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The aplanatic lenses (aplanats), which can in some cases be condenser or objective lenses, are free of spherical aberration and off-axial coma simultaneously. The images fomred by the aplanatic lenses displays an extremely high contrast. Most optical and electron lenses cannot be really aplanatic lenses but many optical lenses, e.g. some sphere lens, have aplanatic points at a radius that is equal to the radius of the sphere divided by the index of refraction of the lens material. An image by this optical system always becomes a virtual image. However, when a negative refraction material in the optical systems is used, it is possible to form a real image by arranging an object plane at the aplanatic point.
The off-axial coma must be eliminated in order to provide a large field of view. The optical arrangement that satisfies these requirements is aplanatic condition. In this case, the imaging characteristics do not vary for small angular beam tilts or with the position of the scatters, in the specimen, in the vicinity of the optic axis. However, the field astigmatism and the image curvature can diminish the resolution in the region far from the optic axis.
Because the spherical aberration in general is unavoidable for rotationally symmetric electron lenses in EMs (electron microscopes), it can never be aplanatic. However, each electron lens has a coma-free point that locates on the optic axis within the field of the lens. No coma is introduced into the images by any off-axial pencil of the rays whose central ray intersects the coma-free point. In aberration-corrected TEMs, in order to eliminate the off-axial coma, the coma-free point of the lens next to the corrector must match the corresponding point of the corrector field.
Note that the aplanatic system based on a hexapole corrector is presently the best choice to have high performance microscopes.
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