Effects of Fresnel Corrections for Phase-Shifting Electron Holography

Abstract

Phase-shifting electron holography [1] is a useful technique for detecting a small phase change of an electron wave. In this method, however, Fresnel diffraction at an electron biprism causes two kinds of problems to the reconstructed phase. One is the influence on the amplitude of the electron wave, i.e. Fresnel fringes, resulting in non-uniform contrast of interference fringes. The non-uniform fringes bring numerical phase errors in reconstructed images. In order to remove the phase errors, we calculated the envelopes of the fringes, and normalized the non-uniform contrast. [2] The other problem is that Fresnel diffraction directly distorts the phase of the electron waves. We prepare the reference holograms that were taken in a vacuum without specimens, and then correct the distortion by subtracting the reconstructed phase of the reference holograms from that of holograms. [2] In this report, we evaluate the effects of the above correction methods (Fresnel corrections) using a computer simulation and show the possibility of observing a very small amount of electric charges.