Reconstructing symmetric images from their undersampled Fourier intensities

Abstract: A solution to the phase problem for diffraction by twodimensional crystalline slabs is described, based on the application of a compact support normal to the slab. Specifically we apply the iterative Gerchberg-Saxton-Fienup algorithm to simulated three-dimensional transmission electron diffraction data from monolayer organic crystals. We find that oversampling normal to the monolayer alone does not solve the phase problem in this geometry in general. However, based on simulations for a crystalline monolayer (tetracyanoethylene), we find that convergence is obtained if phases are supplied from a few high-resolution electron microscope images recorded at small tilts to the beam direction. Since current cryomicroscopy methods required a large number of images to phase tomographic diffraction data, this method should greatly reduce the labor involved in data acquisition and analysis in cryo-electron microscopy of organic thin crystals by avoiding the need to record images at high tilt angles. We discuss also the use of laser tweezers as a method of supporting nanoparticles in TEM for diffractive imagin