1. “Imaging Spectroscopy” with RHESSI visibilities and inverse DRMs J.McTiernan RHESSI/NESSI workshop 4-apr-2006

2. Purpose: To do images in photons, accounting for off-diagonal components of the detector response matrix. Observed counts = DRM # Photon flux If you can invert the response matrix: Photon flux = (DRM) -1 # Observed counts The following is what happens when you just blindly invert the DRM using the IDL invert function (Gauss-Jordan).

3. Motivation from Non-imaging spectroscopy: White: SPEX Red: 1D Pixon Blue: Inverse 24-aug-2002 00:54:00 UT Det 4f

4. Non-imaging spectroscopy, typical results: Photon spectrum from inverted matrix fits “exactly” Х^2 ~ 1.0e-7 Photon spectrum looks strange below 5 keV This does not work well for ΔE < 1 keV -- the spectrum is negative for low energies.

5. Procedure for visibilities: First create visibilities for different energies, arrange in an array versus energy for each (u, v) point. Multiply each component (totflux, real, imaginary) of visibilities by the diagonal energy response to change units to counts. For each (u, v), obtain the full DRM for that detector and invert the matrix. Replace the original components in the visibility structure with (DRM) -1 times the original component:

6. Or: vis.totflux = vis.totflux X diagonal_DRM float(vis.obsvis) = float(vis.obsvis) X diagonal_DRM imaginary(vis.obsvis) = imaginary(vis.obsvis) X diagonal_DRM Then: vis.totflux = (DRM) -1 # vis.totflux float(vis.obsvis) = (DRM) -1 # float(vis.obsvis) imaginary(vis.obsvis) = (DRM) -1 # imaginary(vis.obsvis)

7. Now you can do what you want with the visibilities. Here, just run HIS_VIS_FWDFIT on the “photon” visibilities and compare with results from the originals. Energy bands: 1 keV bins from 3 to 10 keV, binsize increases after by 10% for each bin. Energy range From 3 to 280 keV. Detectors: 3f, 4f, 5f, 6f, 8f, 9f

8. Plot of total photon flux: (single sources) White: Original Blue: Result from invert Dashes: SPEX This does not so good, particularly < 10 keV

9. This looks much better, but < 6 keV dip…

10. Not so bad here, but < 6keV dip is disturbing

11. Atten_st = 3 Dude, where’s my Iron line?

12. Conclusions: This looks much less promising than in the original non- imaging case. Possible improvements? More care taken in the imaging. I am still a visibility novice. Larger energy bins. Results for > 2keV energy bins are much better, but at least some of the motivation for this is to work with the Fe line and using large bins for low energies would make this not too useful.