### 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*)
**Further reading:**

http://en.wikipedia.org/wiki/Interferometric_visibility

http://en.wikipedia.org/wiki/Van_Cittert-Zernike_theorem

https://www.mpifr-bonn.mpg.de/3244039/IMPRS_BB_HRK4.pdf

http://www.ita.uni-heidelberg.de/~dullemond/lectures/obsastro_2011/chap_interferometry.pdf

http://www.atnf.csiro.au/research/radio-school/2014/talks/ATNF2014-Intro.pdf

https://www.eso.org/sci/meetings/2015/eris2015/L1_Jackson_Interferometry.pdf

**Referenced by pages:**

u-v plane

Index