  With the advent of large-scale weak lensing surveys there is a need to
understand how realistic, scale-dependent systematics bias cosmic shear and
dark energy measurements, and how they can be removed. Here we describe how
spatial variations in the amplitude and orientation of realistic image
distortions convolve with the measured shear field, mixing the even-parity
convergence and odd-parity modes, and bias the shear power spectrum. Many of
these biases can be removed by calibration to external data, the survey itself,
or by modelling in simulations. The uncertainty in the calibration must be
marginalised over and we calculate how this propagates into parameter
estimation, degrading the dark energy Figure-of-Merit. We find that noise-like
biases affect dark energy measurements the most, while spikes in the bias power
have the least impact, reflecting their correlation with the effect of
cosmological parameters. We argue that in order to remove systematic biases in
cosmic shear surveys and maintain statistical power effort should be put into
improving the accuracy of the bias calibration rather than minimising the size
of the bias. In general, this appears to be a weaker condition for bias
removal. We also investigate how to minimise the size of the calibration set
for a fixed reduction in the Figure-of-Merit. These results can be used to
model the effect of biases and calibration on a cosmic shear survey accurately,
assess their impact on the measurement of modified gravity and dark energy
models, and to optimise surveys and calibration requirements.
