Measurement and compensation of defocusing and aberrations by Fourier processing of electron micrographs

Abstract

The effects of defocusing and spherical aberration in the electron microscope image are most simply and directly displayed in the Fourier transform of the image. We have investigated the process of image formation by determining the changes in the transform of the image of a thin crystal of catalase, which has discrete diffraction maxima in the resolution range of 10 to 2.5 nm, as a function of defocusing. The changes in amplitude and phase of these diffraction maxima have been measured and compared with the predictions of a first-order theory of image formation. The theory is generally confirmed, and the transfer function of the microscope is completely determined by finding the relative contributions from phase and amplitude contrast. A ‘true’ maximum contrast image of the catalase crystal, compensated for the effects of defocusing, is reconstructed from the set of micrographs in the focal series. The relation of this compensated image to individual underfocused micrographs, and the use of underfocus contrast enhancement in conventional electron microscopy, are discussed. This approach and the experimental methods can be extended to high resolution in order to compensate for spherical aberration as well as defocusing. In as much as spherical aberration is the factor presently limiting the resolution of electron lenses, this could provide a considerable extension of the resolution of the electron microscope.