Nonuniqueness results for X-ray problems with point sources

Let be any finite set with no three points on a line. Then we construct explicitly families of bounded Borel sets which are not uniquely determined by their X-ray images from the points inX. This result is in sharp contrast to the known uniqueness results for convex sets (Hammer's X-ray problem). This research was partially supported by the Italian “Consiglio Nazionale delle Ricerche.”