Memo Review Memo: 427 - Antenna Position Calibration Wright, 2002May16 Reviewer: Craig Walker Date Received: 2002Jul29 Review: The scheme for fitting the baselines using phase differences is just an implementation of the usual geodetic VLBI "bandwidth synthesis" technique. The phase difference is just the delay. Very accurate work can be done this way by observing multiple bands as far separated as possible, along with some in between to help resolve ambiguities. Single band delays (phase slopes) can also be used to resolve ambiguities. A well implemented system could be made which is not subject to problems with ambiguities. In fact, the spanned bandwidths at mm wavelengths can be larger than the RF at X band where geodesy is usually done, so mm bandwidth synthesis delays might be more accurate than X band phase measurements. The scheduling style involving observations of sources all over the sky is typical of all baseline observations including VLBI geodesy and VLA. For VLBI baseline measurements, the troposphere is the major limiting factor. This cancels out on short baselines, but I would think it might be wise to leave some capability to fit for the zenith delay when solving for the longest ALMA baselines. For VLBI geodesy, an attempt to separate the tropospheric effect is made by observing at very low elevations where you are looking through many atmospheres. Of course, for VLBI, one can do this for one antenna at a time which could not be done for ALMA. Also note that one should at least think about the ionosphere. Geodetic VLBI observations use a combination of S and X band to solve for and remove the ionospheric contribution. It is typical to think that the ionosphere can be ignored at high frequencies, but this is not entirely true. It is capable of contributing a full turn of phase at 100 GHz, or equivalently, about 3 mm of path delay. For differential work such as on ALMA, and especially for baseline solutions done at night when the contribution is an order of magnitude smaller, this probably works out to be negligable. But if you want one tenth wavelength at 1000 GHz, that is 0.03 mm which is only 1 percent of the full contribution at the 100 GHz frequency where the baselines might be measured. Note that other geophysical effects, such as Earth tides, cannot be totally ignored. A rough back-of-the-envelope calculation suggests that tides will contribute an effect at about the millimeter level on the longest baselines. I would also not be surprised if there are effects from the temperature of the antenna structures and from the temperature and moisture content of the soil that are not completely neglegible. The use of subarrays to find locations of newly moved antennas is typical of VLA operations and would be natural for ALMA. There are a few items that I would recommend for ALMA related to the geometry. The first is to use the CALC server for the correlator model as is being done for the VLBA and will be done for the EVLA. The CALC model, which is the full up geodetic model from the Goddard geodesy group, is probably overkill for short baseline interferometers, but the computations are not difficult and a simple computer can keep up easily. Besides it already exists. If CALC is used, then it is highly unlikely that anyone will ever run into limitations from the correlator model. If a less accurate model is used, who knows. The second suggestion would be to get a highly functional baseline fitting tool implemented in AIPS++. At the moment, the available off-line tools for fitting for baselines or source positions from either the VLA or the VLBA are primitive to say the least. The VLA baseline solutions are done on-line while the VLBA depends on the generosity of the Goddard group. A fitting tool should have much of the functionality of the SOLVE program of the geodetic software (it sounds like the Miriad task BEE discussed in the memo has some of this). One question is whether to have an ability to fit using combinations of historical data which is the mechanism by which the geodesy groups get their best results. Maybe we should leave that level of complexity to them. Note that the quasar positions used for accurate baseline fitting probably are those from the geodetic VLBI group. Those positions are measured at 8.4 GHz. It is not obvious that the emission centroid at 100 GHz and higher is aligned with the 8.4 GHz position at the sub-mas level. Some mm astrometric work will be needed, either with VLBI or the mm interferometers, to clarify this and perhaps to get new mm-based positions. I have not worked through the numbers, but I would think ALMA could be a very good astrometric tool. The resolution is not as high as VLBI, but it only has to deal with differential, not total, tropospheric and geophysical effects.