Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy

Coene, W.; Thust, A.; Beeck, Marc Op De; Dyck, D. Van

doi:10.1016/0304-3991(96)00010-1

Cited by 367 publications

(207 citation statements)

References 12 publications

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“…The observed lower lattice parameter reported for CF indicates that this phase may undergo significant lattice corrugation that will impair its utility in any application requiring a 'flat' 2D morphology. Here we show, using electron diffraction (ED) and aberration-corrected transmission electron microscopy (AC-TEM) in tandem with exit wave reconstruction (EWR) [16][17][18][19] , that the DFT-predicted phase C 2 F chair 10 is both stable and demonstrates a far higher degree of pristine long-range structural and morphological order than CF or any other chemical derivative of graphene. Our observations also support theoretical predictions 10 that, due to energetic considerations, ordered domains of C 2 F chair are functionalized exclusively on one side, a result with profound implications for the preparation of 2D devices and, furthermore, the formation of secondary chemical derivatives such as those formed by alkylation, hydroxylation and amino-functionalization 20 .…”

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confidence: 99%

“…High-angle annular dark field imaging performed in scanning transmission electron microscopy (STEM) produces higher definition images, but may degrade thin monolayers due to the high electron flux of the highly focused electron beam. EWR [16][17][18][19] can recover more information from AC-TEM by combining data from a focal series of low beam density images, providing light element sensitivity and even 3D information 21 .…”

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Atomically resolved imaging of highly ordered alternating fluorinated graphene

et al. 2014

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One of the most desirable goals of graphene research is to produce ordered two-dimensional (2D) chemical derivatives of suitable quality for monolayer device fabrication. Here we reveal, by focal series exit wave reconstruction (EWR), that C 2 F chair is a stable graphene derivative and demonstrates pristine long-range order limited only by the size of a functionalized domain. Focal series of images of graphene and C 2 F chair formed by reaction with XeF 2 were obtained at 80 kV in an aberration-corrected transmission electron microscope. EWR images reveal that single carbon atoms and carbon-fluorine pairs in C 2 F chair alternate strictly over domain sizes of at least 150 nm 2 with electron diffraction indicating ordered domains Z0.16 mm 2 . Our results also indicate that, within an ordered domain, functionalization occurs on one side only as theory predicts. In addition, we show that electron diffraction provides a quick and easy method for distinguishing between graphene, C 2 F chair and fully fluorinated stoichiometric CF 2D phases.

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Atomically resolved imaging of highly ordered alternating fluorinated graphene

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“…The former extends the interpretable resolution to the axial information limit [3] and has been applied to aberration corrected images [5]. However, the latter provides information beyond the axial information limit of the microscope [4].…”

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Aberration Correction and Exit Wave Reconstruction Using Tilt Azimuth Data

Kirkland

Haigh

2009

Microsc Microanal

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Electron optical aberration correction in both TEM and STEM geometries is now been established [1,2] with a variety of imaging and probe corrected instruments installed at several laboratories around the world.An alternative, complementary approach to direct correction involves computational compensation of measured coefficients of the wave aberration function, a posteriori during exit wave reconstruction from series of images recorded with different focus values [3], or with different illumination tilts [4]. The former extends the interpretable resolution to the axial information limit [3] and has been applied to aberration corrected images [5]. However, the latter provides information beyond the axial information limit of the microscope [4].For corrected instruments computational reconstruction is beneficial in both geometries as it compensates for higher order aberrations, which cannot currently be directly corrected. It can also be used to locally refine the residual lower order aberrations as a function of image space. Exit wave reconstruction also gives access to complex data set not obtainable from a single image.Data presented in this paper uses exit waves reconstructed using a Weiner restoring filter. Aberrations were initially measured globally to 5 th order from a Zemlin tableau of diffractograms and electron optically corrected to 3 rd order. Subsequently, the measured aberrations were locally refined to 5 th order using image subregions by means of a phase correlation function / phase contrast index approach [6]. Focal series datasets consisted of 16 images separated by a focal increment of 7 nm with the series centered about the Gaussian focus condition. Tilt series comprised of 6 short focal series (of three images) with additional axial images to assess overall focal drift taken at illumination tilts with tilt angles of 18.4 mrad. For the illumination tilts used, the samples were sufficiently thin that parallax effects could be ignored. Experimental verification of the resolution improvement using aberration corrected tilted illumination images used a specimen with a real space lattice separation beyond the axial information limit. A gold foil oriented along a <123> direction satisfies this requirement Figure 1 compares the phase and moduli of exit wavefunctions restored using both focal series and tilt defocus data sets. The only lattice detail present in the phase and modulus of the exit wavefunction ( figure 1 (a) and (b)) recovered from the focal series dataset are the {111} planes corresponding to a 0.235 nm lattice spacing. In contrast, the wavefunction recovered using tilted illumination data contains information from the {331}, {420} and {242} reflections corresponding to lattice spacings of 0.093 nm, 0.091 nm and 0.083 nm that are beyond the 0.1nm axial information limit of the microscope used

