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Radio Science, Volume 33, Number 5, Pages 1297-1318, September-October 1998
Phase compensation experiments with the paired antennas method
2. Millimeter-wave fringe correction using
centimeter-wave reference
Yoshiharu Asaki, i Katsunori M. Shibata, 2'3 Ryohei Kawabe,
Masao Saito, 6 Ko-Ichiro Morita, 4 and Tetsuo Sasao 2
4 Duk-Gyoo Roh, 5
Abstract. An experiment for compensating interferometer phase fluctuations due to the
turbulent troposphere was conducted with the paired antennas method (PAM) using
different sky frequencies for a target and reference source. A celestial source 3C279 was
observed at 146.81 GHz with the Nobeyama millimeter array (NMA), while a
geostationary satellite was observed as a reference source at 19.45 GHz with commercially
available antennas. Each of the antennas was installed near one of the NMA antennas,
thus giving us 10 pairs of nearly parallel baselines up to 316 m. Large fluctuations in the
interferometer phase of 3C279 were mostly eliminated on almost all baselines by
subtracting the reference phase multiplied by a ratio of the observing frequencies. The
standard deviations of the compensated interferometer phase were under the level of 20 ø
where the angular separation between the two sources was within 2 ø , while those of the
original phase were typically at the level of 400-50 ø . The phase compensation was much
improved to the level of the differential excess path length of 0.06-mm rms (11 ø at 146.81
GHz) in inserting a time lag proportional to the separation angle to the reference phase
time series. These results have practical significance for the millimeter- or submillimeter-
wave interferometry because there is rarely a suitable reference source in the vicinity of
scientifically interesting sources at such high frequencies. The present experiment shows
that it is quite effective in the PAM to use the reference phase at centimeter-wave for
compensating the millimeter-wave phase for future large millimeter-wave arrays.
1. Introduction
Radio interferometry is one of the most powerful
tools for revealing detailed structures of celestial
objects at high resolution. Radio interferometry ar-
rays at centimeter or millimeter wavelengths have
brought to us remarkable images of molecular clouds,
supernova remnants, and galaxies, with a typical
resolution of several hundreds of milliseconds of arc
(mas). Very long baseline interferometry (VLBI) at
centimeter or shorter wavelengths with a baseline
• National Astronomical Observatory, Tokyo.
2 Mizusawa Astrogeodynamics Observatory, National Astro-
nomical Observatory, Iwate, Japan.
3 Now at National Astronomical Observatory, Tokyo.
4 Nobeyama Radio Observatory, National Astronomical Obser-
vatory, Nagano, Japan.
s Taeduk Radio Astronomy Observatory, Korea Astronomy
Observatory, Taejon, Korea.
6 Harvard-Smithsonian Center for Astrophysics, Cambridge,
Massachusetts.
Copyright 1998 by the American Geophysical Union.
Paper number 98RS01607.
0048-6604/98/98RS-01607511.00
longer than 1000 km has reached the resolution of a
few milliseconds of arc or higher and has shown
superluminal jets in active galactic nuclei, great
crowds of astronomical maser spots in star-forming
regions, and as well as in circumstellar shells around
late type stars. On the other hand, VLBI measure-
ments of the positions of strong celestial radio sources
have yielded an accuracy much higher than 1 mas, and
an aggregate of VLBI measurements has enabled the
detection of minute changes in Earth's orientation in
space and motions of the tectonic plates to be mea-
sured [Dickey, 1993; Stein, 1993]. Several new inter-
ferometry systems have been proposed; for example,
the large millimeter and submillimeter array (LMSA)
[Ishiguro et al., 1994]; the millimeter array (MMA)
[Brown, 1994]; and the VLBI exploration of radio
astrometry (VERA) [Sasao and Morimoto, 1991]. In
order to achieve the desired 100-mas or higher spatial
resolution at submillimeter wavelengths with con-
nected arrays or the positional accuracy of the order
of 10 tx arc sec with VLBI, we have to calibrate the
interferometer phase at an rms level smaller than 0.1
mm in the differential electrical path length.
