### visibility

(mathematical representation of interferometer's view)

In interferometry, the term visibility refers to the output of the interferometer's correlator, output which corresponds not to the signal from the observed portion of the sky, but a representation of a portion of a Fourier transform of that signal along the direction of the baseline between the receivers. This correspondence between interferometer output and such a Fourier transform is termed the van Cittert-Zernike theorem. The visibility is a representation of a fringe pattern (the result of interference) indicating the amplitude of the spatial frequency of a line along that direction across the source's signal. This amplitude along with the phase of this spatial frequency can be represented by a complex number (a complex visibility). The term visibility is commonly used regarding radio interferometry and I've seen it used in descriptions of optical interferometry as well. Visibilities are typically expressed in the u-v plane, defined as a plane parallel to the portion of the celestial sphere under observation and scaled using the wavelength as its distance unit.

Creating an image using interferometry, which is termed aperture synthesis, consists of collecting visibilities along a number of baselines with varying directions, and determining an image of the likely pattern of signals that produced these visibilities. This involves compensating for expected noise and filling in the gaps in the data since the baselines of the observation do not cover every possible direction and spatial frequency.

(interferometry)