  We investigate the thermodynamics of one-dimensional Bose gases in the
strongly correlated regime. To this end, we prepare ensembles of independent 1D
Bose gases in a two-dimensional optical lattice and perform high-resolution in
situ imaging of the column-integrated density distribution. Using an inverse
Abel transformation we derive effective one-dimensional line-density profiles
and compare them to exact theoretical models. The high resolution allows for a
direct thermometry of the trapped ensembles. The knowledge about the
temperature enables us to extract thermodynamic equations of state such as the
phase-space density, the entropy per particle and the local pair correlation
function.
