Editing Very-long-baseline interferometry (section)

== Method ==
[[File:Recording data at each of the telescopes in a VLBI array.gif|thumb|350px|Recording data at each of the telescopes in a VLBI array. Extremely accurate high-frequency clocks are recorded alongside the astronomical data in order to help get the synchronization correct]]

In VLBI, the digitized antenna data are usually recorded at each of the telescopes (in the past this was done on large magnetic tapes, but nowadays it is usually done on large arrays of computer disk drives). The antenna signal is sampled with an extremely precise and stable atomic clock (usually a hydrogen [[maser]]) that is additionally locked onto a GPS time standard. Alongside the astronomical data samples, the output of this clock is recorded. The recorded media are then transported to a central location. More recent{{when|date=February 2020}} experiments have been conducted with "electronic" VLBI (e-VLBI) where the data are sent by fibre-optics (e.g., 10&nbsp;Gbit/s fiber-optic paths in the European [[GEANT2]] research network) and not recorded at the telescopes, speeding up and simplifying the observing process significantly. Even though the data rates are very high, the data can be sent over normal Internet connections taking advantage of the fact that many of the international high speed networks have significant spare capacity at present.

At the location of the correlator, the data is played back. The timing of the playback is adjusted according to the atomic clock signals, and the estimated times of arrival of the radio signal at each of the telescopes. A range of playback timings over a range of nanoseconds are usually tested until the correct timing is found.

[[File:Vlbi data playback 2.gif|thumb|350px|Playing back the data from each of the telescopes in a VLBI array. Great care must be taken to synchronize the play back of the data from different telescopes. [[Atomic clock]] signals recorded with the data help in getting the timing correct.]]

Each antenna will be a different distance from the radio source, and as with the short baseline radio [[interferometer]]  the delays incurred by the extra distance to one antenna must be added artificially to the signals received at each of the other antennas. The approximate delay required can be calculated from the geometry of the problem. The tape playback is synchronized using the recorded signals from the atomic clocks as time references, as shown in the drawing on the right. If the position of the antennas is not known to sufficient accuracy or atmospheric effects are significant, fine adjustments to the delays must be made until interference fringes are detected. If the signal from antenna A is taken as the reference, inaccuracies in the delay will lead to errors <math>\epsilon_{B}</math> and <math>\epsilon_{C}</math> in the phases of the signals from tapes B and C respectively (see drawing on right). As a result of these errors the phase of the complex visibility cannot be measured with a very-long-baseline interferometer.

Temperature variations at VLBI sites can deform the structure of the antennas and affect the baseline measurements.<ref>{{Cite journal|
last1=Wresnik|first1=J.|last2=Haas|first2=R.|last3=Boehm|first3=J.|last4=Schuh|first4=H.|date=2007|title=Modeling thermal deformation of VLBI antennas with a new temperature model|journal=Journal of Geodesy|language=en|volume=81|issue=6–8|pages=423–431|doi=10.1007/s00190-006-0120-2|bibcode=2007JGeod..81..423W|s2cid=120880995}}</ref><ref name="EG-PASP">{{Cite journal|last=Ghaderpour|first=E.|date=2020|title=Least-squares wavelet and cross-wavelet analyses of VLBI baseline length and temperature time series: Fortaleza-Hartrao-Westford-Wettzell|journal=Publications of the Astronomical Society of the Pacific|language=en|volume=133|pages=1019|doi=10.1088/1538-3873/abcc4e|s2cid=234445743|doi-access=free}}</ref> Neglecting atmospheric pressure and hydrological loading corrections at the observation level can also contaminate the VLBI measurements by introducing annual and seasonal signals, like in the Global Navigation Satellite System time series.<ref name="EG-PASP"/>

The phase of the complex visibility depends on the symmetry of the source brightness distribution. Any brightness distribution can be written as the sum of a [[symmetric component]] and an [[anti-symmetric component]]. The symmetric component of the brightness distribution only contributes to the real part of the complex visibility, while the anti-symmetric component only contributes to the imaginary part. As the phase of each complex visibility measurement cannot be determined with a very-long-baseline interferometer the symmetry of the corresponding contribution to the source brightness distributions is not known.

[[Roger Clifton Jennison]] developed a novel technique for obtaining information about visibility phases when delay errors are present, using an observable called the [[closure phase]]. Although his initial laboratory measurements of closure phase had been done at optical wavelengths, he foresaw greater potential for his technique in radio interferometry. In 1958 he demonstrated its effectiveness with a radio interferometer, but it only became widely used for long-baseline radio interferometry in 1974. At least three antennas are required. This method was used for the first VLBI measurements, and a modified form of this approach ("Self-Calibration") is still used today.