Aberration integrals for the low-voltage foil corrector
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The main factors limit the field of the magnetic lenses are the current density σ and the accelerating voltage Vr. Optical properties such as chromatic and spherical aberration have been studied in terms of σ and Vr. Values of the other aberration coefficients for the optimum lens size corresponding to the desired minimum aberration are estimated.
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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.
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In any electron optical system, compensating for the lens aberrations is the key to improving the spatial resolution. Ofall the dominant aberrations, only the spherical aberration and chromatic aberration continue to limit the performance ofmicroscopes. In the plane ofthe Gaussian image, these aberrations are given by: spherical aberration: ö = Cs a chromatic aberration: ö C a öV/V, Where C5 and C are the coefficients of spherical aberration and chromatic aberration, respectively. a is the divergent angle ofthe electron path with respect to the axis. 8V is the energy spread ofthe electron source and V is the electron energy, in eV. Several systems, such as a magnetic sextupole and quadrupole configuration [1,2], have been proposed to correct these aberrations. Recently, Crewe proposed a simple "mirror corrector" system for correcting them by reversing their coefficient signs [3]. However, it will be some time before any ofthese proposed systems will prove to be applicable on a practical basis. In the meantime, it may be profitable to concentrate on how to choose the best operating parameters for any existing system, in order to optimize the resolution. The resolution of a system is calculated by combining the effect ofthe dominant aberrations with the effects of diffraction and defocus: diffraction: 8d 0.6 lAJa, defocus: C5 a2c where X =(15O/V)' A isthe electron wavelength, and c is the defocus parameter, defined in this paper as 0 at the Gaussian image plane and 1 at the marginal plane. The optimum resolution is achieved by choosing a and to attain the minimum combined aberration. Conventionally, a is chosen to be the largest possible divergent angle, which is the angle determined by the aperture size. This considers only the worstcase situation and ignores the fact that the path of the optical ray is critically dependent on a. Simply because there are some large divergent angles does not mean necessarily that those contributions dominate the formation of the electron probe. Ignoring the possible range of a results in the loss of all the details of the probe pattern. This prevents one from deriving any information about the resolution from the internal details of the probe. Calculations based on a single, maximum value of a can be expected to be conservative and to underestimate the power of the microscope. Recently, Rempfer and Mauck investigated the interior intensity pattern of an electron probe by ray tracing the path ofeach individual electron[4J. Their results showed that the intensity distribution ofthe probe varied greatly in different defocus planes, and was extremely nonuniform in every plane. This paper presents a study in which a numerical simulation is used to determine the probe pattern resulting from the spherical aberration, chromatic aberration, source size, and defocus. The probe pattern in different defocus planes is then convoluted with two types of simulated samples in order to directly investigate the possible resolution. The results show that the conventional calculations ofresolution may not be appropriate for all circumstances. Also, the optimal operational parameter can be very different, depending on what information the operator wishes to get from the microscope.
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A modern microscope is a series of lenses arranged on-axis to give an image appropriate for viewing by eye or with a camera. Optical aberrations arise from the dioptric nature of how lenses work. This chapter discusses the nature and effects of these optical aberrations. Most aberrations are taken care of by the manufacturer when designing the objective and other optical components. Aberrations are grouped as on-axis or off-axis types. The three on-axis aberrations are spherical aberration, astigmatism and chromatic aberration. Off-axis aberrations - which have a greater potential effect in high numerical aperture objectives - are: coma, field curvature, astigmatism, distortion and lateral chromatic aberration. Star test can be employed to recognise spherical aberration. A knowledge of these inherent aberrations and how they are minimised helps formulate criteria for working with and choosing the objectives best suited to the imaging task.
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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.
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