m under a moderately
good atmospheric condition (2.2 mm of PWV). We also offer several
suggestions for the future MMA radiometer system
that should result in significant improvements.
M. S. Yun
National Radio Astronomy Observatory
M. C. Wiedner
Smithsonian Astronomical Observatory
February 18, 1999
We report the performance of the 183 GHz radiometer system for
the CSO-JCMT interferometer during the October 1998 run.
The phase correction using the radiometers produced the rms
phase fluctuations by a factor (a factor of five less in
signal loss due to decorrelation) and achieved a corrected rms path length
fluctuation of 60 m under a moderately
good atmospheric condition (2.2 mm of PWV). We also offer several
suggestions for the future MMA radiometer system
that should result in significant improvements.
Water vapor in the atmosphere affects the index of refraction
of the troposphere. The variation in the precipitable
water vapor (PWV) causes phase variations for a electromagnetic
wave propagating through it and results in ``phase noise".
An excellent review of the topic and the techniques of using
radiometers to reduce this phase fluctuations is given in
Wiedner (1998) and the MMA Memo 210 by Carilli, Lay, & Sutton (1998) and
references therein. The water line opacity at
the Chajnantor site is very low (median 
and
median PWV 
mm, see
http://www.tuc.nrao.edu/mma/sites/Chajnantor/data.c.html),
and it is likely that an array of radiometers
monitoring the 183 GHz water line is going to be used
for the tropospheric phase correction for the MMA. The
beam of the 183 GHz radiometer should also overlap the astronomical
beams more closely than a low frequency system. The only
currently operating 183 GHz phase correction radiometer system
is the one for the CSO-JCMT interferometer described
in the PhD thesis of M. Wiedner (1998, also available at
http://www.mma.nrao.edu/workinggroups/cal_imaging/183GHz.html).
M. Yun attended the first week of the 10 days long CSO-JCMT Interferometer run in October 1998 and participated in the setup and calibration of the radiometers. Here we report the performance of the 183 GHz radiometer system and compare its performance with the existing 22 GHz radiometer systems. We also discuss concerns and improvements desirable for the future MMA radiometer system.
The 183 GHz radiometers for the CSO-JCMT interferometer are double sideband heterodyne systems with uncooled Shottky mixers. The IF signal is mixed down to three frequencies of 1.2, 4.2, and 7.8 GHz away from the water line center at 183.31 GHz, and the three radiometer channels have individual bandwidths of 0.4, 1.0, and 1.0 GHz, respectively (see Figure 1). All the electronics are temperature regulated, and a phase lock loop is used to stabilize the LO frequency.
Figure 1: The three double-sideband frequency channels of the water
vapor radiometer are shown superposed on the spectrum of the 183.31
GHz water line for 0.5, 1, 2, and 4 mm of PWV.
The calibration of the radiometers is performed using two temperature
loads at 35
C (``warm") and 100C (``hot") and a flip
mirror that cycles through these calibration loads and the sky at
1 Hz frequency. The temperatures of the hot and warm load are
calibrated daily using liquid nitrogen. Knowing the
absolute temperature of each load is not critical since the
phase correction utilizes differential measurements. On the
other hand, the short term stability of the load temperature is
crucial as it directly limits the ability to track the radiometer
gain. The load temperatures are measured to be stable
to about 10 mK on time scales of minutes. The overall system
temperature of the each radiometer is about 2500 K.
Figure 2: The raw astronomical interferometer phase (green solid line),
the phase correction predicted from the radiometer measurement
(blue dashed line), and the corrected interferometer phase (red
solid line) are shown for each of the three radiometer channels.
After subtracting a linear phase drift due to the interferometer
baseline error, the rms phase fluctuations are computed as listed above.
Figure 3: Same as Figure 2 but for 05:30 - 06:00 UT on October 24, 1998.
Figure 4: The radiometric phase correction for the Channel 2 is shown
in detail. The lines shown are the same as in Figure 2. The radiometric
phase correction closely track the astronomical data, and the
significant improvement is obvious in the lower panel.
The 183 GHz radiometer data were recorded simultaneously with the astronomical interferometer observations whenever possible. The data discussed below were taken between 05:00 UT and 06:00 UT on October 24, 1998 under a good but not exceptional atmospheric condition. The PWV estimated from the atmospheric data was 2.2 mm, and the CSO 225 GHz opacity was 0.11. The astronomical phase data shown are those of the hydrogen recombination line maser at 353.6 GHz in MWC 349 measured by the CSO-JCMT interferometer.
The astronomical phase data and the corresponding 183 GHz radiometer phases for all three radiometer channels are compared in Figures 2 & 3. In each panel, green solid line is the raw interferometer phase, blue dashed line is the phase correction predicted from the radiometer measurements, and the red solid line is the corrected interferometer phase. The rms phase fluctuations are measured after subtracting a linear phase drift that is most likely due to interferometer baseline error. A detailed comparison of the pre- and post-correction results for the Channel 2 data is also shown in Figure 4. The predicted phase from the radiometer data track the astronomical phase extremely well, and the improvement in the corrected phase is obvious.
The radiometric phase correction has achieved more than a factor of
two reduction in the rms phase fluctuation. The raw rms phase
fluctuation in the astronomical data at 353.6 GHz is 60.1 degrees,
which corresponds to the raw path length fluctuation of 143 m.
