Wide area Large-Scale Structure ( LSS ) surveys are planning to map a substantial fraction of the visible universe to quantify dark energy through Baryon Acoustic Oscillations ( BAO ) .
At increasing redshift , for example that probed by proposed 21-cm intensity mapping surveys , gravitational lensing potentially limits the fidelity ( Hui et al. , 2007 ) because it distorts the apparent matter distribution .
In this paper we show that these distortions can be reconstructed , and actually used to map the distribution of intervening dark matter .
The lensing information for sources at z = 1 - 3 allows accurate reconstruction of the gravitational potential on large scales , l \lesssim 100 , which is well matched for Integrated Sachs-Wolfe ( ISW ) effect measurements of dark energy and its sound speed , and a strong constraint for modified gravity models of dark energy .

We built an optimal quadratic lensing estimator for non-Gaussian sources , which is necessary for LSS .
The phenomenon of “ information saturation ” ( Rimes & Hamilton , 2005 ) saturates reconstruction at mildly non-linear scales , where the linear source power spectrum \Delta ^ { 2 } \sim 0.2 - 0.5 .
We find that steeper power spectra , saturate more quickly .
We compute the effective number densities of independent lensing sources for LSS lensing , and find that they increase rapidly with redshifts .
For LSS/21-cm sources at z \sim 2 - 4 , the lensing reconstruction is limited by cosmic variance at l \lesssim 100 .