Calibration issues

Since the instrumental polarization tolerances will not be zero, what is the best overall strategy for calibration to determine the actual polarization of each antenna? Moreover, besides knowing polarizations of the antennas, it is also necessary to know the complex gains of the receivers. To a large extent, this is the same as is required for observations of sources that are assumed unpolarized or where only total intensity is to be measured. An exception is that polarimetry requires knowledge of the ratio of the complex gains of the two channels, whereas total intensity measurement does not. Conventional astronomical calibration determines the amplitudes of these gains separately (and hence their ratio) provided that the calibrator's polarization is known (preferably unpolarized); it can determine the phase difference only if the calibrator is appropriately polarized (preferable strongly so). What, then, is the best overall strategy for receiver gain calibration? These points must be considered in the contexts of both interferometer mode observations and single-dish mode observations. The single-dish mode is the more difficult. For the ALMA, it may be that the engineering reality is that all receivers will be connected to antenna ports that are approximately linearly polarized, and thus a poor approximation to being circularly polarized. MMA#208 states that the principal reason for this is that it allows larger bandwidth; this is roughly true at centimeter wavelengths, but it is not correct for the ALMA. At the shorter wavelengths, various antenna elements besides the polarizer are either impossible to construct or are excessively lossy if they operate on waves that are nearly circularly polarized. An element that selects a single linear polarization with very low loss and very large bandwidth is easily built (a wire grid), whereas nothing similar exists for circular polarization. It is possible to insert a ``quarter wave plate" to convert circular to linear polarization with good accuracy over a narrow band, but with some noise penalty due to ohmic losses. Thus, engineering reality may preclude the possibility of having the ALMA optimized for linear polarization by having near-circular polarization feeds, except as a potential add-on, with limitations. It should be clear that this is an engineering limitation and not a decision that optimizes for polarization science. Many of the difficulties cited by Cotton in MMA#208 would be overcome by having a calibration source of known polarization with a very strong linearly-polarized component (assuming that we are more interested in mapping the linear polarization component than the circular one of unknown sources). Although such things do not exist in the natural sky, it should be straightforward to have one built into each ALMA antenna. One attractive possibility for the calibration of the dual polarization receivers is to provide an intense millimeter wavelength CW signal that can be coupled into the receivers at their inputs. Such a signal could be coupled into the receivers through a small aperture in the middle of the secondary mirror. It could be highly linearly polarized but at a position angle of 45 degrees, so that it couples equally and coherently to both the horizontal and vertical polarization receivers. In this way, it could provide a very accurate relative calibration of the two receivers. A total power spectral correlation measurement would provide both amplitude and phase calibration between the two receivers. Presumably this CW millimeter wavelength signal could be tuned to different frequencies as needed. A further possibility would be that the same coherent millimeter CW signal could be injected into every front end. For example, the signal might be provided as the beat note between two optical laser signals. In this case, the coherence of the signals would allow the phase (and amplitude) relative calibration of all the receivers, including their two polarizations. This internal polarization calibration source would of course calibrate the system from the feeds on; instrumental polarization of the primary and secondary reflecting surfaces would have to be calibrated astronomically. In order not to spent excess time on such calibrations, the design should focus strongly on making the instrumental polarization that must be calibrated astronomically as stable in time, elevation angle, and position over the beam as possible. Obtaining single antenna and short spacing polarization data will be a challenge for the ALMA. A plan to obtain such intensity data by ``on-the-fly" mapping with the ALMA antennas should work for polarization also so long as full polarization information is obtained and the system is sufficiently stable. A stability of at least 1 part in 10,000 seems to be necessary, sufficient, and achievable, but this spec needs to be investigated specifically for polarization calibration. A system to cross-correlate the signals from the orthogonally polarized receivers on each antenna in order to produce single-dish polarization data while ``on-the-fly" mapping is being carried out should work, but needs to be investigated. A system which requires physical rotation of polarizers should be avoided; it would be difficult to achieve the required accuracy and would be time consuming.