  Weak lensing is emerging as a powerful observational tool to constrain
cosmological models, but is at present limited by an incomplete understanding
of many sources of systematic error. Many of these errors are multiplicative
and depend on the population of background galaxies. We show how the commonly
cited geometric test, which is rather insensitive to cosmology, can be used as
a ratio test of systematics in the lensing signal at the 1 per cent level. We
apply this test to the galaxy-galaxy lensing analysis of the Sloan Digital Sky
Survey (SDSS), which at present is the sample with the highest weak lensing
signal to noise and has the additional advantage of spectroscopic redshifts for
lenses. This allows one to perform meaningful geometric tests of systematics
for different subsamples of galaxies at different mean redshifts, such as
brighter galaxies, fainter galaxies and high-redshift luminous red galaxies,
both with and without photometric redshift estimates. We use overlapping
objects between SDSS and the DEEP2 and 2SLAQ spectroscopic surveys to establish
accurate calibration of photometric redshifts and to determine the redshift
distributions for SDSS. We use these redshift results to compute the projected
surface density contrast DeltaSigma around 259 609 spectroscopic galaxies in
the SDSS; by measuring DeltaSigma with different source samples we establish
consistency of the results at the 10 per cent level (1-sigma). We also use the
ratio test to constrain shear calibration biases and other systematics in the
SDSS survey data to determine the overall galaxy-galaxy weak lensing signal
calibration uncertainty. We find no evidence of any inconsistency among many
subsamples of the data.