The corrected phase using the radiometric data from the
Channels 1, 2, and 3 has reduced rms phase fluctuations of
38.4, 26.3, and 39.7 degrees, respectively. These reductions
correspond to path length fluctuations of
92, 61, and 95 m (
).
For the phase correction, we can use the most sensitive channel
or any combination of the channels. The best result achieved in Channel 2
is within a factor three of the target
value for the MMA (15 m per antenna). The relatively
poor performance of the Channel 1, which is located closest to the line
center, is due to the line saturation, which occurs with
mm of PWV. The radiometer sensitivity of the
Channel 2 is about 50% better than the Channel 3, which
covers only the outer line wings. We note that the reduced
phase noise from 
to 26
corresponds to nearly a factor five improvement in signal
loss due to decorrelation - i.e., the signal coherence improves
from 50% to 90%.
The radiometer measurement (
) to the phase correction
(
) conversion factor for this and other radiometer
systems is usually chosen ad hoc to minimize the
rms phase in the calibration data. As discussed in Wiedner (1998),
the conversion factor from to depends
primarily on the PWV with secondary dependences
on the vertical temperature and pressure profile in the atmosphere.
By modeling the water line emission using an atmospheric model
and ground meteorological measurements, the conversion factor can
also be computed explicitly. The theoretical
conversion factor based on the meteorological data is 20%
larger (4.8 K/turn) than the ``best" conversion factor that
minimizes the residual rms phase (3.9 K/turn), but the phase correction
using this theoretical conversion factor is only slightly worse,
27.9 degrees versus 26.3 degrees. This success of the
theoretically derived conversion factor suggests that the 183
GHz water line is reasonably well understood and modeled.
The results presented here are representative of the
radiometer performance under good (but not exceptional)
weather conditions.
The corrected rms phase was generally higher under
poorer weather conditions because of reduced radiometer
sensitivity (see Wiedner 1998). In an earlier run under
a somewhat worse condition, a corrected phase fluctuation of
38 degrees (90 m) was achieved (from uncorrected rms
phase of 127 degrees) with 3.5 mm of PWV - still a
significant improvement, from complete decorrelation to
only 20% loss in amplitude.
We now compare the performance of the 183 GHz radiometer with that of the 22 GHz water line monitor system operating at the Owens Valley Radio Observatory (OVRO). The OVRO 22 GHz radiometer system is also a 3 channel system with channel widths of 2 GHz each. The two outer channels are used to determine the continuum level for the middle channel, which covers the 2 GHz band centered on the 22 GHz water line itself. A detailed description of the OVRO 22 GHz system is found in Marvel & Woody (1998).
Despite the very low electronic noise,
the radiometric phase correction using the 22 GHz system is
still challenging because the 22 GHz water line is
significantly weaker than the 183 GHz line.
As summarized in Table 1, the system temperature of the 22 GHz
system is 10 times smaller than the 183 GHz system, but
the sensitivity, 
, is also at least
10 times lower. The best phase
correction achieved with the OVRO 22 GHz system is about
100 m in ``good" conditions (4 mm of PWV). In comparison,
the phase correction achieved with the 183 GHz system discussed
in the previous section range between 60 and 90 m with
2-4 mm of PWV. Both systems work significantly better
under more favorable conditions (smaller PWV), and the data taken
under similar conditions suggest that the 183 GHz system
may perform slightly better phase correction than the 22 GHz system.
At the Chajnantor site where the median PWV is only about 1 mm,
the weakness of the 22 GHz water line may pose a challenge for
the 22 GHz system. On the other hand, the sensitivity of the
183 GHz system should improve dramatically (by factors >2 for
PWV 
1 mm) under the excellent conditions expected
because the line center is no longer saturated
and the center channel provides the best overall sensitivity.
Further, the strength of the 183 GHz line also
makes the effects of ground pick-up or clouds less problematic
than the 22 GHz line systems.
| 183 GHz (SBI) | 22 GHz (OVRO) | |
 | 2500 K | 200 K |
 | 0.4-1.0 GHz | 2 GHz |
|
| 4-20 K/mm | 0.4 K/mm |
Corrected rms  | 60-90 m | 100-300 m |
There are several obvious improvements that will make the 183 GHz radiometer system significantly more sensitive. We suggest following improvements for the future 183 GHz radiometer system for the MMA:
Phase correction using the 183 GHz water line
radiometer data has reduced the rms phase fluctuations
in the astronomical data taken with the CSO-JCMT interferometer
by a factor of two or more.
The path length fluctuation was reduced to about
60 m in good weather conditions (2 mm PWV) and to
about 90 m under poor weather conditions (4 mm PWV).
The corresponding reduction in amplitude loss due to
decorrelation is even larger.
The radiometric measurement to path length delay conversion
factor derived theoretically using an atmospheric model and
meteorological data was highly effective, giving some
confidence that the 183 GHz water line is well understood
and modeled.
The performance of the 183 GHz radiometer system is comparable or better than the existing 22 GHz radiometer system and should offer a superior performance at the very dry Chajnantor site. Significantly better results are expected from future improvements such as cooled systems, widband spectrometer backends, and refined data reduction method.
