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Showing papers on "Contrast transfer function published in 1971"


Journal ArticleDOI
TL;DR: In this paper, the Fourier transform of the image of a thin crystal of catalase, which has discrete diffraction maxima in the resolution range of 10 to 2.5 nm, as a function of defocusing, was determined by finding the relative contributions from phase and amplitude contrast.
Abstract: The effects of defocusing and spherical aberration in the electron microscope image are most simply and directly displayed in the Fourier transform of the image. We have investigated the process of image formation by determining the changes in the transform of the image of a thin crystal of catalase, which has discrete diffraction maxima in the resolution range of 10 to 2.5 nm, as a function of defocusing. The changes in amplitude and phase of these diffraction maxima have been measured and compared with the predictions of a first-order theory of image formation. The theory is generally confirmed, and the transfer function of the microscope is completely determined by finding the relative contributions from phase and amplitude contrast. A 'true' maximum contrast image of the catalase crystal, compensated for the effects of defocusing, is reconstructed from the set of micrographs in the focal series. The relation of this compensated image to individual underfocused micrographs, and the use of underfocus contrast enhancement in conventional electron microscopy, are discussed. This approach and the experimental methods can be extended to high resolution in order to compensate for spherical aberration as well as defocusing. In as much as spherical aberration is the factor presently limiting the resolution of electron lenses, this could provide a considerable extension of the resolution of the electron microscope.

339 citations


Journal ArticleDOI
TL;DR: Results indicate that such an 'electrostatic phase plate' can provide significant improvements in contrast and signal/noise ratio over normal bright field images without loss in resolution.
Abstract: A simple electrostatic device has been constructed which, when inserted in the optical system of an electron microscope, functions as an absorbing phase plate. Its operation depends on the central portion of a thin poorly conducting thread generating a stable potential under the influence of the electron beam and creating a particular form of electric field. An electron interference technique is employed to study the stabilizing mechanism and to develop a method for achieving the required magnitude of potential. The performance of this device is gauged by optical diffraction of electron micrographs of a thin carbon film; its application is illustrated by examining some negatively stained biological specimens. The results indicate that such an 'electrostatic phase plate' can provide significant improvements in contrast and signal/noise ratio over normal bright field images without loss in resolution.

44 citations


Journal ArticleDOI
W. Hoppe1
TL;DR: In this paper, the use of redundancy principles (similar to X-ray structure determination) is discussed and demonstrated for electron microscopy of organic specimens, especially in the case of radiation damage.
Abstract: Electron microscopy using microscopes with conventional magnetic lenses is restricted in resolution by spherical aberration. The 'zonal correction principle' allows this limit to be overcome. Its use in image reconstruction schemes allows separation of the influence of defocusing, astigmatism, etc., from the physically significant structure. The use of three-dimensional methods of image differencing is necessary in order to get interpretable results in the study of the not 'infinitely thin' objects in electron microscopy at atomic level. The use of redundancy principles (similar to X-ray structure determination) is discussed and demonstrated. The most severe difficulty, especially in electron microscopy of organic specimens, is radiation damage.

32 citations


Journal ArticleDOI
TL;DR: In this article, it is shown that a system of interference fringes photographed on a photographic plate has very interesting properties when used as a diffraction grating and the nature of variation of spherical aberration between these zero-aberration positions is presented in the form of curves computed from the theory of these gratings.
Abstract: It is now well known that a system of interference fringes photographed on a photographic plate has very interesting properties when used as a diffraction grating. This paper considers two cases. One is when the photographic plate is a plane surface; the aberration properties of this are worked out as a function of wavelength. There are three positions for which the spherical aberration is zero. Of these, one is of little interest as this is simply zero-order position. Another case considered was that of a photographic plate in the form of a concave spherical surface. In this case, there are three positions at which the spherical aberration is zero. The nature of variation of spherical aberration between these zero-aberration positions is presented in the form of curves computed from the theory of these gratings.

