High-resolution electron holography

1991 ◽  
Vol 49 ◽  
pp. 494-495
Author(s):  
Hannes Lichte
Keyword(s):  
Transfer Functions ◽  
Rotational Symmetry ◽  
Object Wave ◽  
Electron Holography ◽  
Fourier Space ◽  
Large Area ◽  
Pupil Function ◽  
Spatial Frequencies ◽  
Resolution Electron ◽  
Wave Aberration

The performance of an electron microscope usually is described in Fourier space by means of the wave transfer function WTF(R) = B(R) exp(iχ(R)) with the pupil function B(R) and the wave aberration χ(R). R means the spatial frequency, rotational symmetry is assumed.The exp(iχ(R)) term describes the coherent transfer of the object wave a(r)exp(iφ(r)) into the image wave A(r)exp(iФ(r)). For weak specimen (a≈1 and φ<<27π) this transfer can be sketched by means of fig. 1 which shows that a mixing occurs between the amplitudes and phases according to the respective transfer functions cosχ and sinχ. Usually, it is desirable to direct by an appropriate wave aberration x the phase of the object wave - containing the most interesting information about the object structure - into the image intensity A2. This is achieved best at Scherzer focus, however, only a comparably narrow band of spatial frequencies is evenly transferred. Lower spatial frequencies (“Large area phase contrast“) are not found in the image.

Electron Holography Improving Transmission Electron Microscopy

1990 ◽  
Vol 48 (1) ◽  
pp. 208-209
Author(s):  
Hannes Lichte
Keyword(s):  
Electron Microscopy ◽  
Transfer Functions ◽  
Imaging System ◽  
Spherical Aberration ◽  
Image Plane ◽  
Chromatic Aberration ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
Wave Aberration

Generally, the electron object wave o(r) is modulated both in amplitude and phase. In the image plane of an ideal imaging system we would expect to find an image wave b(r) that is modulated in exactly the same way, i. e. b(r) =o(r). If, however, there are aberrations, the image wave instead reads as b(r) =o(r) * FT(WTF) i. e. the convolution of the object wave with the Fourier transform of the wave transfer function WTF . Taking into account chromatic aberration, illumination divergence and the wave aberration of the objective lens, one finds WTF(R) = Echrom(R)Ediv(R).exp(iX(R)) . The envelope functions Echrom(R) and Ediv(R) damp the image wave, whereas the effect of the wave aberration X(R) is to disorder amplitude and phase according to real and imaginary part of exp(iX(R)) , as is schematically sketched in fig. 1.Since in ordinary electron microscopy only the amplitude of the image wave can be recorded by the intensity of the image, the wave aberration has to be chosen such that the object component of interest (phase or amplitude) is directed into the image amplitude. Using an aberration free objective lens, for X=0 one sees the object amplitude, for X= π/2 (“Zernike phase contrast”) the object phase. For a real objective lens, however, the wave aberration is given by X(R) = 2π (.25 Csλ3R4 + 0.5ΔzλR2), Cs meaning the coefficient of spherical aberration and Δz defocusing. Consequently, the transfer functions sin X(R) and cos(X(R)) strongly depend on R such that amplitude and phase of the image wave represent only fragments of the object which, fortunately, supplement each other. However, recording only the amplitude gives rise to the fundamental problems, restricting resolution and interpretability of ordinary electron images:

Real-time reconstruction of electron-off-axis holograms recorded by means of a high-pixel CCD camera

1991 ◽  
Vol 49 ◽  
pp. 680-681
Author(s):  
W.D. Rau ◽  
H. Lichte ◽  
E. Voelkl ◽  
U. Weierstall
Keyword(s):  
Nonlinear Response ◽  
Transfer Functions ◽  
Ccd Camera ◽  
Photographic Emulsion ◽  
Electron Holography ◽  
Large Area ◽  
Reconstruction Procedure ◽  
Numerical Reconstruction ◽  
Whole Process ◽  
Spatial Frequencies

Electron holography using the electron biprism is about to become a powerful tool to overcome the restrictions of the electron microscope, i.e. the lack of large area phase contrast and the limitation of resolution due to the oscillations of the transfer functions for high spatial frequencies. Up to now, the whole process of hologram detection and reconstruction takes a few hours: After a hologram is recorded on photographic plates, it needs development and digitizing. Then a correction of the nonlinear response of the photographic emulsion to electron exposure is indispensable, before the numerical reconstruction procedure can be started.

Is electron holography at atomic dimensions going to meet the expectations of Dennis Gabor?

