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.

Current and future aberration correctors for the improvement of resolution in electron microscopy

2009 ◽  
Vol 367 (1903) ◽  
pp. 3665-3682 ◽  
Author(s):  
M. Haider ◽  
P. Hartel ◽  
H. Müller ◽  
S. Uhlemann ◽  
J. Zach
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Low Voltage ◽  
Spherical Aberration ◽  
Chromatic Aberration ◽  
Objective Lens ◽  
Voltage Electron ◽  
System A ◽  
Transmission Electron ◽  
Correction System

The achievable resolution of a modern transmission electron microscope (TEM) is mainly limited by the inherent aberrations of the objective lens. Hence, one major goal over the past decade has been the development of aberration correctors to compensate the spherical aberration. Such a correction system is now available and it is possible to improve the resolution with this corrector. When high resolution in a TEM is required, one important parameter, the field of view, also has to be considered. In addition, especially for the large cameras now available, the compensation of off-axial aberrations is also an important task. A correction system to compensate the spherical aberration and the off-axial coma is under development. The next step to follow towards ultra-high resolution will be a correction system to compensate the chromatic aberration. With such a correction system, a new area will be opened for applications for which the chromatic aberration defines the achievable resolution, even if the spherical aberration is corrected. This is the case, for example, for low-voltage electron microscopy (EM) for the investigation of beam-sensitive materials, for dynamic EM or for in-situ EM.

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.

Beyond One Angstrom

1990 ◽  
Vol 48 (1) ◽  
pp. 204-205
Author(s):  
Albert. V. Crewe
Keyword(s):  
Electron Microscopy ◽  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Low Energy ◽  
Objective Lens ◽  
Squeeze Out ◽  
Electron Microscopes

I believe everyone would agree we have just about reached the limit of performance of today's electron microscopes. This is not to say that additional advances will not take place, because there is always one more drop of blood to squeeze out. But it is certainly becoming increasingly apparent that we can not expect more out of the magnetic lenses that we now have. I am sure that everyone who has ever been concerned with this problem has arrived at the same set of conclusions but it may help to set them down one more time.The available resolution in electron microscopy is distressingly poor compared to the wavelength of the electrons. The culprit is always the objective lens. For low energy, say less than 5,000 volts, chromatic aberration is the offending element whereas at high voltages it is the spherical aberration coefficient which we must be concerned with. In both cases, there are some basic restrictions which apply. In the case of chromatic aberration it is always very closely equal with the focal length of the lens and for the spherical aberration coefficient the best we can do is about 1/4 or 1/2 the focal length.

High Resolution Transmission Electron Microscopy at Zero Cs

1998 ◽  
Vol 4 (S2) ◽  
pp. 382-383
Author(s):  
Michael A. O'Keefe
Keyword(s):  
Electron Microscopy ◽  
Transmission Electron Microscopy ◽  
High Resolution ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Objective Lens ◽  
Transmission Electron ◽  
High Resolution Tem ◽  
Model Structures ◽  
Image Simulations

Now that correctors for objective lens spherical aberration are becoming feasible, questions have been raised about the usefulness of high-resolution transmission electron microscopy at zero Cs and the possible difficulties of interpretation of such images. In general, high resolution TEM images are interpreted either by comparison with simulations from model structures or by contrast transfer functions (CTFs) to determine the weight (and sense) of spatial contributions to images from corresponding diffracted beams. At zero Cs, HREM image simulations will work, but a projected charge density theory should be used (instead of CTF theory) to interpret images. Both theories use approximations; CTF theory relies on kinematic scattering and PCD theory on zero Cs and limited defocus.

Comparison of Deterministic and Linear Cosine Spatial Filtering of Transmission Electron Micrographs

1972 ◽  
Vol 30 ◽  
pp. 596-597
Author(s):  
David A. Ansley
Keyword(s):  
Spherical Aberration ◽  
Focal Length ◽  
Chromatic Aberration ◽  
Spatial Filter ◽  
Operating Conditions ◽  
Objective Lens ◽  
List Type ◽  
Spatial Filters ◽  
Transmission Electron ◽  
Wide Range

The coherence of the electron flux of a transmission electron microscope (TEM) limits the direct application of deconvolution techniques which have been used successfully on unmanned spacecraft programs. The theory assumes noncoherent illumination. Deconvolution of a TEM micrograph will, therefore, in general produce spurious detail rather than improved resolution.A primary goal of our research is to study the performance of several types of linear spatial filters as a function of specimen contrast, phase, and coherence. We have, therefore, developed a one-dimensional analysis and plotting program to simulate a wide 'range of operating conditions of the TEM, including adjustment of the:(1) Specimen amplitude, phase, and separation(2) Illumination wavelength, half-angle, and tilt(3) Objective lens focal length and aperture width(4) Spherical aberration, defocus, and chromatic aberration focus shift(5) Detector gamma, additive, and multiplicative noise constants(6) Type of spatial filter: linear cosine, linear sine, or deterministic

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.

