  In the cold dark matter (CDM) picture of structure formation, galaxy mass
distributions are predicted to have a considerable amount of structure on small
scales. Strong gravitational lensing has proven to be a useful tool for
studying this small-scale structure. Much of the attention has been given to
detecting individual dark matter subhalos through lens modeling, but recent
work has suggested that the full population of subhalos could be probed using a
power spectrum analysis. In this paper we quantify the power spectrum of
small-scale structure in simulated galaxies, with the goal of understanding
theoretical predictions and setting the stage for using measurements of the
power spectrum to test dark matter models. We use a sample of simulated
galaxies generated from the \texttt{Galacticus} semi-analytic model to
determine the power spectrum distribution first in the CDM paradigm and then in
a warm dark matter scenario. We find that a measurement of the slope and
amplitude of the power spectrum on galaxy strong lensing scales ($k\sim 1$
kpc$^{-1}$) could be used to distinguish between CDM and alternate dark matter
models, especially if the most massive subhalos can be directly detected via
gravitational imaging.
