Visibility of cold atomic gases in optical lattices for finite temperatures

In nearly all experiments with ultracold atoms time-of-flight pictures are the only data available. In this paper we present an analytical strong-coupling calculation for those time-of-flight pictures of bosons in a three-dimensional optical lattice in the Mott phase. This allows us to determine the visibility, which quantifies the contrast of peaks in the time-of-flight pictures, and we suggest how to use it as a thermometer.