ALMA Memo #404
Atmospheric Dispersion and Fast Switching Phase Calibration
M.A. Holdaway (NRAO/Tucson) and J.R. Pardo(Inst. Estructura de la Materia Dpto. Fsica Molecular Serrano)
2001/12/19
The differential atmospheric phase of an interferometer has an
approximate linear variation with frequency up to about 300 GHz.
However, near absorption lines, and especially in the sub-millimeter
wavelength atmospheric windows where the absorption lines are very
strong and always near, the assumption of a non-dispersive atmosphere
breaks down markedly.
We present simulations performed with the ATM atmospheric transmission
model (Pardo et. al, 2001), tailored to the specific observing
conditions at the Chajnantor site and we propose specific observing
strategies to employ for the ALMA telescope. While the *absolute* wet
and dry dispersive phase (ie, the part of the phase which deviates
from the phase which is linear with frequency) can be very large
through the atmosphere, the *differential* dispersive phases (ie, the
difference in the dispersive phases above two antennas paired in an
interferometer) are much smaller. We find that the differential dry
atmospheric dispersion is essentially zero at all frequencies of
relevance to the ALMA for the expected pressure fluctuations within
the area covered by the interferometer. The differential wet
dispersion can be large enough to be of concern in the 350, 400-500,
650, and 850 GHz windows.
In fast switching, we expect to observe a calibrator source at 90 GHz
and scale the phase solutions to the target frequency. If time
dependent wet and dry phase errors occur, ALMA has a potential problem
because the wet and dry phases will scale differently with frequency
in the sub-millimeter windows. Separation of the phases into wet and
dry components may be possible, but this sounds very messy and
uncertain, requiring multi-frequency calibrator observations or
associated radiometric measurements and good atmospheric modeling. If
dry phase errors are negligible and the phase errors can be split
between electronic and atmospheric components, then the
frequency-dependent phase scaling factor can be determined by a model
such as ATM to accurately account for the dispersion. As we do not
have a good handle on the magnitude of dry phase errors, we cannot
estimate the success of such a strategy. A worst case scenario would
be to assume that the dry phase errors are larger than the dispersive
phase. By using the ratio of the frequencies to scale the phase
solutions to the target frequency, we correct for the dry errors, but
miss the differential wet dispersive phase. The differential wet
dispersive phase will manifest itself as some fraction of the phase
errors which are just not calibrated. These residual phase errors
will be larger during unstable atmospheric conditions, at the edges of
the transmission windows, and on longer baselines. During the 10th
percentile atmospheric stability conditions, on baselines of 1000 m,
the fast switching residual phase will be dominated by the
uncompensated dispersive phase at the edges of the sub-millimeter
windows (ie, at frequencies where the transmission is less than 50%
of the peak transmission for that window). This will markedly affect
the ability of fast switching to correct atmospheric phase errors for
sub-millimeter observations. Longer baselines could be accommodated by
observing during better conditions or by observing near the window
center where the dispersive phase is close to zero. If dry phase
fluctuations are smaller than the dispersive phase, as will almost
certainly occur far from the window centers, the dry phase can be
ignored and a correct accounting for the dispersive phase from a
transmission model such as ATM can be applied.
If radiometric phase correction were used, a differential dry delay
could be quite damaging for sub-millimeter observations. However, if
the dry phase were very small, the differential dispersive phase could
be calculated from transmission models and applied to correct the
phase more perfectly, just as in fast switching with a negligible dry
term.
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