On the way to full-field X-ray fluorescence spectroscopy imaging with coded apertures: theoretical considerations and simulations
The imaging with X-rays is a challenging field, due to the optical properties of X-rays. The fabrication of the appropriate optics is usually expensive and requires an elaborate manufacturing process. One simpler and less expensive possibility of imaging high energy radiation is coded aperture imaging, a technique well established in astrophysics and also used in nuclear medicine or radiation detection, e.g., for nuclear decommissioning. Our aim is to adapt the coded aperture imaging for X-ray fluorescence spectroscopy in the nearfield. In this work we show theoretical considerations and preliminary simulations of image formation through a coded aperture and three different reconstruction methods to prepare the experiments. We used a new mask based on an inverted modified uniformly redundant array that could be used for the construction of a decoding mask for all investigated geometrical arrangements. It turned out that the most commonly used reconstruction method, which is based on the convolution of the detected image with the decoding mask, does not produce satisfactory results in all cases, especially for small distances between object, mask and detector. Hence, we developed two new reconstruction methods, one based on an iterative algebraic optimization and another one based on a genetic algorithm. Both show good performance even in those cases where the convolution method fails. The results of our simulations show that our new reconstruction methods allow reliable reconstructions for arbitrary geometric arrangements and thus provide a basis for further investigations of the ideal parameters for near field coded aperture imaging and refinements of the algorithms.