Feasibility Simulations of and Improvements upon the X-Ray Occulting Steerable Satellite

1. Feasibility Simulations of and Improvements upon the X-Ray Occulting Steerable Satellite Melissa M DeLucchi Case Western Reserve University, Department of Physics Figure 1a: Acyclic mask design, used in physical setup. Figure 1b: Cyclic mask as it appears in the simulation. Figure 1: A schematic of the translating Uniformly Redundant Array (URA) mask. Grayed areas are 1cm of lead, which attenuates 87% of gamma rays. Clear areas are gamma-transparent plexi-glass. Introduction The X-Rays emitted by high energy astrophysical systems can be used to create images of these sources, which help us to better understand the structure of our universe. Unfortunately, current X-Ray detection methods achieve relatively low angular resolution, as this aspect is often compromised in favor of collecting more photons. The best angular resolution that can be achieved with detectors which are currently in space is on the order of 500 milli-arc seconds, worse by a factor of 100 than the fundamental constraint from diffraction, 3 milli-arc seconds. The purpose of the X-Ray Occulting Steerable Satellite (XOSS) project is to explore a method that could greatly increase the resolution of images taken of astronomical objects, utilizing existing X-ray detection technologies[1]. The method employed by XOSS involves passing a coded mask between the X-ray source and the detector. The mask consists of a sheet of lead with a pattern of apertures that would allow photons to only pass through certain areas of the mask during a certain time period. Using coded aperture imaging allows for a more accurate image of the sky as the mask passes the detector. From this information, we can acquire a more accurate calculation of intensity and position of such sources, to the end of improving X-ray imaging. It is the purpose of this project to study the possibility of a new mask design, utilizing properties of a uniformly redundant array. This mask could be used in the future space-based X-Ray observatory, Constellation-X. We will study the improved mask design using a computer simulation. Along the way, a new reconstruction method is developed for generating two-dimensional images of arbitrary source configurations. Monte Carlo Simulation Design A simulation was constructed to mimic the design of a lab-scale prototype of the project, constructed some years ago. The setup can be viewed in Figure 2 below. The simulation was written in C++, using ROOT graphing libraries. The simulation currently accounts for a number of natural phenomena present in real data taking on the lab-scale prototype. These phenomena include Poisson discrete probabilistic nature of particle radiation, partial attenuation of the lead mask, and inconsistencies in mask velocity. The output of the simulation is similar to that of the experimental protocol: particle counts from the detector summed over 6 second intervals of the mask’s translation between the detector and source. A typical output is seen in Figure 3. Two-Dimensional Reconstruction The main assumption of the reconstruction attempts is that all of the one dimensional images contain all the information needed to reconstruct the original image of the source. With this knowledge, it should be relatively easy to reconstruct the image analytically, just by combining what is known about each pixel from the intersecting slices. The resulting image, in Figure 5(f), is one which bears a striking resemblance to the original point source. Results Using simulated data, we were able to form a very close guess about the two-dimensional structure of radioactive sources. Not only was it possible to reconstruct the simplest case - a single point source - but more complicated sources came out of the simulations and preliminary reconstruction guesses. Several other types of source configurations were attempted to make sure that the routine could work for arbitrarily complex source images. A sample of these configurations can be found in Figure 6. Figure 5(a):Each one dimensional image was scaled down to have a zero baseline and renormalized so that each contained the same total sum of intensity. This could be different for each slice due to normal statistical variation in the particle emission. Each slice was then stretched and implanted onto a circle. Figure 6(a): Two point sources, equidistant from the center of the image. Figure 6(b): Two point sources and a half-circle, lovingly called “the frog”. Figure 5(b)Each projection was then added in the same manner, summing each pixel over each projection. Care was taken to put the image on the circle with the same angle as was used in collecting the data. (With 11 passes, there would not actually be any two passes perpendicular, as seen here) Figure 6: Some images reconstructed using the partial-reconstruction scheme developed in this project. All steps in the method appear in Figure 5 Figure 2: A simplified schematic of the prototype setup, mimicked in the code of the simulation. The mask translates 55 cm during the course of experiment. Conclusions As of now, a full reconstruction of a ring source has been made by Craig Copi, seen in Figure 7(b). This is very promising evidence that the new mask design can help improve angular resolution of reconstructed images. The resolution of the simulated data reconstruction has the image spanning only a few pixels. With the knowledge gained with this project, there is much potential for