1297
1298 ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2
Fluctuations in the fringe phase (i.e., the phase in
the correlated signals of an interferometer) cause
blurring of synthesized images and staggering of
source positions in radio interferometry. Also, the
fluctuations make the sensitivity of the interferometry
system lower due to serious coherence loss. The
fluctuations occur both in the instrumentation and
propagation media. Instrumental phase fluctuations
can be made sufficiently small in present interferom-
etry systems and are easily corrected by observing
calibrator sources with well-known positions.
The finite refractivity of the Earth's atmosphere
causes an excess path for the incident radio wave. The
total excess path length is obtained by means of
integrating the refractivity from the ground to the
upper atmosphere along the line of sight. The refrac-
tivity consists of contributions from the water vapor
component and the other components (dry air). The
contribution of dry air can be easily estimated be-
cause it is homogeneously distributed and well corre-
lated with ground-based meteorological parameters.
The most serious fluctuation in the fringe phase is
caused by the water vapor in the troposphere, which
is neither well mixed nor homogeneously distributed.
The water vapor distribution is not as correlated with
the ground-based meteorological parameters, and so
the fringe phase fluctuations due to the water vapor
are highly unpredictable. The fluctuations in the
fringe phase due to the water vapor have character-
istic timescales ranging from a few seconds to a few
days and an amplitude often greater than a few
centimeters in the peak-to-peak excess path length.
Therefore it is necessary to develop a suitable way to
compensate the phase fluctuations due to the water
vapor components in the troposphere for future radio
interferometers.
Several techniques have been proposed for effec-
tive correction of the tropospheric phase fluctuations:
an antenna-switching differential VLBI method [e.g.,
Lestrade et al., 1990; Lara et al., 1996]; a radiometric
phase correction method [Welch, 1994; Bremer et al.,
1996; Linfield et al., 1996]; a fast switching method in
which target and reference sources are separately
observed with fast slewing antennas [Holdaway, 1992;
Holdaway and Owen, 1995]; and a paired antennas
method in which target and reference sources are
simultaneously observed with a clustered antenna
system [Counselman et al., 1974; Asaki et al., 1996].
The phase compensation techniques which make use
of the reference calibrators are classified as phase-
referencing. The candidates of the reference sources
in the phase-referencing are extragalactic radio
sources (mostly quasars).
The paired antennas method (PAM), along with
the radiometric correction method, has the advantage
of using a time-synchronized reference phase. This
makes it possible to conduct a continuous temporal
integration. The simultaneous observations will also
show superior performance in subtracting the refer-
ence fringe phase, while the interleaved observations
need the phase-connection procedure to appropri-
ately interpolate the reference fringe phase. On the
other hand, the paired antennas method would imply
either a higher cost or less spatial Fourier compo-
nents compared with the fast antenna switching
method or the radiometric phase correction method.
Bremer et al. [1996] showed that the radiometric
correction method achieved the phase correction to
the level of 0.09 mm rms in excess path length over
1-min integration at 230 GHz under clear-sky condi-
tions. The radiometric correction method should
work out some difficult techniques in developing
highly stable receivers to measure the minute spatial
and temporal variations in the radiation from the
water vapor and in obtaining the precise conversion
factor from the brightness temperature to the excess
path length.
It has been successfully demonstrated by Asaki et
al. [1996] on the basis of experiments at a centimeter
wavelength using a radio array with a 500-m baseline
that the paired antennas method is a promising
technique if we can find an adjacent reference source
very close to a target source with closely located
paired antennas. On the other hand, the phase-
referencing may have difficulty when applied to the
observations at wavelengths shorter than a few milli-
meters because the number of suitable quasars de-
creases with increasing frequency. If we cannot find a
suitable reference source within a few degrees from
the source of interest, the effectiveness of the phase-
referencing will be diminished [Asaki et al., 1996].
A possible solution to this problem is to observe
reference sources at centimeter wavelength, where
many bright compact quasars are available. Since the
refractivity of water vapor is thought to be almost
constant (nondispersive) from decameter to millime-
ter wavelengths [Thompson et al., 1986], it is possible
to calibrate the higher-frequency fringe phase by
using the lower-frequency reference phase. Kasuga et
al. [1990] showed by quasi-simultaneous dual-fre-
quency measurements of the atmospheric radio see-
ing that the fringe phase fluctuations had an almost
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1299
linear relationship with the observing frequency be- source
tween 7.0- and 3.4-mm wavelength. This result is very /source B
encouraging and led us to examine whether the
effective phase correction can be experimentally per-
formed between different sky frequencies.
