The Fresnel effect of a defocused biprism on the fringes in inelastic holography Jo Verbeeck a,b Giovanni Bertoni b Peter Schattschneider c,a a Institute for Solid State Physics, Vienna University of Technology, A-1040 Vienna, Austria. b EMAT, University of Antwerp, Groenenborgerlaan 171, 2020 Antwerpen, Belgium. c CEMES CNRS, Rue Jeanne Marvig 29, BP 94347, 31055 Toulouse Cedex 4 , France. Abstract We present energy filtered holography experiments on a thin foil of Al. By prop- agating the reduced density matrix of the probe electron through the microscope, we quantitatively predict the fringe contrast as a function of energy loss. Fringe contrast simulations include the effect of Fresnel fringes created at the edges of the defocused biprism, the effect of partial coherence in combination with inelastic scattering, and the effect of a finite energy distribution of the incoming beam. Key words: holography, EELS, inelastic scattering, coherence, density matrix PACS: 34.80.Pa, 82.80.Pv 1 Introduction Although the study of partial coherence is a well developed field in optics, relatively few publications deal with its consequences for electron microscopy. This is remarkable since it is well known that a typical electron beam is far from fully coherent and it is expected that partial coherence must have a large influence on the images formed in an electron microscope. Usually its effect on TEM image formation is approximated by the coherent envelope function which dampens the high spatial frequencies of the microscope transfer function. This approach however fails completely to describe the outcome of Email address: jo.verbeeck@ua.ac.be (Jo Verbeeck). Preprint submitted to Elsevier Science 20 June 2007