Closure invariants for polarised radio interferometric observations: A graph theoretical approach

Aperture synthesis observations in radio wavelengths with full polarisation, have long been used to study the magnetic fields of synchrotron-emitting sources. Recently proposed closure invariants – quantities immune to antenna-specific signal corruptions – give us a powerful method for extracting information from measured visibilities, which are corrupted by antenna and polarisation-dependent gains. This paper extends a formalism developed earlier for complete graphs (where all visibilities are available) to incomplete graphs. The formalism provides a complete and independent set of closure invariants from the measured visibilities in a general situation, where not all visibilities are available. We then show in a simulated, quasi-realistic case, that the invariants developed here contain usable information even in the presence of noise.