Seth Redfield (Tufts University)
VLBA Atmospheric Phase Statistics
My project involved answering fundamental questions about phase-referencing
for the VLBA. The use of phase-referencing allows observations of sources
that are too weak to be self-calibrated. By observing nearby calibrator
source, the information from the calibrator can be used to calibrate
the target source. The two parameters of phase-referencing are the
distance between the calibrator and the source, and the length of time the
source can be observed before observation of the calibrator is needed.
This project aims to make conclusions about the switching time
needed for phase-referencing.
Tropospheric turbulence produces fluctuation in the phase of the
signal, and this fluctuation is what forces phase-referencing,
else the signal gets lost in the noise. The VLBA observes with ten
antennas, all looking through completely uncorrelated segments of
the troposphere. In order to make conclusions about switching
times, a measure of tropospheric phase fluctuations needs to be
made at each single antenna site. The Structure Function is used
to provide this measure where the Structure Function is the ensemble
average of the square of the difference of some phase at time t + dt and
some phase at time t. Therefore as dt gets larger and the
structure function will get larger, until at some point complete
sampling of the troposphere has occurred and the phase ceases to get
any worse with increasing dt.
We used 17 experiments, between June 1995 and April 1997, observed
in all seasons, at all elevations, at various separation angles, at
15 GHz, and with a switching time of three minutes. For all sources
in all experiments the baseline based Structure Functions (SF's)
were calculated. I produced the IDL code to separate the three minutes
segments and unwrap the phase, calculate the SF and correct for the
intrinsic thermal phase noise. With the help of Mark Holdaway, the
45 baseline based SF's could be decomposed into the ten single antenna
based SF's. Thus giving us a measure of the tropospheric phase fluctuations
for each antenna.
One of the conclusions that we were able to make was the limits of
switching times. In order to unambiguously phase-connect a source,
the rms phase at 15 GHz needs to be less than pi/3. So as an example
for source 1928+738 in April, limited by your worst antenna (which is
identified by the most dramatically increasing SF) in this case St.
Croix, pi/3 corresponds to a switching time on the order of 30 seconds.
Such information could be applied to other frequencies, since we
know the scaling for 45 GHz is 3 times worse than 15 GHz and the
switching time needs to be on the order of 6 seconds. More statistics
need to be gathered for more general statements concerning the
switching time. The second conclusion we can make is concerning the
seasonal variation of the SF. This information would provide important
insight into favorable observing time for the VLBA. It is important to
investigate the seasonal variations. Essentially the limit of
understanding at this time is that St. Croix seems to stand alone as
the worst antenna and all the others are basically the same in terms of
seasonal variation.
More work is planned in order to increase the SNR, by using geostationary
satellite. We need to gather more statistics on the phase-switching times
and understand both the potential of the decomposition technique and the
seasonal variations of the SF's.