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These images show the effects of using only 2 or 4 HESSI collimators on mapping combined small and large sources. The motivation for this is to illustrate the tradeoffs required at high energies where only two grids will be thick enough to modulate photons.
The first image shows the same model used to make dirty maps as discussed above and a Maximum Entropy map which minimizes the chi-squared value computed from the simulated count rate from the model source and the count rate derived from the MEM map.
The data at the top show the parameters of the mapping. The two top maps are the model and the raw MEM map, while the two bottom maps show the same maps convolved with the "clean beam", a cone with the same FWHM as the modulation pattern of collimator 6. (There is not much difference between the convolved and unconvolved maps in this case, but in general there may be. The convolution is necessary to obtain true fluxes from MEM maps.)
Note that the full size of the extended source is not perfectly reconstructed, although its shape and flux appear to be. Other methods of image reconstruction, such as the Richardson-Lucy algorithm, may do better in this regard.
The second image shows the reconstruction using only collimators 6 and 9. This is effectively the configuration for photons of sufficient energy (e.g. 2 MeV) that the thin collimators 7 and 8 do not modulate. Note the similarity to the reconstruction done with 4 collimators. Although this result is not completely realistic in several ways (the modulation efficiency of the thick grids 6 and 9, for example, is not unity), it indicates the likely capability of HESSI for imaging point-like and extended gamma-ray (E > 500 keV) sources in sufficiently large flares.
In this reconstruction, the MEM map divides the flux between the compact and extended components in the proportions 38%:44%. (About 18% of the flux is in the extended emission that appears as a "background" in the MEM map.) Note that in this case, the MEM map overestimates the relative flux of the extended component by about 2.5%. Given that the total number of counts per detector here is 4500, the expected error due to Poisson statistics would be about 3%.
Note that the modulation profile shows lower modulation amplitude in the first half (for collimator 6) than in the second half (collimator 9). This is expected because the finer collimator over resolves the extended source. The RMS deviations from the mean of the two halves lie in the proportions 0.567:1, meaning that collimator 6 "sees" only a little more than half of the extended structure that collimator 9 "sees".
The results of a more stringent test , in which the extended source is broader, the same flux as the compact source, but with only 1/25 of the peak brightness, is shown in the next figure. The count rate this time is half the previous. The MEM map using only collimators 6 and 9 shows the extended source again, albeit with somewhat ragged contours. Surprisingly, boxes around the compact and extended sources contain fluxes equal to within 1%, even though some 16% of the total flux lies in the upper left and lower right parts of the map, outside the boxes. (The box coordinates were 0,0,20,20 and 21,21,63,63, respectively.) The total number of counts per detector = 2700, so the fluxes per collimator can be determined to about 2% if only Poisson statistics are involved.
Last updated December 19, 1997.
