Three-dimensional reconstruction by Chahine’s method from electron microscopic projections corrupted by instrumental aberrations

Three-dimensional reconstruction of nano-scale objects (such as biological macromolecules) can be accomplished using data recorded with a transmission electron microscope. An image obtained by a transmission electron microscope can be conceived of as an ‘ideal’ projection subjected to a contrast transfer function, which attenuates most frequencies, reverses the phase of others and even eliminates some of them. Such instrumental aberrations make the problem of reconstruction from such data difficult. We reformulate the problem so that Chahine’s method becomes applicable to it. We demonstrate the performance of our approach with numerical evidence using both simulated and actual electron microscopy data.