  Inhomogeneous reionization gives rise to angular fluctuations in the Cosmic
Microwave Background (CMB) optical depth tau(n) to the last scattering surface,
correlating different spherical harmonic modes and imprinting characteristic
non-Gaussianity on CMB maps. Recently the minimum variance quadratic estimator
has been derived using this mode-coupling signal, and found that the optical
depth fluctuations could be detected with (S/N)^2 ~ 100 in futuristic
experiments like CMBPol. We first demonstrate that the non-Gaussian signal from
gravitational lensing of CMB is the dominant source of contamination for
reconstructing inhomogeneous reionization signals, even with 98% of its
contribution removed by delensing. We then construct unbiased estimators that
simultaneously reconstruct inhomogeneous reionization signals tau(n) and
gravitational lensing potential phi(n). We apply our new unbiased estimators to
future CMB experiment to assess the detectability of inhomogeneous reionization
signals. With more physically motivated simulations of inhomogenuous
reionizations that predict an order of magnitude smaller optical depth power
spectrum than previous studies, we show that a CMBPol-like experiment could
achieve a marginal detection of inhomogeneous reionization,(S/N)^2 ~ O(1) with
this quadratic estimator to ~O(10) with the analogous maximum likelihood
estimator.
