Correction of Aberrations

The Scherzer theorem imposes limitations on the performance of electron microscopes and other instruments employing round lenses. However, a positive-definite integrand of the integrals of the coefficients of spherical and chromatic aberration does not suffice to draw conclusions about the performance of round lenses. Although we cannot nullify the aberration coefficients, it may be possible to minimize the aberrations by skillful design to such an extent that their effect on the resolution is negligibly small. Unfortunately, this conjecture does not hold true because constraints exist for the design of realistic lenses. These limits are, for example, the maximum strength of the electric field, the magnetic saturation, a field-free working distance, and restrictions in realizing the required configurations of the electrodes and pole pieces. As a result, the relative flux density gradient B′/B of magnetic lenses cannot exceed a maximum value. By taking into account this constraint and employing the calculus of variations, Tretner [131,132] optimized round lenses and derived minimum attainable values for their chromatic and spherical aberration coefficients. In the important case of magnetic round lenses, he found.