Defocus-gradient corrected back-projection

Three-dimensional reconstructions of icosahedral viruses from cryoelectron microscope images have reached resolutions where the microscope depth of fi eld is a significant resolution-limiting factor. An analytical treatment pr esented here shows how the depth of held limitation can be understood as an envelope function which gradually attenuates the signal, starting well bef ore the numerical depth of field is actually reached. A simple modification to the well-known back-projection reconstruction algorithm is described, c alled the defocus-gradient corrected back-projection, which computationally corrects for the contrast transfer function along a defocus gradient. Comp uter simulations demonstrate how the algorithm effectively eliminates the d epth of held limitation. (C) 2000 Elsevier Science B.V. All rights reserved .