Polarization Mixing Correction (Old)

Explanation of Polarization Mixing

The newer 2.1-m antennas [Ants 1-8 and 12] have AzEl (azimuth-elevation) mounts (also referred to as AltAz, where Altitude and Elevation are used synonymously), which means that their crossed linear feeds have a constant angle relative to the horizon (the axis of rotation being at the zenith). The older 2.1-m antennas [Ants 9-11 and 13], and the 27-m antenna [Ant 14], have Equatorial mounts, which means that their crossed linear feeds have a constant angle with respect to the celestial equator, the axis of rotation being at the north celestial pole. Thus, the celestial coordinate system is tilted by the local co-latitude (complement of the latitude). This tilt results in a relative feed rotation between the 27-m antenna and the AzEl mounts, but not between the 27-m and the older equatorial mounts. This angle is called the "parallactic angle," and is given by:

$\chi =\arctan(\cos \lambda \sin A,\sin \lambda \cos E-\cos \lambda \sin E\cos A)$,

where $\lambda$ is the site latitude, $A$ is the Azimuth angle [0 north], and $E$ is the Elevation angle [0 on horizon]. This function obviously changes with position on the sky, and as we follow a celestial source (e.g. the Sun) across the sky this rotation angle is continuously changing in a surprisingly complex manner.

Fig. 1: Parallactic angle for a range of hour angle and declination. There is a large deviation for sources whose Dec = latitude (37 degrees), when they pass directly overhead.