Study of aberration correction in two types of electrostatic lenses
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Chromatic aberration
Optical aberration
Electrostatic lens
Contrast transfer function
The focal properties and the third-order aberration coefficients of a number of unipotential lenses and a bipotential lens were investigated numerically using digital methods. The differential quotients of aberration coefficients in terms of the entrance pupil position were obtained in excellent agreement with those given by Berek in glass optics. The aberration coefficients were also calculated under the Fraunhofer condition for an infinite image position. For a fixed focal length, spherical aberration coefficients decrease and astigmatism coefficients increase as the length of the center electrode increases for equidiameter unipotential lenses. The symmetrical bipotential lens is almost astigmatism free for various voltage ratios; however, its spherical aberration coefficient is two to five times larger than those of equidiameter unipotential lenses operated at the same focal length.
Chromatic aberration
Electrostatic lens
Astigmatism
Optical aberration
Contrast transfer function
Electron optics
Position (finance)
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We discuss a computerized systematic investigation to find axially symmetric electrostatic lens potentials with acceptable first-order properties and small spherical aberrations. The calculation of the spherical aberration is based on the direct solution of the relativistic trajectory equation in paraxial and nonparaxial approximation. The potentials are characterized by their properties in infinite magnification mode. Conditions for the computations and constraints to satisfy practical requirements are prescribed. A successful axial potential distribution and its relativistic spherical aberration coefficient, the spherical disk radius, and some first-order optical parameters, are also presented in the paper as an example.
Electrostatic lens
Axial symmetry
Contrast transfer function
Optical aberration
Geometrical optics
Spherical Geometry
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Chromatic aberration
Optical aberration
Electrostatic lens
Contrast transfer function
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Chromatic aberration
Electrostatic lens
Triode
Optical aberration
Curved mirror
Contrast transfer function
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Contrast transfer function
Chromatic aberration
Optical aberration
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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.
Chromatic aberration
Coma (optics)
Contrast transfer function
Acceleration voltage
Optical aberration
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Chromatic aberration
Contrast transfer function
Aperture (computer memory)
Optical aberration
Acceleration voltage
Curved mirror
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The paper describes the principle of operation of a relatively simple aberration corrector for the transmission electron microscope objective lens. The electron-optical system of the aberration corrector consists of the two main elements: an electrostatic mirror with rotational symmetry and a magnetic deflector formed by the round-shaped magnetic poles. The corrector operation is demonstrated by calculations on the example of correction of basic aberrations of the well-known objective lens with a bell-shaped distribution of the axial magnetic field. Two of the simplest versions of the corrector are considered: a corrector with a two-electrode electrostatic mirror and a corrector with a three-electrode electrostatic mirror. It is shown that using the two-electrode mirror one can eliminate either spherical or chromatic aberration of the objective lens, without changing the value of its linear magnification. Using a three-electrode mirror, it is possible to eliminate spherical and chromatic aberrations of the objective lens simultaneously, which is especially important in designing electron microscopes with extremely high resolution.
Chromatic aberration
Electrostatic lens
Contrast transfer function
Electron optics
Optical aberration
Curved mirror
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Chromatic aberration
Electron optics
Electrostatic lens
Optical aberration
Geometrical optics
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Both the spherical and the chromatic aberration of electron microscope objectives may, in principle, be corrected with the aid of a uniform retarding field acting as a mirror. Such an arrangement has the drawback of requiring a conducting film in the ray path and the insertion of the specimen in a region of high field strength. The employment of concave electron mirrors with concentrated field distribution, forming a real image of approximately unity magnification, is free from this drawback. The formulas for spherical and chromatic aberration, presented in a form suitable for calculation, are applied to a characteristic electron mirror field of this type (Φ = C+tanh(sinhz)). It is found that the aberration coefficients of the mirror are so large, however, that this method of aberration correction encounters serious practical difficulties.
Chromatic aberration
Contrast transfer function
Optical aberration
Electron optics
Curved mirror
Optical path
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