Coherent Diffractive Imaging: From Nanometric Down to Picometric Resolution

De, Liberato; Carlino, Elvio; Siliqi, Dritan; Giannini, Cinzia

doi:10.1007/978-1-4614-5176-1_8

Cited by 4 publications

(5 citation statements)

References 47 publications

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“…Conversely, the projected average potential obtained by the measured intensities not restored (black curve in Figure 6c) is characterized by a wrong relative position of the two sphalerite sub-lattices, which appears separated in fractional coordinates of 0.29 in the [110] projection. This finding can be considered as a direct consequence of the dynamical scattering, which affects the measured diffraction pattern, and it confirms what already was obtained in a previous work in the study of the [211]-oriented Si samples [9,16]. Figure 7 shows the whole projected potential derived from the rescaled diffraction pattern shown in Figure 5b.…”

Section: Deconvolution Of C(r): Non-centrosymmetric Casesupporting

confidence: 89%

“…Experimentally, only scattered wave intensities are measured because phase information is lost. Moreover, the experimental diffraction pattern is limited by its finite Numerical Aperture (NA), type of detector [8], instability of the sample, use of a central beam stopper, signal-to-noise ratio, and completeness of the recorded data [9]. Nevertheless, if the diffraction data still contains enough information proportional to the FT modulus of the sample scattering function, the image can be reconstructed by using a phase recovering method.…”

Section: Introductionmentioning

confidence: 99%

“…For a TEM thin specimen the diffraction pattern is not affected by high-order aberrations [5]. Hence, if the phase can be correctly recovered, it is possible to achieve a lens-less image of the sample at a resolution only limited by the intensities corresponding to the higher spatial frequencies recorded in the pattern [9]. Retrieving the correct phase in EDI experiments requires, however, a non-trivial data reduction before any phasing algorithm can be applied [5][6][7]14].…”

Section: Introductionmentioning

confidence: 99%

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Determination of the Projected Atomic Potential by Deconvolution of the Auto-Correlation Function of TEM Electron Nano-Diffraction Patterns

Scattarella

Carlino

2016

Crystals

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Abstract:We present a novel method to determine the projected atomic potential of a specimen directly from transmission electron microscopy coherent electron nano-diffraction patterns, overcoming common limitations encountered so far due to the dynamical nature of electron-matter interaction. The projected potential is obtained by deconvolution of the inverse Fourier transform of experimental diffraction patterns rescaled in intensity by using theoretical values of the kinematical atomic scattering factors. This novelty enables the compensation of dynamical effects typical of transmission electron microscopy (TEM) experiments on standard specimens with thicknesses up to a few tens of nm. The projected atomic potentials so obtained are averaged on sample regions illuminated by nano-sized electron probes and are in good quantitative agreement with theoretical expectations. Contrary to lens-based microscopy, here the spatial resolution in the retrieved projected atomic potential profiles is related to the finer lattice spacing measured in the electron diffraction pattern. The method has been successfully applied to experimental nano-diffraction data of crystalline centrosymmetric and non-centrosymmetric specimens achieving a resolution of 65 pm.

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Section: Deconvolution Of C(r): Non-centrosymmetric Casesupporting

confidence: 89%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Determination of the Projected Atomic Potential by Deconvolution of the Auto-Correlation Function of TEM Electron Nano-Diffraction Patterns

Scattarella

Carlino

2016

Crystals

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“…Wavelength, noise, radiation damage, thermal and mechanical stability of the experimental setup, dynamics of the detector, etc. 7 could limit the spatial resolution achievable.…”

