  Upcoming photometric lensing surveys will considerably tighten constraints on
the neutrino mass and the dark energy equation of state. Nevertheless it
remains an open question of how to optimally extract the information and how
well the matter power spectrum must be known to obtain unbiased cosmological
parameter estimates. By performing a Principal Component Analysis (PCA), we
quantify the sensitivity of 3D cosmic shear and tomography with different
binning strategies to different regions of the lensing kernel and matter power
spectrum, and hence the background geometry and growth of structure in the
Universe. We find that a large number of equally spaced tomographic bins in
redshift can extract nearly all the cosmological information without the
additional computational expense of 3D cosmic shear. Meanwhile a large fraction
of the information comes from small poorly understood scales in the matter
power spectrum, that can lead to biases on measurements of cosmological
parameters. In light of this, we define and compute a cosmology-independent
measure of the bias due to imperfect knowledge of the power spectrum. For a
Euclid-like survey, we find that the power spectrum must be known to an
accuracy of less than 1% on scales with k = 7 h /Mpc This requirement is not
absolute since the bias depends on the magnitude of modelling errors, where
they occur in k-z space, and the correlation between them, all of which are
specific to any particular model. We therefore compute the bias in several of
the most likely modelling scenarios and introduce a general formalism and
public code, RequiSim, to compute the expected bias from any non-linear model.
