Memo Review

Memo: 427 - Antenna Position Calibration
      Wright, 2002May16

Reviewer: Craig Walker

Date Received: 2002Jul29


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.