A common problem associated with x-ray imaging using coded apertures is the reconstruction of low-intensity extended objects. In the decoding of such objects, the overlapping images from the multiple pinholes give rise to noise cross talk and, in many cases, also to signal cross talk. In this paper, we propose an alternate approach based on the principle used in our earlier laboratory device for the real-time viewing of x-ray objects. It is shown that with this approach, the nonoverlapping redundant array, the sidelobes in the point spread function are not eliminated but merely displaced through a suitable choice of geometry. In this manner, the sidelobes no longer contribute to the background in the vicinity of a reconstructed image, and both signal and noise cross talks are completely eliminated. It may now be possible to reconstruct extended x-ray objects in 3-D by simple optical correlation and tomographically by a computer.
Lo-I Yin, J. I. Trombka, S. M. Seltzer, and M. J. Bielefeld., "X-ray imaging of extended objects using nonoverlapping redundant array," Appl. Opt. 22, 2155-2160 (1983)