  We develop a method of reconstructing the lensing field from lensed CMB
temperature and polarization maps in real space as an alternative to the
harmonic space estimators currently in use by extending an existing real space
lensing estimator for temperature to polarization. Real space estimators have
the advantage of being local in nature and they are thus equipped to deal with
the nonuniform sky coverage, especially galactic cuts and point source
excisions, found in experimental data. We characterize some of the properties
and limitations of these estimators and test them on simulated maps with
Planck, AdvACT and CMB-S4 noise. We show that the reconstructions for
large-scale lensing fields are accurate, and that the polarization
reconstructions improve on those from CMB temperature maps for future
experiments as expected. High-fidelity lensing maps can be reconstructed with
futuristic experiments like CMB-S4.
