  Single molecule localization microscopy has the potential to resolve
structural details of biological samples at the nanometer length scale.
However, to fully exploit the resolution it is crucial to account for the
anisotropic emission characteristics of fluorescence dipole emitters. In case
of slight residual defocus, localization estimates may well be biased by tens
of nanometers. We show here that astigmatic imaging in combination with
information about the dipole orientation allows to extract the position of the
dipole emitters without localization bias and down to a precision of ~1nm,
thereby reaching the corresponding Cram\'{e}r Rao bound. The approach is
showcased with simulated data for various dipole orientations, and parameter
settings realistic for real life experiments.
