PHASE EXTENSION IN ELECTRON CRYSTALLOGRAPHY USING THE MAXIMUM-ENTROPY METHOD AND ITS APPLICATION TO 2-DIMENSIONAL PURPLE MEMBRANE DATA FROM HALOBACTERIUM-HALOBIUM

We consider the situation where an electron diffraction pattern has been obtained from a crystal; from the same sample an image is also produced which, when Fourier-transformed, yields phases for some, but not all, of the diffraction intensities. In particular the image yields information of lower resolution than the corresponding diffraction pattern. To phase the remaining diffraction reflections, and thus enhance the image resolution, the phased reflections are used as constraints in an entropy maximisation. The resulting maximum entropy map is then used to generate a centroid electostatic potential map in which the diffracted intensities are phased and assigned weights that reflect the reliability of the new phase information. Using data from purple membrane, this method achieves a resolution enhancement of up to 25%.