Instrumental polarization issues

As noted above, science drivers imply that most polarization work will be in linear polarization. The main science driver for circular polarization work is Zeeman work, for which the requirements are less severe (see below). Thus, if it is necessary to optimize the ALMA for observations of linear or circular polarization, the science implies optimization for linear polarization observations. If this is not possible for all bands, consideration should be given to optimization for linear polarization observations at a prime polarization band; perhaps the 345 GHz band is best. The science goal is that the total instrumental polarization be less than 0.1% without major loss of observing time for calibration. This tolerance cannot be met without calibration, but achieving the closest possible approach to zero instrumental polarization must be a design criterion in order to meet the science goal. Meeting this goal requires consideration of the following areas:

• Absolute polarization of each of two (nominally orthogonal polarization) ports.
• Orthogonality of the polarizations of the two ports of one antenna.
• Uniformity of polarization among antennas of the array.
• Orthogonality of opposite ports between antenna pairs of the array.
• Variation of each of the above with direction of arrival over the main beam.
• Temporal stability of each of the above, short- and long-term.
• Effects of elevation dependence; designs that call for the antennas to be stiff or that allow them to sag with refocusing both require attention to the polarization effects.

Although one often speaks of linearly or circularly polarized feeds, it should be noted that ``feeds" are never purely linearly nor purely circularly polarized, though they are often a close approximation to one of these. The mathematics makes it clear that so long as the telescopes have orthogonal polarization receivers, one can derive the full polarization information (i.e., all four Stokes parameters). One can choose any pair of orthogonal polarization states as ``basis" states, so that any arbitrary state is describable as a linear combination of them. To be accurate, it is the polarization state of the whole antenna that matters. For most radio telescopes, this includes the main reflector; subreflector; other mirrors (flat or curved); other optical elements (including wire grids and lenses); and finally something to convert the free-space, multi-mode beam into a guided, single-mode wave. The last element is often a polarization-insensitive horn followed by a ``polarizer" with two single-mode ports, each coupling to a different polarization of a plane wave incident on the whole antenna. Each of these cascaded elements affects these final two polarizations. Those elements that have sufficient symmetry can be treated as polarization-insensitive. In the simplest case only the polarizer is significant, but in practice the situation is often more complicated. The sensitivity can be reduced if the polarizer introduces noise, or if a significant fraction of the observing time must be devoted to calibrating the instrumental polarization in order to achieve the required sensitivity. The BIMA system, which has only a single receiver per telescope, employs a transmission polarizer consisting of a grooved dielectric plate in front of the receiver to select the desired polarization basis state; this plate adds significantly to the noise of the system. Second, if the polarization state of each antenna is complicated (for example, if it differs significantly from the desired basis state or varies both in time or over the field of view), a large fraction of the observing time must be spent in calibration, which will significantly reduce the sensitivity. Hence, a design that has the lowest instrumental polarization and the lowest possible, most time stable instrumental polarization will maximize sensitivity. The optical design is crucial for polarization mapping over extended areas. The best optical system is a ``straight through" design, with no off-axis elements or oblique reflections. Both will produce instrumental polarization that varies over the primary beam of the telescopes. If an off-axis system is necessary, careful calibration of its instrumental polarization effects will be necessary. Since this will be time consuming, it will be important that the optical system be kept invariant so that a calibration may be used over a long period of time. It would make sense to choose a primary band for linear polarization work (probably 345 GHz would be best) and optimize the optics of that band for polarization. Again, ideally, this would be on axis. If that is impossible, at least a dual-mirror system should be chosen with reflections designed for the polarization basis state of each channel. Having reflections as close as possible to normal (to the mirror) for the primary polarization band should be a design consideration. Another issue is whether there is a significant advantage to a choice as close as possible to a linear or a circular basis state, and second, what deviation from a particular basis state may be tolerated without making the calibration less accurate and/or more difficult and time consuming. Although in principle even large instrumental polarization effects may be calibrated, in practice the best approach is to have the polarization state of each antenna to be intrinsically as close as possible to the desired ideal state. In practice, accurate polarimetry must account for the actual polarization state of the antenna; extraordinary efforts to produce a basis state that approaches circular or linear to high accuracy is not important. Cotton (1998; MMA Memo 208) discussed calibration of interferometer polarization data and the merits of linear or circularly polarized feeds. There are a number of strong disadvantages of linear feeds, including especially the facts that p-q (orthogonal polarizations) phase fluctuations can significantly increase the noise in linearly polarized data, that no polarization ``snapshots" are possible since extended observations are required to measure calibrator Q and U, and that any p-q phase difference corrupts polarization data. Circularly polarized feeds overcome these disadvantages for polarization work, and have the additional advantages that calibrator polarization only weakly affects gain calibration, that there is good separation of source and instrumental polarization with parallactic angle, and that instrumental polarization can be determined from a calibrator of unknown polarization. If, as argued above, linear polarization science observations will be the most important, having the polarization basis states as close as possible to circular would be best. Since Zeeman observations are spectral-line observations, the observed polarization is a relative measurement. That is, the circular polarization as a function of frequency must be measured. The most important instrumental polarization effect is beam squint - the pointing of the two circularly polarized beams in slightly different directions. More generally, beam squint may be considered to be the total (including sidelobes) difference in instrumental positional response between the two senses of circular polarization. In the presence of velocity gradients in molecular clouds, beam squint will produce false Zeeman signatures. However, so long as the primary beam squint is not too bad, and especially if it is known and stable, its effects can be calibrated and corrected. Small (< 5%) impurity in instrumental circular polarization and difference in gain between the two polarization channels can be calibrated out using standard Zeeman analysis techniques. Moreover, simultaneous observations of thermal continuum and/or of non-Zeeman spectral lines within the observation window may be used to calibrate the instrumental circular polarization.