Lattice imaging of poly-4-methyl-pentene-1 single crystals; use and misuse of fourier averaging techniques

Pradère, P.; Revol, J.‐F.; Nguyen, Long V.; Manley, R. St. John

doi:10.1016/0304-3991(88)90408-1

Cited by 25 publications

(9 citation statements)

References 20 publications

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“…Edge-dislocations and grain boundaries caused by a succession of edge-dislocations have indeed been recorded in original HREM micrographs (e.g., Tsuji et al, 1989b). Pradere et al (1988a) however point out one pitfall of the use of Fourier filtration performed to enhance the signal to noise ratio. They observe indeed that for original noisy pictures, artifactual edgedislocations and defects may appear in the reconstructed lattice images.…”

Section: Lattice Imaging Of Single Crystalsmentioning

confidence: 99%

Structure of Polymer Single Crystals

Lotz

Wittmann

2006

Materials Science and Technology

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Section: Lattice Imaging Of Single Crystalsmentioning

confidence: 99%

Structure of Polymer Single Crystals

Lotz

Wittmann

2006

Materials Science and Technology

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“…The attached post-column Gatan imaging filter (GIF Tridiem) allows for energy filtered imaging, and the zero loss peak was limited by a 10 eV window. Electron Diffraction patterns were obtained by Fourier transform (FT) using the Gatan Digital Micrograph software, where the ring mask method was used to prevent lattice fringe extrapolations 31,32 .…”

Section: Transmission Electron Microscopymentioning

confidence: 99%

Elastic properties of MgO nanocrystals and grain boundaries at high pressures by Brillouin scattering

et al. 2011

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“…Traditional Fourier filtering satisfies (1) and (2) but not (3), as has been shown (Forslund, 1969;Pradere et al, 1988) and which we demonstrate in the Results section. However, if the Fourier moduli are restored not by filtering but rather by applying the principle of maximum entropy, the third requirement can also be satisfied.…”

Section: Introductionmentioning

confidence: 52%

“…For the interpretation of data from periodic structures, Fourier-space data offer the advantage of condensing a great deal of structural detail into discrete Fourier-lattice spikes, often leading to a much higher signal-to-noise ratio than in the direct image. However, recent work has shown that conventional Fourier filtering may lead to spurious features (Forslund, 1969;Pradere, Revol, Nguyen & Manley, 1988). The user can create artifacts from noisy data by arbitrarily selecting certain Fourier components and masking others.…”

Section: Introductionmentioning

confidence: 99%

Maximum-entropy data restoration using both real- and Fourier-space analysis

Anderson¹,

Martin²,

Thomas³

1989

Acta Cryst Sect A

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MULTIPLE REFLECTIONS IN A PLANE-PARALLEL MOSAIC CRYSTALand then look for those values of A other than 0 or which cause the right-hand side of (25) to vanish. In practice it has been observed that there is only one such value, ,4 0 , which is the root, when it exists, of a transcendental equation. As a consequence, there may be a dip at the centre of the reflection and a maximum at ,40. Notice that the existence of the dip is not confined to the approximate solution (22) in which case it could be a mathematical artefact.In conclusion, we can say that the present investigation has shown that, in the case of multiple scattering of electromagnetic radiation, in general there is coupling between the two states of polarization either through the amplitudes or through the intensities. Only in the coplanar case do the two X-ray components act independently and can be decoupled. The numerical examples which have been reported are the first exact or almost exact calculations of the effect of multiple reflections in a mosaic crystal within the limits of validity of the transfer equations. These calculations show that application of the kinematical approximation to crystals having reflectivities comparable to those of copper can be grossly in error (up to a factor of two) if the crystal thickness is of the order of what is used in practice (~ol-1 for X-rays and /xol-0.01 for neutrons). This discrepancy can be significantly reduced using the two-beam formulas; however, if one is interested in obtaining accurate structure factors, multiple reflections have to be taken into account. Equations (22), (23) and (24) AbstractAn extension of the maximum-entropy (ME) datarestoration method is presented that is sensitive to periodic correlations in data. The method takes advantage of the higher signal-to-noise ratio for periodic information in Fourier space, thus enhancing statistically significant frequencies in a manner which avoids the user bias inherent in conventional Fourier * Current address: Physical Chemistry 1, Chemical Center, University of Lund, PO Box 124, S-221 00 Lund, Sweden. filtering. This procedure incorporates concepts underlying new approaches in quantum mechanics that consider entropies in both position and momentum spaces, although the emphasis here is on data restoration rather than quantum physics. After a fast Fourier transform of the image, the phases are saved and the array of Fourier moduli are restored using the maximum-entropy criterion. A first-order continuation method is introduced that speeds convergence of the M E computation. The restored moduli together with the original phases are then Fourier inverted to yield a new image; traditional real-space ME restoration is applied to this new image completing one stage in the restoration process. In test cases with various types of added noise and in examples of normal and high-resolution electron-microscopy images, dramatic improvement can be obtained from 0108-7673/89/100686-13503.00

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Lattice imaging of poly-4-methyl-pentene-1 single crystals; use and misuse of fourier averaging techniques

Cited by 25 publications

References 20 publications

Structure of Polymer Single Crystals

Structure of Polymer Single Crystals

Elastic properties of MgO nanocrystals and grain boundaries at high pressures by Brillouin scattering

Maximum-entropy data restoration using both real- and Fourier-space analysis

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