23 citations


Journal ArticleDOI
TL;DR: In this paper, the application of transfer theory to image formation in the electron microscope is discussed and the equivalence of the transfer theory and the diffraction integral formulation of image formation is established for a coherent monochromatic incident electron beam, and for elastic electron scattering.
Abstract: The application of transfer theory to image formation in the electron microscope is discussed. The equivalence of the transfer theory and the diffraction integral formulation of image formation is established for a coherent monochromatic incident electron beam, and for elastic electron scattering. The transfer theory is extended to include partially coherent and nonmonochromatic radiation. The use of the results of the transfer theory leads to the diffraction integral formulation, which includes the effects of chromatic aberration (thermal energy effect) and the coherence of the incident electron beam. The modification to a criterion for optimum contrast in the final image when chromatic aberration is taken into account is discussed.

19 citations


Journal ArticleDOI
TL;DR: In this paper, the effect of chromatic aberration on the resolution of an electron microscope image has been investigated using a model specimen of an unstained biological material with a variation in mass thickness.
Abstract: On the assumption that inelastic electron scattering in a specimen is localized and gives rise to an incoherent beam, an estimate is made of the effect of chromatic aberration on an electron microscope image. A model specimen of an unstained biological material with a variation in mass thickness is used to calculate the incoherent inelastic image; the aberration function is applied to this image to give an image with spherical and chromatic aberration defects. From this procedure, an estimate is made of the loss in resolution for the inelastic image due to chromatic aberration for two specimens of very different mass thickness (40 and 200 mg m−2 of carbonaceous materials) and for objective aperture sizes corresponding to semi-angles of 00025, 0005 and 001 rad (incident electron energy 100 keV). It is concluded that chromatic aberration results in a loss in resolution on a 5-10 A scale within the approximations of this work. The deterioration in resolution due to chromatic aberration is not very dependent on the size of the objective aperture. The conclusions of the present work are consistent with recent experimental work on the effect of chromatic aberration on the electron microscope image.

9 citations



Journal ArticleDOI
TL;DR: In this paper, the limits of resolution dependent on defocusing and spherical aberration were calculated and the partial coherence in connection with the aberrations of the electron lenses limits the possible resolution.
Abstract: Enhancement of resolution in electron microscopy can be achieved by use of electron image holography. In order to compensate for the aberrations of the electron lenses the reconstruction is performed with laser light in an optical system with suitably adapted aberrations. The partial coherence in connection with the aberrations of the electron lenses limits the possible resolution. The limits of resolution dependent on defocusing and spherical aberration are calculated.

7 citations


Book ChapterDOI
01 Jan 1971

6 citations



Journal ArticleDOI
TL;DR: In this paper, a far field intensity distribution has been plotted for a circular aperture suffering from spherical aberration and illuminated by quasi-monochromatic partially space-coherent light.
Abstract: Far-field intensity distribution has been plotted for a circular aperture suffering from spherical aberration and illuminated by quasi-monochromatic partially space-coherent light. Gaussian and besinc forms of correlation have been assumed. It is shown that higher values of coefficient of aberration can be tolerated as the value of number of correlation intervals contained in the aperture increases.


Journal ArticleDOI
TL;DR: In this paper, a simple setup is described that simulates an electron microscope imaging a two-dimensional lattice, and the diffraction pattern in the back focal plane is large enough to be easily observed and manipulated.
Abstract: A simple setup is described that simulates an electron microscope imaging a two-dimensional lattice. The diffraction pattern in the back focal plane is large enough to be easily observed and manipulated. The origin of contrast can be demonstrated by filtering out the image contributions of the individual Fourier components. The experiment can be used to demonstrate Abbe's theory of the microscope, origin of phase contrast, and two-dimensional Fourier transforms.

Journal ArticleDOI
TL;DR: In this paper, Fraunhofer diffraction patterns produced by a circular aperture suffering from spherical aberration and illuminated by partially coherent light are presented, and tolerances for the value of the coefficient of aberration based on the Strehl criterion have been calculated for various values of correlation intervals contained in the aperture.
Abstract: Fraunhofer diffraction patterns produced by a circular aperture suffering from spherical aberration and illuminated by partially coherent light are presented. Improvement in the images has also been shown when an appropriate amplitude filter is used. Tolerances for the value of the coefficient of aberration based on the Strehl criterion have been calculated for various values of correlation intervals contained in the aperture. Two forms of mutual coherence function and four values of aberration coefficient have been assumed.