Imaging X-ray sources at a finite distance in coded mask instruments

We present a method we developed for the correction of the beam divergence in finite distance sources imaging through coded mask instruments. We discuss the defocusing artifacts induced by the finite distance showing two different approaches to remove such spurious effects. We applied our method to one-dimensional coded-mask systems, although it is also applicable to 2D systems as well. We provide a detailed mathematical description of the adopted method and of the systematics introduced in the reconstructed image (e. g. the fraction of source flux collected in the reconstructed peak counts). The accuracy of this method was tested by simulating point-like and extended sources at finite distance with the instrumental set-up of the SuperAGILE experiment, the one dimensional coded-mask X-ray imager on-board the AGILE mission. We obtained reconstructed images of good quality and high source location accuracy. Finally, we show the results obtained by applying this method to real data collected during the calibration campaign of SuperAGILE. Our method was demonstrated to be a powerful tool to investigate the imaging response of the experiment, particularly, the absorption due to the materials intercepting the line of sight of the instrument and the conversion between detector pixel and sky direction.