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Many weak lensing calculations make use of the Born approximation where thelight ray is approximated by a straight path. We examine the effect ofBorn-corrections for lensing of the cosmic microwave background in ananalytical approach by taking perturbative corrections to the geodesic intoaccount. The resulting extra power in the lensing potential spectrum iscomparable to the power generated by nonlinear structure formation and affectsespecially the polarisation spectra, leading to relative changes of the orderof one per cent for the $E$-mode spectrum and up to 10 per cent on all scalesto the $B$-mode spectrum. In contrast, there is only little change of spectrainvolving the CMB temperature. Additionally, the corrections excite one moredegree of freedom resulting in a deflection component which can not bedescribed as a gradient of the lensing potential as it is related to imagerotation in lens-lens coupling. We estimate the magnitude of this effect on theCMB-spectra and find it to be negligible.

Born-corrections to weak lensing of the cosmic microwave background temperature and polarisation anisotropies