New Aspects in the Design of Electron Optical Magnification Systems

1972 ◽  
Vol 30 ◽  
pp. 606-607
Author(s):  
Willem H.J. Andersen
Keyword(s):  
Electron Microscope ◽  
Imaging System ◽  
Chromatic Aberration ◽  
Research Tool ◽  
Energy Losses ◽  
Objective Lens ◽  
Theoretical Limit ◽  
Optical Magnification ◽  
Chromatic Aberrations ◽  
High Degree

Electron microscope design, and particularly the design of the imaging system, has reached a high degree of perfection. Present objective lenses perform up to their theoretical limit, while the whole imaging system, consisting of three or four lenses, provides very wide ranges of magnification and diffraction camera length with virtually no distortion of the image. Evolution of the electron microscope in to a routine research tool in which objects of steadily increasing thickness are investigated, has made it necessary for the designer to pay special attention to the chromatic aberrations of the magnification system (as distinct from the chromatic aberration of the objective lens). These chromatic aberrations cause edge un-sharpness of the image due to electrons which have suffered energy losses in the object.There exist two kinds of chromatic aberration of the magnification system; the chromatic change of magnification, characterized by the coefficient Cm, and the chromatic change of rotation given by Cp.

Analytic integration of contrast transfer functions

1988 ◽  
Vol 46 ◽  
pp. 822-823
Author(s):  
Peter Rez
Keyword(s):  
Wave Function ◽  
Transfer Function ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Continuous Distribution ◽  
Objective Lens ◽  
Direction Parallel ◽  
Scattering Angle ◽  
Analytic Integration ◽  
Image Position

In high resolution microscopy the image amplitude is given by the convolution of the specimen exit surface wave function and the microscope objective lens transfer function. This is usually done by multiplying the wave function and the transfer function in reciprocal space and integrating over the effective aperture. For very thin specimens the scattering can be represented by a weak phase object and the amplitude observed in the image plane is1where fe (Θ) is the electron scattering factor, r is a postition variable, Θ a scattering angle and x(Θ) the lens transfer function. x(Θ) is given by2where Cs is the objective lens spherical aberration coefficient, the wavelength, and f the defocus.We shall consider one dimensional scattering that might arise from a cross sectional specimen containing disordered planes of a heavy element stacked in a regular sequence among planes of lighter elements. In a direction parallel to the disordered planes there will be a continuous distribution of scattering angle.

Electron holography of p-n junctions

1996 ◽  
Vol 54 ◽  
pp. 974-975
Author(s):  
B.G. Frost ◽  
D.C. Joy ◽  
L.F. Allard ◽  
E. Voelkl
Keyword(s):  
Electron Beam ◽  
Electron Microscope ◽  
Field Emission ◽  
Ccd Camera ◽  
Image Plane ◽  
Reference Wave ◽  
Field Of View ◽  
Control Mode ◽  
Objective Lens ◽  
Electron Holography

A wide holographic field of view (up to 15 μm in the Hitachi-HF2000) is achieved in a TEM by switching off the objective lens and imaging the sample by the first intermediate lens. Fig.1 shows the corresponding ray diagram for low magnification image plane off-axis holography. A coherent electron beam modulated by the sample in its amplitude and its phase is superimposed on a plane reference wave by a negatively biased Möllenstedt-type biprism.Our holograms are acquired utilizing a Hitachi HF-2000 field emission electron microscope at 200 kV. Essential for holography are a field emission gun and an electron biprism. At low magnification, the excitation of each lens must be appropriately adjusted by the free lens control mode of the microscope. The holograms are acquired by a 1024 by 1024 slow-scan CCD-camera and processed by the “Holoworks” software. The hologram fringes indicate positively and negatively charged areas in a sample by the direction of the fringe bending (Fig.2).

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