title: Direct single-shot phase retrieval from the diffraction pattern of separated objects.
abstract: The non-crystallographic phase problem arises in numerous scientific and technological fields. An important application is coherent diffractive imaging. Recent advances in X-ray free-electron lasers allow capturing of the diffraction pattern from a single nanoparticle before it disintegrates, in so-called 'diffraction before destruction' experiments. Presently, the phase is reconstructed by iterative algorithms, imposing a non-convex computational challenge, or by Fourier holography, requiring a well-characterized reference field. Here we present a convex scheme for single-shot phase retrieval for two (or more) sufficiently separated objects, demonstrated in two dimensions. In our approach, the objects serve as unknown references to one another, reducing the phase problem to a solvable set of linear equations. We establish our method numerically and experimentally in the optical domain and demonstrate a proof-of-principle single-shot coherent diffractive imaging using X-ray free-electron lasers pulses. Our scheme alleviates several limitations of current methods, offering a new pathway towards direct reconstruction of complex objects.
authors.affiliation: Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Ben
authors.initials: B
authors.lastname: Leshem
authors.affiliation: Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, California 90095, USA.
authors.forename: Rui
authors.initials: R
authors.lastname: Xu
authors.affiliation: Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Yehonatan
authors.initials: Y
authors.lastname: Dallal
authors.affiliation: Department of Physics and Astronomy and California NanoSystems Institute, University of California, Los Angeles, California 90095, USA.
authors.forename: Jianwei
authors.initials: J
authors.lastname: Miao
authors.affiliation: Department of Computer Science and Applied Mathematics , Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Boaz
authors.initials: B
authors.lastname: Nadler
authors.affiliation: Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Dan
authors.initials: D
authors.lastname: Oron
authors.affiliation: Department of Physics of Complex Systems, Weizmann Institute of Science, Rehovot 76100, Israel.
authors.forename: Nirit
authors.initials: N
authors.lastname: Dudovich
authors.affiliation: Department of Chemistry and Biochemistry, University of Maryland, College Park, Maryland 20742, USA.
authors.forename: Oren
authors.initials: O
authors.lastname: Raz