Enforcing irreducibility for phase retrieval in two dimensions

Unique phase recovery from a single two-dimensional intensity data set depends on the complex function's being represented by a globally irreducible entire function. Functions of two complex variables, in general, are likely to be irreducible, but no conditions have been stated to ensure this except for objects consisting of specific arrays of points. A condition based on Eisenstein's criterion for irreducibility is given here that requires two reference points in the object plane.