Origin of small but non-zero closure phases

Determine the physical and experimental causes of the small yet statistically non-zero closure phases (typically up to about 2 degrees) measured with the ALBA optical synchrotron radiation interferometry using non-redundant aperture masks, despite the factorization of element-based phase errors and the source being only marginally resolved, in order to establish whether these deviations arise from centering differences, Airy-disk sampling, or other systematic effects in the setup.

Background

Closure phase, the sum of visibility phases over a closed baseline triangle, is robust to element-based phase errors and is a key diagnostic of source symmetry. In these experiments, closure phases are highly stable over time but consistently near, though not exactly, zero.

Although the electron beam is only marginally resolved and the closure phases are generally within 2 degrees, the experiments show small but statistically significant non-zero values. The paper notes that such non-zero closure phases might originate from experimental factors such as image centering or Airy-disk sampling, but the precise cause has not yet been established.