  We analyze the information content of density profiles for an ultracold Bose
gas of atoms and extract resolution limits for observables contained in these
images. Our starting point is density correlations that we compute within the
Bogoliubov approximation, taking into account quantum and thermal fluctuations
beyond mean-field theory. This provides an approximate way to construct the
joint counting statistics of atoms in an array of pixels covering the gas. We
derive the Fisher information of an image and the associated Cramer-Rao
sensitivity bound for measuring observables contained in the image. We
elaborate on our recent study on position measurements of a dark soliton
[Negretti et al., Phys. Rev. A 77, 043606 (2008)] where a sensitivity scaling
with the atomic density as n^{-3/4} was found. We discuss here a wider class of
soliton solutions and present a detailed analysis of the Bogoliubov excitations
and the gapless (Goldstone) excitation modes. These fluctuations around the
mean field contribute to the noise in the image, and we show how they can
actually improve the ability to locate the position of the soliton.
