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The aim of this paper is to pursue the investigation of the phase retrieval problem for the fractional Fourier transform   started by the second author. We here extend a method of A. E. J. M. Janssen to show that there is a countable set  such that for every finite subset  ⊂ , there exist two functions ,  not multiple of one another such that |  | = |  | for every  ∈ .This is done by constructing two functions ,  such that    and    have disjoint support for each  ∈ . To do so, we establish a link between  [],  ∈  and the Zak transform [] generalizing the well known marginal properties of .

Zak transform and non-uniqueness in an extension of Pauli’s phase retrieval problem