  Weak gravitational lensing causes subtle changes in the apparent shapes of
galaxies due to the bending of light by the gravity of foreground masses. By
measuring the shapes of large numbers of galaxies (millions in recent surveys,
up to tens of billions in future surveys) we can infer the parameters that
determine cosmology. Imperfections in the detectors used to record images of
the sky can introduce changes in the apparent shape of galaxies, which in turn
can bias the inferred cosmological parameters. In this paper we consider the
effect of two widely discussed sensor imperfections: tree-rings, due to
impurity gradients which cause transverse electric fields in the Charge-Coupled
Devices (CCD), and pixel-size variation, due to periodic CCD fabrication
errors. These imperfections can be observed when the detectors are subject to
uniform illumination (flat field images). We develop methods to determine the
spurious shear and convergence (due to the imperfections) from the flat-field
images. We calculate how the spurious shear when added to the lensing shear
will bias the determination of cosmological parameters. We apply our methods to
candidate sensors of the Large Synoptic Survey Telescope (LSST) as a timely and
important example, analyzing flat field images recorded with LSST prototype
CCDs in the laboratory. We find that tree-rings and periodic pixel-size
variation present in the LSST CCDs will introduce negligible bias to
cosmological parameters determined from the lensing power spectrum,
specifically w, {\Omega}m and {\sigma}8.
