Let f be a function on  and w be a finite subset of  Discrete tomography reconstructs the function f from the data This problem is proved by Hazama to be described completely by the zero locus of a certain polynomial in n variable associated with w. The purpose of this paper is to apply his result to the zero-sum arrays when the window w has the form  Furthermore, we describe the way how one can find the rational zero-sum arrays for w.

discrete tomography, point sequence, Gauss sum.