The oversampling phasing method

Sampling the diffraction pattern of a finite specimen more finely than the Nyquist frequency (the inverse of the size of the diffracting specimen) cor responds to surrounding the electron density of the specimen with a no-dens ity region. When the no-density region is bigger than the electron-density region, sufficient information is recorded so that the phase information ca n be retrieved from the oversampled diffraction pattern, at least in princi ple. By employing an iterative algorithm, the phase information from the ov ersampled diffraction pattern of a micrometre-sized test specimen has been successfully retrieved. This method is believed to be able to open a door f or high-resolution three-dimensional structure determination of complex and non-crystalline biological specimens, i.e. whole cells and sub-micrometre molecular clusters and micrometre-sized protein crystals. With the possible appearance in the future of X-ray free-electron lasers, it may become poss ible to image single molecules by recording diffraction patterns before rad iation damage manifests itself.