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confidence: 99%

Facing the phase problem in Coherent Diffractive Imaging via Memetic Algorithms

Colombo¹,

Galli²,

De³

et al. 2017

Sci Rep

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Coherent Diffractive Imaging is a lensless technique that allows imaging of matter at a spatial resolution not limited by lens aberrations. This technique exploits the measured diffraction pattern of a coherent beam scattered by periodic and non-periodic objects to retrieve spatial information. The diffracted intensity, for weak-scattering objects, is proportional to the modulus of the Fourier Transform of the object scattering function. Any phase information, needed to retrieve its scattering function, has to be retrieved by means of suitable algorithms. Here we present a new approach, based on a memetic algorithm, i.e. a hybrid genetic algorithm, to face the phase problem, which exploits the synergy of deterministic and stochastic optimization methods. The new approach has been tested on simulated data and applied to the phasing of transmission electron microscopy coherent electron diffraction data of a SrTiO 3 sample. We have been able to quantitatively retrieve the projected atomic potential, and also image the oxygen columns, which are not directly visible in the relevant high-resolution transmission electron microscopy images. Our approach proves to be a new powerful tool for the study of matter at atomic resolution and opens new perspectives in those applications in which effective phase retrieval is necessary.Full-field and scanning microscopes can be either lens-based or lensless imaging systems. Coherent Diffractive Imaging (CDI) is a lensless technique that permits imaging matter at a spatial resolution not limited by lens aberrations. The seminal idea of CDI was due to David Sayre in 1952 1 but it was only experimentally demonstrated for X-rays in 1999 2 and, more recently, also for electrons, using a Transmission Electron Microscope (TEM), giving rise to the Electron Diffractive Imaging (EDI) [3][4][5] .The goal is to retrieve a qualitative/quantitative image of a scattering function related to a physical property of the scattering object, such as the electron density (X-ray CDI) or the atomic potential (EDI). High Resolution TEM (HRTEM) images of the projected atomic potential are phase-contrast images limited by the high-order aberrations of the objective lens, which distort the phase of the scattered wave function, giving rise to images of the sample, which in general are not immediately interpretable in terms of its atomic structure 6 . Instead, diffraction patterns of scattering objects are not affected by these aberrations. Therefore they contain, in principle, undistorted information on the scattering function at a better spatial resolution with respect to lens-based imaging systems 3-5 . The diffracted intensity, for weak-scattering objects, is proportional only to the modulus of the Fourier Transform (FT) of the scattering function. Any phase information, which is experimentally lost (phase problem 1 ), has to be retrieved by means of suitable algorithms. The lensless image of the scattering function, obtained by means of an inverse FT of the diffraction pattern once that the correct phase ...

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“…CDI has been developed as a very promising tool for materials investigation at the nanoscale. In this technique, a coherent X-ray beam, scattered by an ensemble of objects (without any spatial correlation), freely propagates until it reaches a 2D detector, where its diffraction pattern is registered 20 21 22 .…”

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confidence: 99%

Ptychographic Imaging of Branched Colloidal Nanocrystals Embedded in Free-Standing Thick Polystyrene Films

Altamura

Arciniegas

et al. 2016

Sci Rep

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Research on composite materials is facing, among others, the challenging task of incorporating nanocrystals, and their superstructures, in polymer matrices. Electron microscopy can typically image nanometre-scale structures embedded in thin polymer films, but not in films that are micron size thick. Here, X-ray Ptychography was used to visualize, with a resolution of a few tens of nanometers, how CdSe/CdS octapod-shaped nanocrystals self-assemble in polystyrene films of 24 ± 4 μm, providing a unique means for non-destructive investigation of nanoparticles distribution and organization in thick polymer films.

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Coherent Diffractive Imaging: From Nanometric Down to Picometric Resolution

Cited by 4 publications

References 47 publications

Determination of the Projected Atomic Potential by Deconvolution of the Auto-Correlation Function of TEM Electron Nano-Diffraction Patterns

Determination of the Projected Atomic Potential by Deconvolution of the Auto-Correlation Function of TEM Electron Nano-Diffraction Patterns

Facing the phase problem in Coherent Diffractive Imaging via Memetic Algorithms

Ptychographic Imaging of Branched Colloidal Nanocrystals Embedded in Free-Standing Thick Polystyrene Films

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