We calculate the systematic errors in the weak gravitational lensing power
spectrum which would be caused by spatially varying calibration (i.e.
multiplicative) errors, such as might arise from uncorrected seeing or
extinction variations. The systematic error is fully described by the angular
two-point correlation function of the systematic in the case of the 2D lensing
that we consider here. We investigate three specific cases: Gaussian,
``patchy'' and exponential correlation functions. In order to keep systematic
errors below statistical errors in future LSST-like surveys, the spatial
variation of calibration should not exceed 3% rms. This conclusion is
independently true for all forms of correlation function we consider. The
relative size the E- and B-mode power spectrum errors does, however, depend
upon the form of the correlation function, indicating that one cannot repair
the E-mode power spectrum systematics by means of the B-mode measurements.Comment: 8 pages, 3 figures. Changes reflect PRD published versio