  We perform large-scale Quantum Monte Carlo (QMC) simulations for strongly
interacting bosons in a 2D optical lattice trap, and confirm an excellent
agreement with the benchmarking in-situ density measurements by the Chicago
group [1]. We further present a general finite temperature phase diagram both
for the uniform and the trapped systems, and demonstrate how the universal
scaling properties near the superfluid(SF)-to-Mott insulator(MI) transition can
be observed by analysing the in-situ density profile. The characteristic
temperature to find such quantum criticality is estimated to be of the order of
the single-particle bandwidth, which should be achievable in the present or
near future experiments. Finally, we examine the validity regime of the local
fluctuation-dissipation theorem (FDT), which can be a used as a thermometry in
the strongly interacting regime.
