  In recent years, gravitational lensing has been used as a means to detect
substructure in galaxy-sized halos, via anomalous flux ratios in
quadruply-imaged lenses. In addition to causing anomalous flux ratios,
substructure may also perturb the positions of lensed images at observable
levels. In this paper, we numerically investigate the scale of such astrometric
perturbations using realistic models of substructure distributions.
Substructure distributions that project clumps near the Einstein radius of the
lens result in perturbations that are the least degenerate with the best-fit
smooth macromodel, with residuals at the milliarcsecond scale. Degeneracies
between the center of the lens potential and astrometric perturbations suggest
that milliarcsecond constraints on the center of the lensing potential boost
the observed astrometric perturbations by an order of magnitude compared to
leaving the center of the lens as a free parameter. In addition, we discuss
methods of substructure detection via astrometric perturbations that avoid full
lens modeling in favor of local image observables and also discuss modeling of
systems with luminous satellites to constrain the masses of those satellites.
