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\title{COMMENTS ON SELF CALIBRATION AND FAST SWITCHING }
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\author{M. C. H. Wright}
\affil{Radio Astronomy laboratory, University of California, Berkeley,
    CA, 94720}

\begin{abstract}
We briefly discuss the relative merits and problems of self-calibration and
fast switching calibration for the BIMA a-array.
Self-calibration is very successful for strong sources, but can lead to spurious
results for small arrays of antennas if the source is weak or too complex.
Fast switching between a source and a nearby calibrator can reduce the rms
phase on baselines longer than few hundred meters. Switching times of a few
seconds are desirable, but are inefficient.
\end{abstract}

\section{Introduction}
Measurements of atmospheric phase fluctuations on a 1 km baseline show
RMS pathlength variations of 1 mm on 10 s timescales at millimeter wavelengths.
The standard phase calibration is inadequate; modified observing
and data reduction procedures are required for aperture synthesis at
millimeter wavelengths on long baselines.
 

\section{Self Calibration}
A successful self-calibration depends on the strength and structure of the source.
The best situation is obtained if there is strong unresolved structure so that
we can self-calibrate using an interval shorter than the fluctuation time scale of
the atmosphere.
A strong, compact spectral line, such as the Orion SiO maser can be used to calibrate
extended spectral or continuum emission in the band at the same time;
or a compact continuum source, such as the Cygnus A nucleus, can be used to calibrate
more extended structures. If a compact continuum source is embedded in strong
extended structure, such as in SgrA*, it may not be possible to self-calibrate on
a short time scale because the extended structure changes the phase of the visibility
data, and using a longer time interval to average out the extended structure does not
remove the atmospheric phase fluctuations.  If the source is too weak, or too complex
it is possible to produce false structures using self-calibration on data with large
phase errors.

If self-calibration can not be used initially, it may still be useful to clean up an
image once we have a good source model, either a model based on other data, or from
an initial image obtained using a-priori calibration.

\section{Fast Switching}
Standard phase calibration using a nearby quasar is usually inadequate on long baselines.
Fast switching between the source and a nearby compact continuum or spectral calibrator 
will reduce the atmospheric phase fluctuations if
the effective distance between the source and the calibrator,
$d = \sqrt{(h(s-s_0)) ^2 + (v\Delta{T})^2}$
is smaller than the interferometer baseline, $b$ ,
where $h$ is the height of the turbulence in the direction of the source, and
$v$ the mean turbulent velocity over an interval $\Delta T$
(Holdaway and Owen, 1995; Wright, 1996).
Both source and calibrator suffer atmospheric phase fluctuation given by the
phase structure function $D\phi(b) = \langle(\phi(x+b) - \phi(x))^{2}\rangle$,
where $b$ is the interferometer baseline.
After calibration, the phase fluctuations will be reduced if $d < b$.
 Assuming $h$ = 2 km, a source-calibrator separation = 10 degrees,
$v=5$ m/s, and a switching time, $\Delta T = 1$ minute,
these parameters imply $h(s-s_0) = 350$ m and $v\Delta{T}$ = 300 m.
In these conditions, atmospheric phase fluctuations 
will be reduced on baselines longer than about 460 m.
A greater improvement is expected if the turbulence is closer
to the antennas, or the mean turbulent velocity is smaller than assumed.

\section{Conclusion}

If the source is strong (SNR $>$ 1 in 10 s) and compact (0.4 to 0\farcs7) then 
self-calibration is better than fast switching. 
If the source is weak, or extended, then we must observe a quasar as often as possible.
Alternating between source and calibrator every 2 min say, may not be good enough. 
Alternating between source and calibrator every integration may be too inefficient,
and not much faster unless the calibrator is very close to the source;
better to select a calibration interval which is reasonably efficient.
At least observe a strong quasar every 30min to calibrate the relative phase of sidebands
and spectral windows. 

\begin{references}

% test of fast switching
Holdaway, M.A. and Owen, F.N., 1995, NRAO. Millimeter Array Memo 126.

Wright, M.C.H., 1996, \pasp, 108, 520.
\end{references}

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