In this paper we describe a millimeter-wave phase
compensation experiment with the paired antennas
method (hereinafter referred to as PAM) conducted
at the Nobeyama radio observatory (NRO) using '•'""••' "'" ""•
millimeter-wave and centimeter-wave arrays with ':'•"•iii•,•'Phase Screen
multiple baselines ranging from 61 to 316 m. We used
six antennas of the Nobeyama millimeter array I h
(NMA) and five antennas of the Nobeyama radio 3 1 -'-'------_.•
seeing monitor (NRSM), each of which was installed
near an NMA antenna. Using the combined array of
five paired antennas, we simultaneously observed the
strong quasar 3C279 at 146.81 GHz with the NMA
and a geostationary Japanese communication satellite
at 19.45 GHz with the NRSM. Since the celestial
source 3C279 passed very close to the geostationary
satellite, the experiment was well suited to estimate
the angular separation dependence of the effective-
ness of the PAM [Asaki et al., 1996].
2. Fringe Phase Difference in Paired
Antennas Method Observations
Let us consider fringe phases (I) A and •B obtained
at two nearly parallel baselines; one connecting an-
tennas 1 and 2, which are observing source A, and
another connecting antennas 3 and 4, which are
observing source B, as illustrated in Figure 1. Anten-
nas 1 and 3 and antennas 2 and 4 are assumed to be
located close to each other. The basic configuration of
the PAM is the same as that described by Asaki et al.
[1996]. The only difference is in the use of different
observing frequencies at the nearly parallel baselines.
After eliminating the sum of the effects of the instru-
mental phases and subtracting the a priori geometric
delays, the obtained fringe phases can be described as
follows [Asaki et al., 1996]:
(I) A = 27rl•A(A1-g A q- 1'air{12}) (1)
(I)B = 2rr•'B(A•'gB + 1'air{34}),
(2)
where VA and • are the sky frequencies at the band
center, A rg is the residual geometric delay including
the source structure effect, and 'rair{nm } is the ran-
domly varying difference in the tropospheric excess
path delay between antennas n and m.
Now the fringe phase of source B at the frequency
Figure 1. Configuration of the paired antennas method
(PAM) experiment.
•,B must be converted to the phase at the frequency
1., A by means of a suitable scaling factor because the
direct comparison between •A and • is impossible.
If we assume that the refractivity of the water vapor is
nondispersive, the scaling factor is simply equal to the
frequency ratio •'A/•'•, and we obtain the "frequency-
converted" fringe phase of source B as follows:
VA
(I)• = (I) B X- = 27rl•A(A1-g B q- 1'air{34}). (3)
1,, B
The difference in the fringe phase A• = •A -- • is
then expressed by
A(I) = 27rl•A{(A1-g A -- AI-gB) + (l-air{12 } -- 1'air{34}) }. (4)
In view of the nondispersiveness of the water vapor
refractivity, the excess path delays %ir{12} and •'air{34}
must be constant over the frequency range between
•'A and •,•. Therefore if we simultaneously observe a
very close pair of sources with closely located anten-
nas, the tropospheric phase fluctuations included in
•^ and • should simply disappear in the fringe
phase difference
A(I)' --• 2•rl•A(A1-g A -- AI-gB) , (5)
which can be used as an observable. This is the basic
idea of the phase compensation with the PAM in the
case of different observing frequencies used for a
target and reference source. The purpose of the
present experiment was to clarify how effectively such
a compensation scheme works in the conditions of the
real atmosphere.
1300 ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2
N
A
Nobeyama Millimeter Array
Configuration of Antenna Stations
c
•s• i i i
166m -I a
sourceA
(3C7_79)
source B
(Japanese Communication Satellite)
/
/
/
/
/
/
/
/
Radio Seeing Mtonitor
(19.45GHz)
NMA 10m Antenna
(146.81GHz)
Figure 2. Locations of the Nobeyama millimeter array
(NMA) and the Nobeyama radio seeing monitor (NRSM)
in the phase compensation experiment. (a) The open circles
represent the stations of the NMA, and the five solid circles
represent the stations of, the NRSM. (b) A concept of the
present PAM experiment.
