  We present a method of centroiding undersampled point spread functions (PSFs)
that may be useful, especially when dithering is not an option. If the profile
of the expected PSF is known fairly well through characterization of the
telescope and detector used for observing, one can simulate the undersampled
PSF at many positions on a simulated pixel grid. The true centroid positions
are known since the PSFs are simulated, and so one can match up each
undersampled PSF images to its true centroid location, thus forming a lookup
table. One then assigns the centroid position of an observed PSF to the
position associated with the PSF in the lookup table that has the smallest
squared residual with respect to the observed PSF. We examine a few PSF sizes
and demonstrate that the lookup table provides better centroid positions
compared to a fitting algorithm when the PSFs are undersampled, even in the
presence of noise.
