Defocus-gradient corrected back-projection

Three-dimensional reconstructions of icosahedral viruses from cryoelectron microscope images have reached resolutions where the microscope depth of field is a significant resolution-limiting factor. An analytical treatment presented here shows how the depth of field limitation can be understood as an envelope function which gradually attenuates the signal, starting well before the numerical depth of field is actually reached. A simple modification to the well-known back-projection reconstruction algorithm is described, called the defocus-gradient corrected back-projection, which computationally corrects for the contrast transfer function along a defocus gradient. Computer simulations demonstrate how the algorithm effectively eliminates the depth of field limitation.