1989 ◽  
Vol 47 ◽  
pp. 2-3
Author(s):  
Hannes Lichte
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
High Magnification ◽  
Fourier Space ◽  
Electron Wave ◽  
Object Structure ◽  
Wave Aberration

Electron microscopy faces the following basic situation: The electron wave transmitted through the object is modulated both in amplitude a and phase φ. In order to display the object structure, the object wave a exp(i φ) is transferred by the electron lenses into an image wave A exp(i φ) at sufficiently high magnification, modulated in amplitude and phase as well. However, due to the lens aberrations in the high resolution domain, image and object wave generally do not agree. One has to distinguish between coherent and incoherent aberrations. Coherent aberrations (e.g. spherical) are independent of electron energy andangle of illumination; preferably, their effect is taken into account in Fourier space by means of the wave transfer function WTF(u) = exp(i х (u)) depending on the spatial frequency u; х (u) means the wave aberration of the objective lens.

A simple way for producing holographic filters suitable for image improvement

1978 ◽  
Vol 36 (1) ◽  
pp. 226-227
Author(s):  
K.-H. Herrmann ◽  
E. Reuber ◽  
P. Schiske
Keyword(s):  
Transfer Functions ◽  
Diffraction Order ◽  
Lateral Position ◽  
Simple Method ◽  
Spatial Frequencies ◽  
Resolution Electron ◽  
Wiener Filters ◽  
Image Improvement ◽  
Optical Reconstruction ◽  
Set Up

Aposteriori deblurring of high resolution electron micrographs of weak phase objects can be performed by holographic filters [1,2] which are arranged in the Fourier domain of a light-optical reconstruction set-up. According to the diffraction efficiency and the lateral position of the grating structure, the filters permit adjustment of the amplitudes and phases of the spatial frequencies in the image which is obtained in the first diffraction order.In the case of bright field imaging with axial illumination, the Contrast Transfer Functions (CTF) are oscillating, but real. For different imageforming conditions and several signal-to-noise ratios an extensive set of Wiener-filters should be available. A simple method of producing such filters by only photographic and mechanical means will be described here.A transparent master grating with 6.25 lines/mm and 160 mm diameter was produced by a high precision computer plotter. It is photographed through a rotating mask, plotted by a standard plotter.

Electron holography with a CM30-FEG-special-Tübingen Microscope

1993 ◽  
Vol 51 ◽  
pp. 1074-1075
Author(s):  
Hannes Lichte
Keyword(s):  
Spherical Aberration ◽  
Real Space ◽  
Object Wave ◽  
Electron Holography ◽  
Optical Coupling ◽  
Fourier Space ◽  
Optical Analysis ◽  
Numerical Reconstruction ◽  
Conventional Microscopy ◽  
Flexible Wave

Electron holography offers the advantage over conventional microscopy that full use of the object information can be made especially if numerical reconstruction is applied: By coherent optical coupling of a computer to the electron microscope, the electron object wave is completely available for a very flexible wave optical analysis. For example, besides the correction of the coherent aberrations (e.g. spherical aberration, defocus and astigmatism) and the unique accessability of both amplitude and phase of the object wave in real space and in Fourier space, techniques like nanodiffraction or Selective Imaging can be used to improve our knowledge about the object structure at atomic dimensions.However, there are limits imposed on this scheme by the restrictions given by todays technology for the two steps of data acqusition and processing, i.e taking the hologram and reconstructing the wave.First, the information collected in a hologram is limited by incoherent effects.

Electron holography in materials science

1991 ◽  
Vol 49 ◽  
pp. 670-671
Author(s):  
Hannes Lichte ◽  
Edgar Voelkl
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
Materials Science ◽  
Fourier Spectrum ◽  
Object Wave ◽  
Electron Holography ◽  
Reconstruction Procedure ◽  
Numerical Reconstruction ◽  
Transmission Electron ◽  
Unique Interpretation

The object wave o(x,y) = a(x,y)exp(iφ(x,y)) at the exit face of the specimen is described by two real functions, i.e. amplitude a(x,y) and phase φ(x,y). In stead of o(x,y), however, in conventional transmission electron microscopy one records only the real intensity I(x,y) of the image wave b(x,y) loosing the image phase. In addition, referred to the object wave, b(x,y) is heavily distorted by the aberrations of the microscope giving rise to loss of resolution. Dealing with strong objects, a unique interpretation of the micrograph in terms of amplitude and phase of the object is not possible. According to Gabor, holography helps in that it records the image wave completely by both amplitude and phase. Subsequently, by means of a numerical reconstruction procedure, b(x,y) is deconvoluted from aberrations to retrieve o(x,y). Likewise, the Fourier spectrum of the object wave is at hand. Without the restrictions sketched above, the investigation of the object can be performed by different reconstruction procedures on one hologram. The holograms were taken by means of a Philips EM420-FEG with an electron biprism at 100 kV.

