Over-resolution of compact sources in interferometric observations

We review the effects of source size in interferometric observations and focus on the cases of very compact sources. If a source is extremely compact and/or weak (such that it is impossible to detect signatures of source structure in the visibilities), we describe a test of hypothesis that can be used to set a strong upper limit to the size of the source. We also estimate the minimum possible size of a source whose structure can still be detected by an interferometer (i.e., the maximum theoretical over-resolution power of an interferometer), which depends on the overall observing time, the compactness of the array distribution, and the sensitivity of the receivers. As a result, and depending on the observing frequency, the over-resolution power of forthcoming ultra-sensitive arrays, such as the Square Kilometer Array (SKA), may allow us to study the details of sources at angular scales as small as a few {$μ$}as.