Direct single-shot phase retrieval from the diffraction pattern of separated objects

Ben Leshem (), Rui Xu, Yehonatan Dallal, Jianwei Miao, Boaz Nadler, Dan Oron, Nirit Dudovich and Oren Raz
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Ben Leshem: Weizmann Institute of Science
Rui Xu: University of California
Yehonatan Dallal: Weizmann Institute of Science
Jianwei Miao: University of California
Boaz Nadler: Weizmann Institute of Science
Dan Oron: Weizmann Institute of Science
Nirit Dudovich: Weizmann Institute of Science
Oren Raz: University of Maryland

Nature Communications, 2016, vol. 7, issue 1, 1-6

Abstract: 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.

Date: 2016
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DOI: 10.1038/ncomms10820

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