  We consider time-of-flight measurements in split one-dimensional Bose gases.
It is well known that the low-energy sector of such systems can be described in
terms of two compact phase fields $\hat{\phi}_{a,s}(x)$. Building on existing
results in the literature we discuss how a single projective measurement of the
particle density after trap release is in a certain limit related to the
eigenvalues of the vertex operator $e^{i\hat{\phi}_a(x)}$. We emphasize the
theoretical assumptions underlying the analysis of "single-shot" interference
patterns and show that such measurements give direct access to multi-point
correlation functions of $e^{i\hat{\phi}_a(x)}$ in a substantial parameter
regime. For experimentally relevant situations, we derive an expression for the
measured particle density after trap release in terms of convolutions of the
eigenvalues of vertex operators involving both sectors of the two-component
Luttinger liquid that describes the low-energy regime of the split condensate.
This opens the door to accessing properties of the symmetric sector via an
appropriate analysis of existing experimental data.
