Coherent microscopy at resolution beyond diffraction limit using post-experimental data extrapolation

Latychevskaia, Tatiana; Fink, Hans‐Werner

doi:10.1063/1.4831985

Cited by 23 publications

(25 citation statements)

References 24 publications

(40 reference statements)

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“…5 The reported enhancement in resolution is at least twice the resolution obtained from non-extrapolated images. 2,4 A particular interest for extrapolation exists in coherent diffractive imaging, 6 where the resolution is often limited by the size of the detector. In 1964, Harris speculated that the resolution of an optical system is not limited by the numerical aperture of the system but only by the experimental noise, because even a fraction of the detected spectrum is sufficient to uniquely restore the object details.…”

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“…11 Only recently successful extrapolations of diffraction patterns have been reported. 2,5 In this work, we study how extrapolation can be applied to X-ray experimental data with the missing information. We perform several reconstructions varying different parameters in the extrapolation routine.…”

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confidence: 99%

“…Just zero-padding of a diffraction pattern or a hologram does not increase the numerical aperture of the optical system, and therefore no resolution enhancement is achieved. 2 However, zero-padding enhances sampling of the reconstructions [18][19][20] and represents "ideal" interpolation.…”

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Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns

Latychevskaia

Chushkin

Zontone

et al. 2015

Applied Physics Letters

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Coherent diffraction imaging is a high-resolution imaging technique whose potential can be greatly enhanced by applying the extrapolation method presented here. We demonstrate the enhancement in resolution of a non-periodical object reconstructed from an experimental X-ray diffraction record which contains about 10% missing information, including the pixels in the center of the diffraction pattern. A diffraction pattern is extrapolated beyond the detector area and as a result, the object is reconstructed at an enhanced resolution and better agreement with experimental amplitudes is achieved. The optimal parameters for the iterative routine and the limits of the extrapolation procedure are discussed.

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Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns

Latychevskaia

Chushkin

Zontone

et al. 2015

Applied Physics Letters

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“…25 Here, we apply the same extrapolation method to a diffraction pattern of a crystalline sample with the results shown in Fig. 4.…”

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“…The details of the extrapolation procedure can be found elsewhere. 25,26 In brief, the complex-valued wavefront distribution reconstructed by a conventional phase retrieval algorithm is padded with random complex-valued numbers up to 2000 Â 2000 pixels. The random padding in Fourier domain was updated after each iteration.…”

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Atomically resolved structural determination of graphene and its point defects via extrapolation assisted phase retrieval

Latychevskaia

Fink

2015

Applied Physics Letters

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Previously reported crystalline structures obtained by an iterative phase retrieval reconstruction of their diffraction patterns seem to be free from displaying any irregularities or defects in the lattice, which appears to be unrealistic. We demonstrate here that the structure of a nanocrystal including its atomic defects can unambiguously be recovered from its diffraction pattern alone by applying a direct phase retrieval procedure not relying on prior information of the object shape. Individual point defects in the atomic lattice are clearly apparent. Conventional phase retrieval routines assume isotropic scattering. We show that when dealing with electrons, the quantitatively correct transmission function of the sample cannot be retrieved due to anisotropic, strong forward scattering specific to electrons.We summarize the conditions for this phase retrieval method and show that the diffraction pattern can be extrapolated beyond the original record to even reveal formerly not visible Bragg peaks. Such extrapolated wave field pattern leads to enhanced spatial resolution in the reconstruction. Main textThe study of nanocrystal structures at atomic resolution is an important topic in nanotechnology, solid state physics and especially in biology, where preparing a large perfect crystal is often a challenge and the synthesis of nanocrystals is preferred 1 . It has recently been demonstrated that the structure of a nanocrystal can directly be obtained by coherent diffraction imaging 2 from an electron or X-ray diffraction pattern by applying phase retrieval algorithms [3][4][5][6][7] . The diffraction pattern of a crystalline structure typically consists of distinct Bragg peaks, whereby each peak is convoluted with the Fourier transform of the crystal shape (shape-transform) [8][9] . In the experiments demonstrated so far 3-7 , a regular crystalline structure at sub-nanometer resolution could be retrieved, but the individual atoms remained unresolved and therefore no atomic defects were revealed. The structure retrieval in the reported experiments require the input of an initial low-resolution image of the sample distribution typically provided by other techniques, as for example by transmission electron microscopy (TEM) imaging 3-4 , scanning electron microscopy (SEM) 5 , high-resolution transmission electron microscopy (HRTEM)

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Phase retrieval methods applied to coherent imaging

Latychevskaia

2021

Advances in Imaging and Electron Physics

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Coherent microscopy at resolution beyond diffraction limit using post-experimental data extrapolation

Cited by 23 publications

References 24 publications

Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns

Imaging outside the box: Resolution enhancement in X-ray coherent diffraction imaging by extrapolation of diffraction patterns

Atomically resolved structural determination of graphene and its point defects via extrapolation assisted phase retrieval

Phase retrieval methods applied to coherent imaging

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