success in data taking and reconstruction, to the end of proving the concept of the XOSS project. Figure 3:Particle count data for a typical run, using a point spread function. Low areas reflect times with opaque areas of the mask between source and detector. Peaks reflect times where the source is visible to the detector. Figure 5(b)A total of 11 one-dimensional projections are summed over the circle. The image now looks very little like it should, so some further analysis is required. Over the next three steps, the image will begin to take shape. One-Dimensional Reconstruction The URA was expanded to be the same length as the data set and had the values of -1 for opaque areas and 1 for open sections of the mask. Attempting a correlation of the particle counts with an array representative of the coded aperture mask yields an image of the source plane. It is very important for the one-dimensional reconstruction that the mask used in data taking be cyclic[4]. This image is more useful than just a picture of the image in one slice across source plane: it is the sum of the intensities of all points perpendicular to the cross section. Because the original design did not implement a cyclic mask, this kind of reconstruction was not possible. Very clean reconstructions are possible using this method, like Figure 4, with little noise or distortion, owing to an approximately cyclic mask as opposed to a truly cyclic mask. Figure 5(d)Because of problems with planting lines at arbitrary angles across a circle onto a rectangular squared grid, there is a large spike in the middle after all slices have been added. This is because all projections pass through this point. The trouble spots are removed at this step. Figure 7(a): Reconstruction completed by Craig Copi in late 2005, on real data collected by Michelle Hui Figure 7(b): Reconstruction completed by Craig Copi August 2006 on simulated data. Figure 7: Two reconstructions provided by Craig Copi. The first one used the acyclic mask design, the second one using the cyclic mask. Coded Aperture Imaging The single pinhole camera has long been known to produce images with superior angular resolution. This method amounts to allowing particles to slowly penetrate the single aperture. With weak signals, like those of cosmic X-ray sources, this method could take incredible spans of time, with only a small fraction of particles ever getting through. Coded aperture imaging is used to overcome these problems. With this technique, the single aperture is replaced with a number of apertures arranged in any known pattern. The resulting image consists of a copy of the image for each aperture, each one overlapped with the rest. Understandably, the image often bears no resemblance to the original image and the reconstruction of the image must take into account the structure of the apertures. One of the possible designs for apertures, which has been historically successful, is the URA. A URA mask is a perforated mask with a number of unique properties[2]. Perhaps the most important property is that when one takes the correlation of a URA with itself, the resultant set of points has a peak where the two arrays coincide, and flat side-lobes everywhere else. This aspect will become important when we revisit the mask for image Reconstruction. It is also possible, using URA’s, to eliminate noise that would be otherwise present in images[3]. Acknowledgments I would like to thank Corbin Covault for his direction and support for the project. Donald Driscoll has been a great benefit to the project in guidance through the day to day problems encountered. The rest of the XOSS collaboration, including Craig Copi, Glenn Starkman, and previous senior project students, particularly Michelle Hui, for providing a launch point into the project, with special thanks to Craig Copi for the reconstructions which appear in this poster. The remainder of the High Energy Astrophysics group for their support and unending humor, especially Edgar Wilson, who collaborated on mask design, and Michael Gisondo, who helped with setup of the XOSS apparatus. The SOURCE office has helped this project through generous monetary support in the Summer of 2006 and in any other way they possibly could. Figure 5(e) The image was smoothed using a 3x3 Gaussian smoothing kernel. The only remaining artifact of the method is a plateau surrounding the central peak. Figure 4: One-dimensional reconstruction of a point spread function. The vertical axis is the relative intensity of the source as seen by the detector. References [1] C. J. Copi and G. D. Starkman. The big occulting steerable satellite (BOSS). Astrophys.J, 532:58192, 2000. [2] E. E. Fenimore and T. M. Cannon. Coded aperture imaging with uniformly redundant arrays. Appl Opt, 17(3):337ﾐ 347, Feb 1 1978. [3] C. E. Covault, J. E. Grindlay, R. P. Manandhar, and J. Braga. Techniques for removing non-uniform background in coded-aperture imaging on the energetic x-ray imaging telescope experiment. IEEE Transactions on Nuclear Science, 38(2 pt I):591ﾐ596, Apr 1991. [4] E. E. Fenimore. Coded aperture imaging: Predicted performance of uniformly redundant arrays. Appl Opt, 17(22):3562ﾐ3570, Nov 15 1978. Figure 5(f) The final step is to remove the excess energy implanted on the edges of the circle. A minimum value of the surrounding plateau is determined, and this amount is subtracted from all elements. Elements are also rescaled so that the total energy in the image remains the same. The result is our final image.