George Smeller’s HESSI WWW Site.

Suggested changes by Brian Dennis

To illustrate how the instrument can be used to produce an image of an x-ray point source in the sky, Dr Ed Schmahl has produced the five animated boxes below. The complete movie runs for one half a rotation of the instrument (2 s in actual time for HESSI) and then repeats continuously. The first four boxes are synchronized in time with each other and the fifth shows the final image of the source region reconstructed from the data recorded in the complete half rotation of the movie.

Box 1 is a map of the sky near the assumed point-like x-ray source shown as a circle in the bottom left corner. The instrument axis of rotation is marked with a plus sign at the center of the box. The dark and light bars mark possible positions in the sky where the detected x-ray photons could have originated. This is known as back projection since the detected x-ray photons are "back projected" onto the sky using the possible arrival directions allowed by the grids. At any given time, there is a high probability that the source of the detected x-ray photons is somewhere in the white areas in the box, a low probability that the source is in the black areas, and an intermediate probability that it is in the gray areas. The bar pattern on the sky arises since x-rays from a source located in a white area could have passed unimpeded through a slit in both the upper and lower grids given their straight-line trajectories. X-rays from a source located in a black area would have had to pass through a slat in either the upper or lower grid in order to reach the detector. Since the slats are made of high density material, they are opaque to x-rays (at least for the lower energy photons). Thus, there is little chance that the photons could reach the detector if they have to pass through a slat to get there.

Box 2 represents what the detector "sees" as a function of time as x-ray photons from the off-axis point source indicated in Box 1 pass through the grids. The changing shades of gray represent the changing numbers of x-ray photons that can get through the two grids to the detector as the instrument rotates. This variation in the transmitted flux is shown in Box 3 as a function of time during the half rotation of the movie. Note that the x-ray photons are uniformly distributed in the detector area at any given time.

Box 3 shows the number of x-ray photons that pass through both grids and reach the detector as a function of time as the instrument rotates. Note the changing period of the variations as the point source in Box 1 appears to move across the bar pattern. First it appears to move nearly parallel to the probability bars and produces a gradually varying counting rate in the detector. Then it appears to move more nearly perpendicular to the bars and produces a more rapidly varying counting rate.

Box 4 shows how the image can be reconstructed from the probability distributions shown in Box 1 and the counting rate in the detector shown in Boxes 2 and 3. The reconstruction process is simply to add together all the probability distributions shown sequentially in Box 1 but weighted according to the detector counting rates shown in Boxes 2 and 3. As you will see, the image in Box 4 is initially the same as the image in Box 1 but then more images from Box 1 are added on top of the original image. Finally, at the end of the movie, the reconstructed image is shown and this is duplicated in Box 5. The point source can be clearly seen in the bottom left corner, exactly where we had assumed it to be for the purposes of this demonstration. A second "ghost" source appears in the upper right corner and faint rings, referred to as "side-lobes" appear around both "source" locations. These artifacts can be removed by more sophisticated techniques than can be shown in this demonstration. Using techniques named Clean, Maximum Entropy, Pixons, and Fourier Transform analysis, scientist have been able to reconstruct images that compare in resolution with optical images.

The main limitations of this type of imaging is to be able to see sources that are very extended rather than being point-like and to "see" a weak source in the presence of much stronger sources. Extended sources can be imaged using, surprisingly, pairs of coarser grids in combination with the finer grids that give the finest angular resolution. By using multiple detectors behind grid pairs with a range of slit widths and spacings, images can be reconstructed showing the location and extent of the different sources in the field of view. There is always some maximum source extent that cannot be imaged, however.

The ability to image weak sources in the presence of stronger sources is difficult even at optical wavelengths because of the problem of scattered light. In our case, the difficulty arises because of the need to remove the ghost sources and side-lobes from the strong source before the weaker sources can be seen. This problem has generally limited the useful dynamic range of this technique to less than about ten. HESSI, with its multiple detectors and precisely aligned grids, should achieve a factor of up to ten better.

Box 5 is just the final reconstructed image from Box 4 after all the data from the half rotation has been accumulated.