3-FOLD ASTIGMATISM IN HIGH-RESOLUTION TRANSMISSION ELECTRON-MICROSCOPY

Three-fold astigmatism has almost no effect on a single diffractogram and no readily quantifiable effect on a single image. However, it imposes a limit on the interpretable resolution in bright-field images of d(min) = 1.1G(1/3)lambda(2/3), where G is the coefficient of three-fold astigmatism. G of typical magnitude of 1 mu m gives a resolution limit about equal to the limit imposed by spherical aberration in the highest-performance present-day electron microscopes (0.2 nm at 200 kV, 0.15 nm at 400 kV and 0.10 nm at 1 MV). A particularly simple method of quantifying the astigmatism is an extension of an autoalignment procedure previously developed by us. The method consists of tilting the illumination to 4 positions equally spaced on a circle in the back-focal plane of the microscope's objective lens, and yields the size and orientation of the three-fold astigmatism as well as the true coma-free axis, Correcting the astigmatism will require energizing two crossed sextupoles situated near the back-focal plane, or adding the appropriate correction term in holographic reconstruction. Because diagnosing three-fold astigmatism on-line is probably too complicated for a human operator, it is likely that the only way to correct it will be through computer control of the electron microscope.