Visualisation and Quantitative Evaluation of Small Thickness and Phase Steps from Electron Holograms by Digital Image Processing
Digital image processing proved to be highly suited for the quantitative decoding of the phase information stored in off-axis electron holograms [1]. We want to show here that digital processing is superiour to light optical reconstruction work because of its flexibility and extended possibilities; i.e. phases and amplitudes can be displayed directly, in contrast to modulated intensity patterns in the light optical case. When a hologram is stored digitally, no further optical or photographical processing is necessary. The reconstruction can be done interactively within seconds by means of an image processor with Fast Fourier Transform hardware [2]. We give here some examples:(1) A flat MgO crystal which has been thinned by electron bombardment [3]. Fig.1a is a micrograph, copied on hard paper, where a quadratic deepening becomes just visible. Fig.1b is an off-axis hologram of this area. By light-optical interferometric reconstruction using the second diffraction order of the hologram, the contour map of Fig.1c has been obtained. Figs.1d,e are digital reconstructions where eight lines of equal phase correspond to a phase shift of 2π. This has been achieved with the method described by Ade and Lauer (these Proceedings). The shift d of the fringes corresponds to a height difference of 2.2nm. Fig.If is a superposition of Figs.1d,e giving a topographic view which reveals even smaller thickness variations.