Abstract
A general description of n-dimensional Fourier transforms is given in terms of their complex zero surfaces. The properties of these surfaces are analyzed and then applied to two-dimensional scattered electromagnetic fields in the Fraunhofer region. It is shown that the properties of two-dimensional fields differ inherently from those of one-dimensional fields and that they lead to a reduced ambiguity for object reconstruction from intensity data. A way of estimating this ambiguity is given.