. and Wang, H., The Ribbon-like Hard
X-Ray Emission in a Sigmoidal Solar Active
Region", ApJ., 658, L127-L130, 2007.

• Image Reconstruction Algorithms
• CLEAN
• Quick evaluation of source morphology.
• Same image details as other methods.
• Defaults hide compact source structures.
• taper controls noise from finer subcollimators.
• For finer resolution, use narrower Gaussian
  convolved with point source components found by
  CLEAN.
• Uniform or natural weighting
• Visibilities version in preparation

• Image Reconstruction Algorithms
• MEM_NJIT
• Quick evaluation of source morphology.
• Uses visibilities
• Super-resolution with best subcollimators.
• Over-resolution problem?
• PIXON
• Best photometry lowest background
• Very slow
• Over-resolution problem controlled
  withPixon_resolution and/or pixon_sensitivity
• Visibilities Forward Fit
• For one or two sources only.
• Best for source dimensions.

13 May 2005 Flare starting at 1636 UT
This flare has proven to be particularly
informative about the quality of RHESSI images by
comparison with cotemporaneous TRACE 1600 Å
images. In particular, the optimized RHESSI
images reveal hard X-ray emission from the full
length of the two ribbons seen in the TRACE
images. This is in contrast to the more usual
isolated sources at a few locations along the
ribbons that have been reported previously for
other flares. Figs. 1 2 show the CLEAN images
made with natural and uniform weighting,
respectively, using the default set of
subcollimators (3 to 8). This limits the finest
source dimensions that can be resolved to 10
arcseconds.
Adding the two finest subcollimators in figures 3
and 4 shows that finer structure is present in
the image but it is not clear if it is real or
contains artifacts from the image reconstruction
process. Overlaying contours of the RHESSI image
from figure 4 onto the cotemporaneous TRACE image
in figure 6 shows that all of the structures
match above the 40 contour. The PIXON image in
fig. 7 reveals the same structures seen in the
CLEAN image shown with the same contour overlays.
Note however, that the PIXON image shows broader,
low intensity areas surrounding the two bright
ribbons similar to that shown in the default
CLEAN image in fig. 1. It is not clear if these
features are real since they are not present in
the TRACE image.
Optimizing RHESSI Images All reconstruction
techniques require subjective control of the data
from the finest subcollimators. Each
subcollimator produces a modulation of the
corresponding detector counting rate only if
there is source structure with dimensions equal
to or finer than the resolution of that
subcollimator. If there is no source structure
with dimensions of less than say 10 arcseconds,
then there will be no modulation of the counting
rates through the finest grids. Including data
from the corresponding detectors will only add
noise to the reconstructed image. Currently,
there is no automatic way to determine from the
RHESSI counting rate data which subcollimators
are producing significant modulation in the
detector counting rates. Thus, the user must
decide through trial and error which detectors to
include in the analysis and how to weight them if
they are included.
Fig. 6. TRACE 1600 Å image overlaid with contours
of CLEAN image in fig. 4.
Fig. 7. PIXON image overlaid with contours of
CLEAN image in fig. 4. Shows same features but
with lower PIXON background level.
Fig. 8. MEM-NJIT image overlaid with contours of
25 to 50 keV image in fig. 4. Shows effects of
over-resolution?
Fig. 5. CLEAN images in three 20 s intervals.
Shows little repeatability of smallest features.
Natural vs. Uniform Weighting Weighting schemes
are illustrated in fig. 9. Natural weighting
All subcollimators weighted equally. Strong
side lobes (fig. 10) Uniform weighting Weight
? 1/FWHM Optimal side lobes (fig. 10) Taper
allows exponential suppression of finest
subcollimator data. Fig. 10 shows that the point
spread function for uniform weighting has
significantly smaller side lobes than for natural
weighting. Thus, the combination of uniform
weighting with a judicial choice of the taper
parameter should produce the optimum CLEAN image.
However, if the modulation amplitude for the
finer subcollimators is low, using uniform
weighting can result in the magnification of the
noise and the appearance of false compact sources.
Fig. 10. Point spread functions for individual
subcollimators and for all subcollimators with
natural and uniform weighting. Note the smaller
side lobes for uniform weighting.
Fig. 9. Weight given to each subcollimator for
both natural and uniform weighting and for five
different values of the taper parameter from 0
to 4 arcseconds.
Fig.11. CLEANs default sigma of Gaussian used to
display point-source components. Thus, if
detectors 1 through 9 are chosen, the finest
sources displayed will have a sigma of 2.5 arcsec
(FWHM 6 arcsec) even though detector 1 has a
FWHM resolution of 2.3 arcsec.
Fig.12. CLEAN image with uniform weighting and a
taper of 4 arcsec.
Choice of Subcollimators To obtain the most
detailed images, use all subcollimators that show
significant modulation. For complex sources,
visibility amplitudes can be lt3 sigma for the
finest subcollimators even though there is
significant fine structure see fig. 13 for the
13 May 2005 flare. Visibility amplitudes are
good indicators of significant modulation for
simple sources see figure 14 for the single
compact source seen at the limb for the flare on
20 April 2002. All visibility amplitudes are gt3
sigma and Fig. 15 shows that uniform weighting
can be used with all subcollimators included to
reveal a compact source with a FWHM of ?1.6
arcsec. For other flares, there is currently no
recipe for making the best possible images
showing all of the real fine structure. Various
people are working on this problem.
Fig. 13. Fractional visibility amplitudes plotted
against the subcollimator (SC) number plus the
positional angle. Note that most amplitudes for
SC 6 and below are lt3 sigma.
Fig.15. Smallest source ever imaged in hard
X-rays. Uniform weighting, 0.2 arcsec pixels,
taper 0. FWHM 1.6 arcsec.
Fig. 14. Same as fig 13 for flare on 20 April
2002 at 2326 UT showing gt3 sigma visibility
amplitudes for all subcollimators. The
corresponding image is shown in fig. 15.