We present a method for the correction of 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 (1D) coded-mask systems, although it is also applicable in two-dimensional systems. 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 pointlike and extended sources at a finite distance with the instrumental setup of the SuperAGILE experiment, the 1D coded-mask x-ray imager onboard the AGILE (Astro-rivelatore Gamma a Immagini Leggero) 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.
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