  XL-Calibur is a balloon-borne Compton polarimeter for X-rays in the
$\sim$15-80 keV range. Using an X-ray mirror with a 12 m focal length for
collecting photons onto a beryllium scattering rod surrounded by CZT detectors,
a minimum-detectable polarization as low as $\sim$3% is expected during a
24-hour on-target observation of a 1 Crab source at 45$^{\circ}$ elevation.
Systematic effects alter the reconstructed polarization as the mirror focal
spot moves across the beryllium scatterer, due to pointing offsets, mechanical
misalignment or deformation of the carbon-fiber truss supporting the mirror and
the polarimeter. Unaddressed, this can give rise to a spurious polarization
signal for an unpolarized flux, or a change in reconstructed polarization
fraction and angle for a polarized flux. Using bench-marked Monte-Carlo
simulations and an accurate mirror point-spread function characterized at
synchrotron beam-lines, systematic effects are quantified, and mitigation
strategies discussed. By recalculating the scattering site for a shifted beam,
systematic errors can be reduced from several tens of percent to the
few-percent level for any shift within the scattering element. The treatment of
these systematic effects will be important for any polarimetric instrument
where a focused X-ray beam is impinging on a scattering element surrounded by
counting detectors.
