  Spatially resolved relative phase measurement of two adjacent 1D Bose gases
is enabled by matter-wave interference upon free expansion. However,
longitudinal dynamics is typically ignored in the analysis of experimental
data. We provide an analytical formula showing a correction to the readout of
the relative phase due to longitudinal expansion and mixing with the common
phase. We numerically assess the error propagation to the estimation of the
gases' physical quantities such as correlation functions and temperature. Our
work characterizes the reliability and robustness of interferometric
measurements, directing us to the improvement of existing phase extraction
methods necessary to observe new physical phenomena in cold-atomic quantum
simulators.
