Second-order corrections to weak lensing by large-scale structure

We calculate corrections to the power spectrum predictions of weak lensing by large-scale structure due to higher order effects in the gravitational potential. Using a perturbative approach to third order in transverse displacements, we calculate a second-order correction to the angular power spectra of E- and B-mode shear and convergence resulting from dropping the so-called Born approximation, where one integrates along the unperturbed photon path. We also consider a correction to the power spectra from the coupling between lenses at different redshifts. Both effects generate B-mode shear, and the latter also causes a net rotation of the background galaxy images. We show that all of these corrections are at least 2 orders of magnitude below the convergence or E- mode power and hence relevant only to future ultrahigh-precision measurements. These analytical calculations are consistent with previous numerical estimates and validate the use of current large-scale structure weak-lensing predictions for cosmological studies and future use of B-modes as a monitor of systematic effects.