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.

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:

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.

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.

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.

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.

Electron Holography of Electromagnetic Fields

1997 ◽  
Vol 3 (S2) ◽  
pp. 1059-1060
Author(s):  
J.E. Bonevich
Keyword(s):  
Magnetic Properties ◽  
Software Package ◽  
Phase Changes ◽  
Nanometer Scale ◽  
Objective Lens ◽  
Electron Holography ◽  
Wide Range ◽  
Electric And Magnetic Fields ◽  
Flame Burner ◽  
Conventional Microscopy

Electron holography can lend crucial insights to understanding the subtle manifestations of electro-magnetism in a wide range of materials. Whereas conventional microscopy is sensitive only to the intensity, holography reveals the phase changes in coherent electron wavefronts making it a unique tool to probe electric and magnetic fields on the nanometer scale. We have employed electron holography to characterize materials for mean inner potential measurements and also their electric and magnetic properties.Electron holograms were acquired in a 300 kV FE-TEM under two optical conditions: the standard high resolution mode was employed for mean inner potential measurements; to examine the intrinsic electromagnetic states, a lower resolution mode was used whereby the objective lens is turned off and the diffraction lens images the specimen. Digitally acquired holograms were reconstructed with the HolograFREE software package.Nanophase TiO2 particles generated in a flame burner system were found to have unusual central features. The rutile particles appear to contain faceted voids, raising the question whether the feature is truly a void or a secondary amorphous phase.

Development of Aberration-Corrected Electron Microscopy

2008 ◽  
Vol 14 (1) ◽  
pp. 2-15 ◽  
Author(s):  
David J. Smith
Keyword(s):  
Electron Microscopy ◽  
Spherical Aberration ◽  
Materials Characterization ◽  
Electron Holography ◽  
Aberration Correction ◽  
Future Prospects ◽  
Microscopy Image ◽  
Recent Developments ◽  
Fixed Beam ◽  
Aberration Corrected

The successful correction of spherical aberration is an exciting and revolutionary development for the whole field of electron microscopy. Image interpretability can be extended out to sub-Ångstrom levels, thereby creating many novel opportunities for materials characterization. Correction of lens aberrations involves either direct (online) hardware attachments in fixed-beam or scanning TEM or indirect (off-line) software processing using either off-axis electron holography or focal-series reconstruction. This review traces some of the important steps along the path to realizing aberration correction, including early attempts with hardware correctors, the development of online microscope control, and methods for accurate measurement of aberrations. Recent developments and some initial applications of aberration-corrected electron microscopy using these different approaches are surveyed. Finally, future prospects and problems are briefly discussed.

scholarly journals Interactive Tools for Teaching Fourier Transforms

2020 ◽  
Vol 1 (1) ◽  
pp. 4
Author(s):  
Carlos R. Baiz
Keyword(s):  
Fourier Transforms ◽  
Lesson Plan ◽  
Real Space ◽  
Fourier Space ◽  
Core Component ◽  
Interactive Approach ◽  
Interactive Teaching ◽  
Mathematical Skills ◽  
Interactive Tools ◽  
Upper Level

Fourier transforms (FT) are universal in chemistry, physics, and biology. Despite FTs being a core component of multiple experimental techniques, undergraduate courses typically approach FTs from a mathematical perspective, leaving students with a lack of intuition on how an FT works. Here, I introduce interactive teaching tools for upper-level undergraduate courses and describe a practical lesson plan for FTs. The materials include a computer program to capture video from a webcam and display the original images side-by-side with the corresponding plot in the Fourier domain. Several patterns are included to be printed on paper and held up to the webcam as input. During the lesson, students are asked to predict the features observed in the FT and then place the patterns in front of the webcam to test their predictions. This interactive approach enables students with limited mathematical skills to achieve a certain level of intuition for how FTs translate patterns from real space into the corresponding Fourier space.

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