TY - JOUR
T1 - Inversion of dynamical Bragg intensities to complex structure factors by iterated projections. For Ultramic. 2020. ("Pico" Festschrift, May 2021)
AU - Spence, John C.H.
AU - Donatelli, Jeffrey J.
N1 - Funding Information:
Thanks to all my co-authors, postdocs and students on all my papers on this subject over the past forty years. Supported by ARO award W911NF2010321 , the Advanced Scientific Computing Research and Basic Energy Sciences programs of the Office of Science of Department of Energy (DOE) (Award No. DE-AC02-05CH11231), and by Laboratory Directed Research and Development funds from Berkeley Lab from the Director, Office of Science DOE (Award No. DE-AC02-05CH11231 ).
Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2021/3
Y1 - 2021/3
N2 - A method for recovering complex structure factors from many simultaneously excited Bragg beam in- tensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unit ary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.
AB - A method for recovering complex structure factors from many simultaneously excited Bragg beam in- tensities is described. The method is applied to simulated transmission electron diffraction data over a wide range of crystal thickness and beam energies. The method is based on iterated projections between structure and scattering matrices, which are related by a matrix unit ary transformation, exponential, which we invert. The algorithm removes multiple-scattering perturbations from diffraction data and might be extended to other fields, including X-ray and neutron diffraction and cryo-electron microscopy. Because coherent multiple scattering involves interference between Bragg beams, the method also solves the phase problem. Unlike dynamical inversion from electron microscope images or ptychography data, the method, which starts with Bragg beam intensities, provides complex structure factors unaffected by focusing errors or resolution limitations imposed by lenses. We provide inversions from simulated data with 441 simultaneously excited Bragg beams over a range of thickness and beam energy. We discuss the retrieval of chirality information from enantiomorphs, the efficient incorporation of symmetry information using the irreducible representation of the group of structure matrices, and the effect of HOLZ lines to provide three-dimensional information.
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U2 - 10.1016/j.ultramic.2021.113214
DO - 10.1016/j.ultramic.2021.113214
M3 - Article
C2 - 33561601
AN - SCOPUS:85100687183
SN - 0304-3991
VL - 222
JO - Ultramicroscopy
JF - Ultramicroscopy
M1 - 113214
ER -