On the importance of fifth-order spherical aberration for a fully corrected electron microscope

Next generation aberration correctors will not only eliminate the third-order spherical aberration, but also improve the information limit by correction of chromatic aberration. As a result of these improvements, higher order aberrations, which have largely been neglected in image analysis, will become important. In this paper, we concern ourselves with situations where sub-Å resolution can be achieved, and where the third-order spherical aberration is corrected and the fifth-order spherical aberration is measurable. We derive formulae to explore the maximum value of the fifth-order spherical aberration for directly interpretable imaging and discuss the optimum imaging conditions and their applicable range.