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(abridged) We study the accuracy of various approximations to cosmic shearand weak galaxy-galaxy lensing and investigate effects of Born corrections andlens-lens coupling. We use ray-tracing through the Millennium Simulation tocalculate various cosmic-shear and galaxy-galaxy-lensing statistics. We comparethe results from ray-tracing to semi-analytic predictions. We find: (i) Thelinear approximation provides an excellent fit to cosmic-shear power spectra aslong as the actual matter power spectrum is used as input. Common fittingformulae, however, strongly underestimate the cosmic-shear power spectra. Halomodels provide a better fit to cosmic shear-power spectra, but there are stillnoticeable deviations. (ii) Cosmic-shear B-modes induced by Born correctionsand lens-lens coupling are at least three orders of magnitude smaller thancosmic-shear E-modes. Semi-analytic extensions to the linear approximationpredict the right order of magnitude for the B-mode. Compared to theray-tracing results, however, the semi-analytic predictions may differ by afactor two on small scales and also show a different scale dependence. (iii)The linear approximation may under- or overestimate the galaxy-galaxy-lensingshear signal by several percent due to the neglect of magnification bias, whichmay lead to a correlation between the shear and the observed number density oflenses. We conclude: (i) Current semi-analytic models need to be improved inorder to match the degree of statistical accuracy expected for futureweak-lensing surveys. (ii) Shear B-modes induced by corrections to the linearapproximation are not important for future cosmic-shear surveys. (iii)Magnification bias can be important for galaxy-galaxy-lensing surveys.

Ray-tracing through the Millennium Simulation: Born corrections and lens-lens coupling in cosmic shear and galaxy-galaxy lensing