Origin of the fringe structure observed in high resolution bright-field electron micrographs of amorphous materials

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Abstract
The lattice-like fringes observed in high resolution tilted beam bright-field images of amorphous Ge and carbon films are investigated by developing the transfer theory of the electron microscope. To compare our experimental results with theory, we calculate the spatial power spectrum of the electron microscope image of a modified white noise object taking into account tilted beam illumination, partial coherence and inelastic scattering. These objects closely approximate the observed angular electron scattering distribution of an amorphous film. The experimental power spectrum is obtained from optical Fraunhofer diffractograms of bright-field micrographs of amorphous C and Ge. Our results demonstrate that the appearance of the pseudo fringe structures is an image artifact produced by spatial filtering in the electron microscope which is caused by both the transfer function of the microscope and an incoherent super-position of the image intensity distributions of elastically and inelastically scattered electrons. The fringe-like structure bears no direct relationship to the atomic structure of amorphous Ge. In fact, these pseudo fringes have also been observed in single crystalline Au films. The recent conclusion by other authors that these fringes are the result of astigmatism need not be the case. In an axially symmetric electron optical system with tilted illumination. fringe-like structures can be observed.