Imaging of ferroelectric domain walls by electron holography

1992 ◽  
Vol 50 (1) ◽  
pp. 246-247
Author(s):  
Xiao Zhang
Keyword(s):  
Magnetic Field ◽  
High Resolution ◽  
Domain Walls ◽  
Ferroelectric Domain ◽  
Object Wave ◽  
Electron Holography ◽  
High Resolution Imaging ◽  
Quantitative Measurements ◽  
Resolution Imaging ◽  
Electron Microscopes

Electron holography has recently been available to modern electron microscopy labs with the development of field emission electron microscopes. The unique advantage of recording both amplitude and phase of the object wave makes electron holography a effective tool to study electron optical phase objects. The visibility of the phase shifts of the object wave makes it possible to directly image the distributions of an electric or a magnetic field at high resolution. This work presents preliminary results of first high resolution imaging of ferroelectric domain walls by electron holography in BaTiO3 and quantitative measurements of electrostatic field distribution across domain walls.

Design of a Field-Emission Gun for the Phillips CM20/STEM microscope

1990 ◽  
Vol 48 (2) ◽  
pp. 100-101
Author(s):  
P.M. Mul ◽  
B.J.M. Bormans ◽  
L. Schaap
Keyword(s):  
High Resolution ◽  
Field Emission ◽  
Analytical Electron Microscopy ◽  
Emission Region ◽  
Attractive Alternative ◽  
Electron Holography ◽  
Field Emitter ◽  
Field Emitters ◽  
Resolution Electron ◽  
High Resolution Tem

The first Field Emission Guns (FEG) on TEM/STEM instruments were introduced by Philips in 1977. In the past decade these EM400-series microscopes have been very successful, especially in analytical electron microscopy, where the high currents in small probes are particularly suitable. In High Resolution Electron Holography, the high coherence of the FEG has made it possible to approach atomic resolution.Most of these TEM/STEM systems are based on a cold field emitter (CFE). There are, however, a number of disadvantages to CFE’s, because of their very small emission region: the maximum current is limited (a strong disadvantage for high-resolution TEM imaging) and the emission is unstable, requiring special measures to reduce the strong FEG-induced noise. Thermal field emitters (TFE), i.e. a zirconiated field emitter source operating in the thermal or Schottky mode, have been shown to be a viable and attractive alternative to CFE’s. TFE’s have larger emission regions, providing much higher maximum currents, better stability, and reduced sensitivity to vacuum conditions as well as mechanical and electrical interferences.

The extended Fourier algorithm: Application in discrete optics and electron holography

1994 ◽  
Vol 52 ◽  
pp. 918-919
Author(s):  
E. Voelkl ◽  
L. F. Allard
Keyword(s):  
Fourier Transform ◽  
Fourier Transforms ◽  
Sampling Rate ◽  
Electron Holography ◽  
Optical Bench ◽  
Fourier Space ◽  
Ccd Cameras ◽  
Simulated Image ◽  
Initial Sampling ◽  
Fourier Algorithm

The conventional discrete Fourier transform can be extended to a discrete Extended Fourier transform (EFT). The EFT allows to work with discrete data in close analogy to the optical bench, where continuous data are processed. The EFT includes a capability to increase or decrease the resolution in Fourier space (thus the argument that CCD cameras with a higher number of pixels to increase the resolution in Fourier space is no longer valid). Fourier transforms may also be shifted with arbitrary increments, which is important in electron holography. Still, the analogy between the optical bench and discrete optics on a computer is limited by the Nyquist limit. In this abstract we discuss the capability with the EFT to change the initial sampling rate si of a recorded or simulated image to any other(final) sampling rate sf.

Is there an electron wind?

1990 ◽  
Vol 48 (4) ◽  
pp. 798-799
Author(s):  
L. D. Marks ◽  
J. P. Zhang
Keyword(s):  
Electron Microscopy ◽  
High Resolution Electron Microscopy ◽  
Zone Axis ◽  
Electron Holography ◽  
Electron Wave ◽  
Small Particles ◽  
Resolution Electron ◽  
Pass Through ◽  
Electron Wind ◽  
Inelastic Scatter

A not uncommon question in electron microscopy is what happens to the momentum transferred by the electron beam to a crystal. If the beam passes through a crystal and is preferentially diffracted in one direction, is the momentum ’lost’ by the beam transferred to the crystal? Newton’s third law implies that this must be the case. Some experimental observations also indicate that this is the case; for instance, with small particles if the particles are supported on the top surface of a film they often do not line up on the zone axis, but if they are on the bottom they do. However, if momentum is transferred to the crystal, then surely we are dealing with inelastic scattering, not elastic scattering and is not the scattering probability different? In addition, normally we consider inelastic scatter as incoherent, and therefore the part of the electron wave that is inelastically scattered will not coherently interfere with the part of the wave that is scattered; but, electron holography and high resolution electron microscopy work so the wave passing through a specimen must be coherent with the wave that does not pass through the specimen.

Sign in / Sign up

Export Citation Format

Share Document