  The standard experimental techniques usually adopted in the study of the
behaviour of ultracold atoms in optical lattices involve extracting the atom
density profile from absorption images of the atomic sample after trap release.
Quantum mechanically this procedure is described by a generalized measure
(POVM); interference patterns found in absorption images suggest a generalized
measure based on fixed-phase, coherent-like states. We show that this leads to
an average atomic density which differs from the usually adopted one, obtained
as the expectation value of the atom density operator in the many-body state.
