  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
all these corrections are at least two orders of magnitude below the
convergence or E-mode power and hence relevant only to future ultra high
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.
