POLARIZATION SPECIFICATIONS AND GOALS FOR ALMA First Version 27 March 2000 Revised 2 May 2000 S.T. MYERS (NRAO, Socorro) To get the ball rolling, here is my first go at suggested polarization specs for ALMA. ------------------------------------------------------------------------------- 1. Background In his memo with suggested receiver specs http://www.tuc.nrao.edu/~ldaddari/rcvrSpecs.txt Larry writes Polarization: Simultaneous reception of two orthogonal polarizations is required, with each converted to (one or more) separate IF output(s). The nominal polarization states may be selected separately for each band so as to minimize the receiver noise temperature; that is, either linear or circular is acceptable as the nominal polarization. [At any frequency within the receiver's tuning range, the polarization states of the two channels should conform to:] [2.1 Maximum non-orthogonality TBD, ~-25 dB] [2.2 Maximum polarization mismatch between any pair of antennas in the array TBD, ~-20 dB] [Detailed specifications on polarization performance are under study.] In addition, over a limited portion of the tuning range of any receiver (typically 5% of center frequency), it shall be possible to make the nominal polarizations circular within 1.0 dB. This may be accomplished by an insertable optical device, which may cause an increase in noise temperature not to exceed [TBD]. 2. Current VLA performance In the set of VLA/VLBA polarization calibration data that I have been compiling the past 6 months http://www.aoc.nrao.edu/~smyers/calibration/ I find typical cross-polarization terms ("D-terms") of 1% at C and X band to as much as 5% -- 6% at K and Q band. For an example solution, see http://www.aoc.nrao.edu/~smyers/calibration/antpol.html The effect of the off-diagonal D-terms (eg. d_RL and d_LR) on the polarization calibration is the product of the D matrices for the pairs of antennas. Thus, to linear order, it is the difference ( d1_RL - d2_LR* ) between antennas 1 and 2, for example. Also note that technically the non-orthogonality is the same difference of the off-diagonal terms of the same antenna. These seem to be on the order of the magnitude of the D-terms themselves. The VLA D-terms on the order of 1% - 5% seem to limit the believable fractional polarization (even in bright sources) to around 0.5% for standard observation and analysis schemes due to limitations in the solutions for the D-terms using the usual software. The VLA solutions also do not seem to be time-stable. I am currently looking into this problem as part of the calibration program. D-terms of the order of 1% imply polarization purity (which we will take as non-orthogonality) of -20dB, while 6% corresponds to -12dB. Note that the polarization specs (dB) are for power, not voltage (as the visibility amplitudes give), and thus the specs on power are a factor of two more stringent! Thus, for example, the current VLA has cross-polarization terms of -24 dB to -40 dB down in power, which is fairly difficult to acheive in practice (as the VLA engineers found). 3. However, it does seem that the polarization performance of the VLA is acceptable to most observers and does not seem to seriously limit the scientific applications of polarization observations. Therefore, I would adopt Larry's specs of -25db and -20db respectively for allowed non-orthogonality and mismatch as the design GOALS, and relax the specs somewhat (based on what I interpret as the VLA performance): [2.1 Maximum non-orthogonality Spec: -25dB Goal: -35dB [2.2 Maximum polarization mismatch Spec: -20dB Goal: -30dB between any pair of antennas [2.3 Maximum deviation from stated Spec: -12dB Goal: -20dB linear or circular polarization in voltage (d-term amplitude) These specs should yield polarization vector accuracies of a few degrees which seems sufficient. I added a third spec on the magnitude of the cross-terms in the instrumental polarization matrix of 6% spec and 1% goal (-12dB and -20dB respectively) as these are easier to determine than overall non-orthogonality after passing through some complex and undefined calibration scheme - the d-terms are small, then their fluctuations should also be small! I have stated these in terms of voltage unlike the other two, again because this is more readily measured directly. I am worried that over-stringent polarization characteristics may prove extremely difficult to actually acheive for ALMA, given the experience of the VLA. I have arbitrarily set the "goals" for 2.1 and 2.2 at 10 db below the specs. My guess is that we could live with actual specs on 2.1 and 2.2 somewhat worse than those listed above (-20 db and -15 db for example) if that were necessary for reaching other performance goals, as long as the d-term specs 2.3 were met. 4. With the large tuning bandwidths (as high as 30% fractional bandwidth) it will be difficult to make OMTs, quarter-wave plates or quasi-optical devices that will perform to the above specs over the entire band. For example, for a band-edge 1.15 times the band center, a waveguide quarter-wave retarder (with a dielectric vane for example) could have as much as a $13^\circ$ phase error at band edge, which would roughly give a cross-polarization of 23% (twice this for power instead of voltage)! Therefore I propose the above specs and goals to apply only to the central 5% of bandwidth (eg. 5 GHz at 100 GHz, 32 GHz at 650 GHz), and allow the performance to deviate at band edges. As for circular versus linear, I see no reason to specify anything beyond these specs (eg. Larry's 1db circularity would possibly be a goal). From what I hear from the engineers, getting even the VLA-level performance will be very difficult, and if it is necessary to use linear polarizations to do so then that should be acceptable. 5. If we want tighter specs, I think we need pretty strong scientific drivers (such as expected fractional polarizations for dust emission at sub-mm bands) to argue for this. AGN polarizations seem to be high enough (5% - 10%) that the VLA-level specs are sufficient. Dust polarizations of 1% should be possible to detect and measure with (stable) d-terms of 1%. Some science drivers are given in the memo by Crutcher, Welch and D'Addario, who state that As a practical matter, the goal should be instrumental polarization effects of < 0.1%, after calibration. This seems laudable, and within our goals of -30 dB, but fairly difficult to get in practice. 6. COMMENTS ANYONE?