Among the different field sectors and analyzers, the hemispherical condenser achieves a particular importance. The equation of motion for charged particles in the gap between two concentric and spherical in shape electrodes, mathematically corresponds to the problem solved by Kepler. It is obvious that in the case of an attractive electrostatic central force field, the full period assures the reconstruction of the initial conditions. As a consequence, a “full sphere” analyzer could be a perfect response to the problem of aberration-free achromatic imaging, if not an evident geometrical limitation: access to the field in the gap is not possible in such a closed system. The way to find an instrumental solution is to “open” the system without significant reduction of the ideal symmetry of the sphere condenser. Anno Domini 2000 OPTICON has proposed the first approximation to a full sphere by the combination of two opposite (rotated) hemisphere deflector analyzers (HDA) separated by the special relay lens between them, which reverses the angles and positions, assuring the partial restoration of the symmetry of the system. Symmetry breakage is caused by the spherical and chromatic aberrations of the relay lens, which in consequence leads to the worsening of the theoretical lateral resolution to ~50nm. The idea (US Patent 6,667,477, Journal od Physics: J.Phys.Cond.Matter, **17** (2005) 1351) is illustrated below

Such a huge loss of the lateral resolution

disqualified this solution in competition with

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