Fresnel diffraction effects on high-resolution (< 3 A) images: Effect of spherical aberration on the fresnel fringe

The theory of Fresnel fringes is developed to include the effect of spherical averration in the objective lens of an electron microscope. This is relevant to the interpretation of high-resolution images of crystal structures, where it is necessary to accurately determine both the spherical aberration parameter Cs and the objective lens defocus Δf away from the Gaussian image plane. The theoretical basis for an experimental method to determine both these quantities is described: this requires simultaneous image matching of both the crystal structure image and the Fresnel fringe at the crystal edge. Many features of the Fresnel fringe contrast may be explained adequately using a semi-infinite thin phase object of constant electrostatic potential. The range of application and usefulness of this simpler approximation in investigated. However, at sufficiently high resolution (sub 3 A) the Fresnel fringe itself becomes structure-dependent. This has recently been observed in high-resolution images of the hollandite structure. The extent to which use of an artificial absorption parameter may be used to simulate the effect of exclusion of the outer beams from the objective aperture is also investigated. (orig.)