2. Contribution of the instrumental polarization to the closure phase
Massi et al. (1996) pointed out that the error in the closure phase might mainly be due to the instrumental polarization (D) at the telescope sites. This effect has been assumed in the past to be completely negligible,because affects observations of unpolarized sources only in the second order. This is certainly true for telescopes in which the instrumental polarization is so low that a second order contribution adds an error lower than the expected thermal noise (like the VLBA-telescopes with instrumental polarizations below 2 ) .
For the European telescopes, where the instrumental polarization ranges (at 6cm) from 2 to 22 with an average value of 9 , the contribution results in an additive phase error of 0.4 degree. The expected phase noise for a standard calibrator is around 0.04 degrees, which is one order of magnitude lower.
As stated in Cotton (1989), in practice it is impossible to built perfect feeds that only respond to a given polarization. The instrumental polarization, also called polarization impurity or feed ellipticity, may be seen as the sensitivity of a feed to the other sense of polarization.
where with d of a few percent
and are the left and right circularly polarized components of the electromagnetic wave
is the antenna gain
is the parallactic angle, i.e. the angle between the local vertical on the feed and the direction to the north at the position of the source. It is constant for equatorially mounted antennas and for alt-azimuth mounts varies as:
where is the source declination and H is the hour angle of the antenna having latitude b.
Assuming the circular polarization of the source to be negligible, the response of ai two element interferometer "i,k" will be:
where and M is the visibility that corresponds to the fractional linear polarization.
Due to the low amplitude of the D and M terms we can rewrite the equation as:
In other words: the instrumental polarization contributes in three terms to the parallel hand ( as in the equations above or ) data; the term containing is purely instrumental while the two terms containing are related to the polarization of the observed source. Here our aim is to see how large the instrumental contribution alone may be. Therefore we will assume in the following that M is negligible in comparison with D (i.e. source polarization lower than ).
Rewriting the factor in (Massi et al. 1991) as:
(where d and are the D term amplitude and phase) equation (4) reduces to:
2.2. Closure phase: the Phase of the Bispectrum
If at least three telescopes "i ","k " and "m " are available the quantity called the bispectrum can be computed as the product of the three interferometric outputs:
The phase of the bispectrum is called the "closure phase" (Rogers et al.1974), which theoretically should differ from zero only due to noise contributions if a point source is observed.
In our case the closure phase is:
where all "antenna" terms and cancel each other and the remaining contribution is the instrumental polarization:
In order to see at which level the instrumental polarization influences the data, in the next section we will compare the observed closure phase for the source DA193 with that computed by equation (10). The perfect agreement shown there will prove that the instrumental polarization is responsible for the large observed values of closure phase.
© European Southern Observatory (ESO) 1997
Online publication: July 8, 1998