Reconstruction of objects having latent reference points

A simple recursive algorithm is proposed for reconstructing certain classes of two-dimensional objects from their autocorrelation functions (or equivalently from the modulus of their Fourier transforms—the phase-retrieval problem). The solution is shown to be unique in some cases. The objects contain reference points not satisfying the holography condition but satisfying weaker conditions. Included are objects described by Fiddy et al. [ Opt. Lett.8, 96 ( 1983)] satisfying Eisenstein’s thorem.