The Patterson function as auto-hologram and graph enables the direct solution to the phase problem for coherently illuminated atomistic structures

Calvo-Almazán, Irene; Fenter, Paul

doi:10.1088/1367-2630/ac0d2d

Title: The Patterson function as auto-hologram and graph enables the direct solution to the phase problem for coherently illuminated atomistic structures

Journal Article · Fri Jul 09 00:00:00 EDT 2021 · New Journal of Physics

DOI:https://doi.org/10.1088/1367-2630/ac0d2d· OSTI ID:1835494

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Abstract The coherent Patterson function, derived from the coherent scattering intensities from N atoms, can be described as an auto-holographic image, i.e., the superposition of N -holographic images in which each atom serves as the source of a different reference wave, and as a mathematical graph of the unknown structure. These insights indicate that the unknown structure is significantly over-determined by the inherent information content in a Patterson function by a factor of ( N − 1)/2 (for non-degenerate structures), independent of dimensionality. However, we also show that the ability to resolve the distinct features in the Patterson function depends strongly on details of the experimental design (data range, sampling frequency, and dimensionality). This re-interpretation suggests that the coherent Patterson function provides a natural context for describing the information content in coherent scattering, reveals that there is no inherent phase problem for coherently illuminated pointwise structures, and enables the design of an algorithm which retrieves the structure directly from the Patterson function, without using error metric minimization.

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Research Organization:: Argonne National Laboratory (ANL), Argonne, IL (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC02-06CH11357

OSTI ID:: 1835494

Alternate ID(s):: OSTI ID: 1831744

Journal Information:: New Journal of Physics, Journal Name: New Journal of Physics Vol. 23 Journal Issue: 7; ISSN 1367-2630

Publisher:: IOP PublishingCopyright Statement

Country of Publication:: United Kingdom

Language:: English

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