  Phase retrieval problems occur in a width range of applications in physics
and engineering such as crystallography, astronomy, and laser optics. Common to
all of them is the recovery of an unknown signal from the intensity of its
Fourier transform. Because of the well-known ambiguousness of these problems,
the determination of the original signal is generally challenging. Although
there are many approaches in the literature to incorporate the assumption of
non-negativity of the solution into numerical algorithms, theoretical
considerations about the solvability with this constraint occur rarely. In this
paper, we consider the one-dimensional discrete-time setting and investigate
whether the usually applied a priori non-negativity can overcame the
ambiguousness of the phase retrieval problem or not. We show that the assumed
non-negativity of the solution is usually not a sufficient a priori condition
to ensure uniqueness in one-dimensional phase retrieval. More precisely, using
an appropriate characterization of the occurring ambiguities, we show that
neither the uniqueness nor the ambiguousness are rare exceptions.
