Mathematical Models for Resonant Radiation of Plane Wave Packets on Layered, Cubically Polarizable Gratings – Existence of Solutions

It is often desirable in transmission electron microscopy to know the vertical spacing of points of interest within a specimen. However, in order to measure a stereo effect, one must have two pictures of the same area taken from different angles, and one must have also a formula for converting measured differences between corresponding points (parallax) into a height differential.Assume (a) that the impinging beam of electrons can be considered as a plane wave and (b) that the magnification is the same at the top and bottom of the specimen. The first assumption is good when the illuminating system is overfocused. The second assumption (the so-called “perspective error”) is good when the focal length is large (3 x 107Å) in relation to foil thickness (∼103 Å).

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Interferometric (Fourier-Spectroscopic) Measurement of Electron Energy Distributions

Proceedings, annual meeting, Electron Microscopy Society of America ◽

10.1017/s0424820100134144 ◽

1990 ◽

Vol 48 (2) ◽

pp. 110-111 ◽

Cited By ~ 1

Author(s):

F. Hasselbach ◽

A. Schäfer

Keyword(s):

Group Velocity ◽

Wave Packets ◽

Index Of Refraction ◽

Electron Wave ◽

Fringe Contrast ◽

Faraday Cage ◽

Optical Index ◽

Wien Filter ◽

Coherent Wave ◽

Electric And Magnetic Fields

Möllenstedt and Wohland proposed in 1980 two methods for measuring the coherence lengths of electron wave packets interferometrically by observing interference fringe contrast in dependence on the longitudinal shift of the wave packets. In both cases an electron beam is split by an electron optical biprism into two coherent wave packets, and subsequently both packets travel part of their way to the interference plane in regions of different electric potential, either in a Faraday cage (Fig. 1a) or in a Wien filter (crossed electric and magnetic fields, Fig. 1b). In the Faraday cage the phase and group velocity of the upper beam (Fig.1a) is retarded or accelerated according to the cage potential. In the Wien filter the group velocity of both beams varies with its excitation while the phase velocity remains unchanged. The phase of the electron wave is not affected at all in the compensated state of the Wien filter since the electron optical index of refraction in this state equals 1 inside and outside of the Wien filter.

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