We introduce a new method for constraining the redshift distribution of a set of galaxies , using weak gravitational lensing shear .
Instead of using observed shears and redshifts to constrain cosmological parameters , we ask how well the shears around clusters can constrain the redshifts , assuming fixed cosmological parameters .
This provides a check on photometric redshifts , independent of source spectral energy distribution properties and therefore free of confounding factors such as misidentification of spectral breaks .
We find that \sim 40 massive ( \sigma _ { v } = 1200 km s ^ { -1 } ) cluster lenses are sufficient to determine the fraction of sources in each of six coarse redshift bins to \sim 11 % , given weak ( 20 % ) priors on the masses of the highest-redshift lenses , tight ( 5 % ) priors on the masses of the lowest-redshift lenses , and only modest ( 20-50 % ) priors on calibration and evolution effects .
Additional massive lenses drive down uncertainties as N _ { lens } ^ { - { 1 \over 2 } } , but the improvement slows as one is forced to use lenses further down the mass function .
Future large surveys contain enough clusters to reach 1 % precision in the bin fractions if the tight lens mass priors can be maintained for large samples of lenses .
In practice this will be difficult to achieve , but the method may be valuable as a complement to other more precise methods because it is based on different physics and therefore has different systematic errors .