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Investigation of the tolerance of the phase retrieval algorithm to missing information at the center of a detector in the case of coherent scattering from an ordered structure

V. Ukleev1

1 Laboratory for Neutron Scattering and Imaging (LNS), Paul Scherrer Institute (PSI), CH-5232 Villigen, Switzerland

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DOI: 10.18287/2412-6179-2019-43-6-1088-1092

Pages: 1088-1092.

Full text of article: Russian language.

Abstract:
The hybrid input-output algorithm is a phase retrieval method that provides solution for the phase problem of coherent X-ray diffraction imaging of micro- and nano-objects from the diffraction pattern alone without using any focusing optics. In this paper, we have studied a tolerance of this algorithm to missing information at the center of the diffraction pattern, which is a frequent problem in problems of small-angle scattering. We considered the particular problem of the stability of the algorithm in the case of scattering from an ordered structure and provided a qualitative and quantitative description of the degradation of image reconstruction with an increase in the amount of missing information.

Keywords:
coherent diffraction imaging, phase retrieval, small-angle scattering.

Citation:
Ukleev VA. Investigation of the tolerance of the phase retrieval algorithm to missing information at the center of a detector in the case of coherent scattering from an ordered structure. Computer Optics 2019; 43(6): 1088-1092. DOI: 10.18287/2412-6179-2019-43-6-1088-1092.

Acknowledgements:
This work was supported by the project SNF Sinergia CRSII5-171003 NanoSkyrmionics.

References:
  1. Kuznetsova TI. On the phase retrieval problem in optics. Soviet Physics Uspekhi 1988; 31(4): 364.
  2. Miao J, Charalambous P, Kirz J, Sayre D. Extending the methodology of X-ray crystallography to allow imaging of micrometre-sized non-crystalline specimens. Nature 1999; 400(6742): 342-344.
  3. Robinson I, Harder R. Coherent X-ray diffraction imaging of strain at the nanoscale. Nature Materials 2009; 8(4): 291-298.
  4. Miao J, Sayre D. On possible extensions of X-ray crystallography through diffraction-pattern oversampling. Acta Crystallographica Section A: Foundations of Crystallography 2000; 56(6): 596-605.
  5. Fienup JR. Phase retrieval algorithms: a comparison. Appl Opt 1982; 21(15): 2758-2769.
  6. Marchesini S. Invited article: A unified evaluation of iterative projection algorithms for phase retrieval. Rev Sci Instrum 2007; 78(1): 011301.
  7. Huang X, Nelson J, Steinbrener J, Kirz J, Turner JJ, Jacobsen C. Incorrect support and missing center tolerances of phasing algorithms. Opt Express 2010; 18(25): 26441-26449.
  8. Tripathi A, Shpyrko O, McNulty I, Eyberger C, Lai B. Influence of noise and missing data on reconstruction quality in coherent X-ray diffractive imaging. AIP Conf Proc 2011; 1365(1): 305-308.
  9. He K, Sharma MK, Cossairt O. High dynamic range coherent imaging using compressed sensing. Opt Express 2015; 23(24): 30904-30916.
  10. Ukleev V, Yamasaki Y, Morikawa D, Kanazawa N, Okamura Y, Nakao H, Tokura Y, Arima T-H. Coherent resonant soft X-ray scattering study of magnetic textures in FeGe. Quant Beam Sci 2018; 2(1): 3.
  11. Gulden J, Yefanov OM, Mancuso AP, Abramova VV, Hilhorst J, Byelov D, Snigireva I, Snigirev A, Petukhov AV, Vartanyants IA. Coherent X-ray imaging of defects in colloidal crystals. Phys Rev B 2010; 81(22): 22, 224105.
  12. Ulvestad A, Nashed Y, Beutier G, Verdier M, Hruszkewycz SO, Dupraz M. Identifying defects with guided algorithms in Bragg coherent diffractive imaging. Sci Rep 2017; 7(1): 9920.
  13. Shabalin AG, Meijer JM, Dronyak R, Yefanov OM, Singer A, Kurta RP, Lorenz U, Gorobtsov OY, Dzhigaev D, Kalbfleisch S, Gulden J, Zozulya AV, Sprung M, Petukhov AV, Vartanyants IA. Revealing three-dimensional structure of an individual colloidal crystal grain by coherent X-Ray diffractive imaging. Phys Rev Lett 2016; 117(13): 138002.
  14. Van Heel M, Schatz M. Fourier shell correlation threshold criteria. J Struct Biology 2005; 151(3): 250-262.
  15. Stroke GW. Introduction to coherent optics and holography. New York: Academic Press, 1966.
  16. Mancini GF, Karl RM, Shanblatt ER, Bevis CS, Gardner DF, Tanksalvala MD, Russell JL, Adams DE, Kapteyn HC, Badding JV, Mallouk TE, Murnane MM. Colloidal crystal order and structure revealed by tabletop extreme ultraviolet scattering and coherent diffractive imaging. Opt Express 2018; 26(9): 11393-11406.
  17. Lazarev S, Besedin I, Zozulya AV, Meijer JM, Dzhigaev D, Gorobtsov OY, Kurta RP, Rose M, Shabalin AG, Sulyanova EA, Zaluzhnyy I, Menushenkov AP, Sprung M, Petukhov AV, Vartanyants IA. Ptychographic X-Ray imaging of colloidal crystals. Small 2018; 14(3): 1702575.

 

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