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Atomic Precision Measurement of Individual Atom Positions in Defects by Aberration Corrected HRTEM

Houben

Thust

Urban

2005

MAM

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The combination of imaging in a spherical-aberration corrected transmission electron microscope [1][2] with subsequent numerical focal series reconstruction of the exit-plane wave function (EPW) [3][4] is applied to achieve a reliable quantification of the position of individual atomic columns in defects. An approach for the determination of individual atomic column positions which allows the quantification of the measurement accuracy and is appropriate for non-periodic defects is presented. The approach is based on a regression analysis of peak maxima in the directly interpretable phase image of the EPW retrieved from a focal series of images of a sufficiently thin object. While systematic errors in the positional data are minimized by the compensation of residual aberrations from the EPW, the statistical error due to residual noise in the EPW can be assessed for single, unique atomic columns via the regression analysis.Figs. 1-3 show the application in the case of a 90° [100] tilt grain boundary in YBa 2 Cu 3 O 7-δ (YBCO), where individual positions in the cation and the oxygen sublattice were determined. Fig. 1 displays the EPW retrieved from a focal series taken in a Philips CM200 FEG ST sphericalaberration corrected microscope [2]. The images were acquired at negative spherical aberration to benefit from an enhanced signal of light elements [7]. Residual aberrations are removed from the EPW, resulting in an excellent pattern match with simulated data and a conservation of the symmetry properties of the basic structure in periodic regions. To account for the overlap of neighbouring columns, peak positions for oxygen columns were measured by a multiple Gaussian least-squares fit of phase profiles (Fig. 2a). The regression analysis typically yields a 2σ error radius of 6 pm for oxygen column positions in the periodic parts, increasing to about 20 pm in the grain boundary due to closer spaced columns. For the stronger signal of cation columns 2σ error radii of 2 pm and 4 pm are found respectively. Fig. 3 highlights the individual columns displacements in the reconstructed structure of the grain boundary. Fig. 2b displays the bondlengths between the plane copper Cu2, the chain copper Cu1 and the apical oxygen O1, which are the relevant distances correlated with a charge transfer between the copper planes and the superconducting properties [5]. An excellent match with neutron scattering data from ref. [5] is found in the periodic part, whereas a change of these bondlengths is measured with statistical significance in the grain boundary. Complemented with the sensitivity enhancement for light elements and the possibility of measuring the oxygen occupancy of individual lattice sites offered by the aberration correction [6][7], the atomistic study of the local oxygen coordination at defects in oxide materials can thus provide realistic input data for modelling and understanding electronic-structure relations in these materials.

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Maximum-likelihood method for focus-variation image reconstruction in high resolution transmission electron microscopy

Cited by 367 publications

References 12 publications

Atomically resolved imaging of highly ordered alternating fluorinated graphene

Atomically resolved imaging of highly ordered alternating fluorinated graphene

Aberration Correction and Exit Wave Reconstruction Using Tilt Azimuth Data

Atomic Precision Measurement of Individual Atom Positions in Defects by Aberration Corrected HRTEM

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