Scalar Diffraction Theory in Electron Optics

Komrska, Jiřı́

doi:10.1016/s0065-2539(08)60523-5

Cited by 34 publications

(12 citation statements)

References 39 publications

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“…A solution to obtain better profiles would be to calculate a more refined electrostatic potential that brings under control the lateral distribution of the charge, along the y 0 axis in our configuration. Another possibility would be to develop a more elaborate model in the context of the scalar diffraction theory, as Kormska did to study the fringe pattern of an electron beam scattered by an electrostatic field (Kormska, 1971). By assuming that the condition for applicability of the quasiclassical approximation of quantum mechanics is satisfied (this condition expresses the assumption that the potential energy U ( r ) is a slowly varying function of the position ( r ), it is possible to express the wave function in terms of a diffraction integral which adequately describes the electron beam behind the object plane containing weakly charged objects.…”

Section: Resultsmentioning

confidence: 99%

“…The advantage of the second model is that it can be used to simulate images with variations of charge density, even though from a theoretical point of view these are only a very good approximation of experimental images. Indeed, based on current knowledge, the equivalence of the second model based on the quantum theory of particle diffusion with the correct treatment investigated by Korsmka (Kormska, 1971) had been shown only for a uniformly charged wire. The latter had been developed in the context of the scalar diffraction, in the frame of weak electrostatic fields, but with numerical calculations which are very laborious.…”

Section: Theoretical Aspectmentioning

confidence: 99%

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Charge effect in point projection images of carbon fibres

Prigent

Morin

2000

Journal of Microscopy

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Nanometre‐sized carbon fibres across holes have been observed in a lensless point projection field‐emission microscope operating between 100 and 300 eV. At sufficiently high magnification fringe patterns appear; with the help of simulations we show that they are strongly dependent on the charge density of the fibres. These patterns are characterized by an odd number of fringes with a central fringe that becomes very bright as the charge increases. Average diameter and linear charge density have been obtained with remarkable precision from analysis of fringes. Charge distribution from the middle to the edge of fibres has been investigated as well as narrowings at localized places on the fringe pattern. From these two examples, the limits of the models used for the simulations and those of the data acquisition system are discussed. Finally, this work emphasizes the fact that the fringe pattern masks the actual form of the fibre and that it is necessary to take account of the charge effect to interpret this diffraction pattern.

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Section: Resultsmentioning

confidence: 99%

Section: Theoretical Aspectmentioning

confidence: 99%

Charge effect in point projection images of carbon fibres

Prigent

Morin

2000

Journal of Microscopy

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“…Technology has greatly evolved since electron diffraction in the 1920s to interferometry in a grating with macromolecules like fullerene in the 1999s [2]. Poisson spot has been demonstrated by means of matter-waves with electrons [3] and deuterium molecules [4]. Some theoretical models study the feasibility of the Poisson spot setup for fullerene [5] and gold clusters [6].…”

Section: Introductionmentioning

confidence: 99%

Poisson's spot and Gouy phase

et al. 2016

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Recently there have been experimental results on Poisson spot matter wave interferometry followed by theoretical models describing the relative importance of the wave and particle behaviors for the phenomenon. We propose an analytical theoretical model for the Poisson's spot with matter waves based on Babinet principle in which we use the results for a free propagation and single slit diffraction. We take into account effects of loss of coherence and finite detection area using the propagator for a quantum particle interacting with an environment. We observe that the matter wave Gouy phase plays a role in the existence of the central peak and thus corroborates the predominantly wavelike character of the Poisson's spot. Our model shows remarkable agreement with the experimental data for deuterium (D2) molecules.

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“…Grating diffraction has already been thoroughly studied with electrons [18,19,20], neutrons [21], atoms [22,23,24] and molecules [25,26,27,28]. The Poisson spot was observed with matter waves for the first time with electrons [29,30] and later extended to 1D diffraction behind a wire and 2D interference behind either a free disk or a zone plate using neutrons [31,21], atoms [32,33] and most recently also the diatomic molecule D 2 [34]. In the following we assume quantum physics to be the correct theory for arbitrary particle size and mass, putting aside recently suggested modifications of standard quantum theory [35,36,37,38,39,40,41].…”

Section: Introductionmentioning

confidence: 99%

New Prospects for de Broglie Interferometry

et al. 2010

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We consider various effects that are encountered in matter wave interference experiments with massive nanoparticles. The text-book example of far-field interference at a grating is compared with diffraction into the dark field behind an opaque aperture, commonly designated as Poisson's spot or the spot of Arago. Our estimates indicate that both phenomena may still be observed in a mass range exceeding present-day experiments by at least two orders of magnitude. They both require, however, the development of sufficiently cold, intense and coherent cluster beams. While the observation of Poisson's spot offers the advantage of non-dispersiveness and a simple distinction between classical and quantum fringes in the absence of particle wall interactions, van der Waals forces may severely limit the distinguishability between genuine quantum wave diffraction and classically explicable spots already for moderately polarizable objects and diffraction elements as thin as 100 nm.

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Scalar Diffraction Theory in Electron Optics

Cited by 34 publications

References 39 publications

Charge effect in point projection images of carbon fibres

Charge effect in point projection images of carbon fibres

Poisson's spot and Gouy phase

New Prospects for de Broglie Interferometry

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