  We study how different many body states appear in a quantum gas microscope,
such as the one developed at Harvard [Bakr et al. Nature 462, 74 (2009)], where
the site-resolved parity of the atom number is imaged. We calculate the spatial
correlations of the microscope images, corresponding to the correlation
function of the parity of the number of atoms at each site. We produce analytic
results for a number of well-known models: noninteracting bosons, the large U
Bose-Hubbard model, and noninteracting fermions. We find that these parity
correlations tend to be less strong than density-density correlations, but they
carry similar information.
