Abstract
An imaging model and an image reconstruction algorithm for a transparent X-ray beam imaging and position measuring instrument are presented. The instrument relies on a coded aperture camera to record magnified images of the footprint of the incident beam on a thin foil placed in the beam at an oblique angle. The imaging model represents the instrument as a linear system whose impulse response takes into account the image blur owing to the finite thickness of the foil, the shape and size of camera's aperture and detector's point-spread function. The image reconstruction algorithm first removes the image blur using the modelled impulse response function and then corrects for geometrical distortions caused by the foil tilt. The performance of the image reconstruction algorithm was tested in experiments at synchrotron radiation beamlines. The results show that the proposed imaging system produces images of the X-ray beam cross section with a quality comparable with images obtained using X-ray cameras that are exposed to the direct beam.