3. Measurements
The PAM experiment was conducted for about 3.5
hours on each of January 28 and 29, 1995. The basic
configuration of the experiment is illustrated in Fig-
ure 2. In the experiment we observed the bright
quasar 3C279 as a target source and a Japanese
communication satellite (hereinafter referred to as
CS) as a reference source. The source positions are
listed in Table 1, and the observing times are listed in
Table 2.
The NMA is composed of six parabolic reflectors
with 10-m diameter and is used for imaging celestial
radio sources at millimeter wavelengths [Morita,
1994]. In this experiment the NMA observed the
quasar 3C279 at 146.81 GHz. The frequency-con-
verted and digitized intermediate frequency signals of
the NMA were cross correlated by the fast Fourier
transform spectrocorrelator [Chikada et al., 1987],
with a bandwidth of 320 MHz and 1024 frequency
channels per baseline. We used the central 824 chan-
nels to avoid the band-edge effect. The complex
cross-correlation data were accumulated for 10 s by
the correlator and stored in the NMA database. The
baseline lengths in the experiment ranged from 61 to
316 rn and are listed in Table 2.
The NRSM, which is usually used for monitoring
the radio seeing at Nobeyama, consists of five com-
mercially available offset-Gregorian reflectors with
1.8-m effective diameter [Ishiguro et al., 1990]. The
NRSM antennas are oriented toward the fixed direc-
tion in the sky where the geostationary satellite
resides. The satellite emits a strong carrier signal at
19.45 GHz. The received 19.45-GHz signals at each
NRSM antenna are amplified and downconverted to
278 MHz. The converted signals are passed through
the NMA's highly stable coaxial cables via an under-
ground tunnel to the NMA array operation building.
The five NRSM antennas were installed in the
experiment within several meters of each of the five
NMA antennas. We were not able to install an NRSM
antenna by the sixth NMA antenna (letter F in Figure
2a). Each second, the phase differences between the
signals from NRSM antennas A, B, C, and D and that
from the reference antenna (letter E in Figure 2a)
were measured using four vector voltmeters (HP
8508A). The resultant data were recorded in a per-
sonal computer controlling the vector voltmeters to-
gether with the amplitude data of all the signals.
The serious atmospheric phase fluctuations are
caused mainly in the lower atmosphere up to a height
of a few kilometers [Masson, 1994]. Since the beam of
a radio telescope in, the lower atmosphere can be
Table 1. Source Positions
Right
Ascension Declination
Source (J2000) (J2000) Azimuth Elevation
3C279 1256:11.2 -5ø47'22 ........
Communication ...... 184.16 ø 48.27 ø
satellite
J2000 means Julian calendar 2000.
The Japanese communication satellite is almost stationary, and
3C279 passes very close to the satellite's position.
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1301
Table 2. Observing Time, Baseline Lengths of the Nobeyama Millimeter Array in the Present Experiment, and the
rms Phases of the 3C279, the Japanese Communication Satellite, and the Differential Fringe Phases for the Time
Interval of 1000 s Centered on the Time When the Separation Angle was Minimum
Baseline January 28, 1995, 0215-0550 LT, deg January 29, 1995, 0125-0550, deg
Baseline Length,
Identification rn o'3 c279 O'cs o'3 c279 - cs o'3 c279 O'cs o'3 c2'/• - •b
1 (A-B) 102.0 29.6 29.7 18.1 21.9 22.4 12.5
2 (A-C) 254.3 52.6 49.9 18.4 36.6 39.1 16.9
3 (A-D) 255.0 53.2 52.8 27.1 37.8 40.4 19.8
4 (A-E) 316.2 54.7 49.2 34.6 42.1 36.7 28.6
5 (A-F) 250.5 48.1 ...... 34.2 ......
6 (B-C) 211.2 39.1 37.4 18.0 38.0 38.8 16.4
7 (B-D) 153.0 35.5 39.2 19.2 29.0 31.2 16.7
8 (B-E) 214.2 40.6 33.7 27.9 34.0 29.3 25.2
9 (B-F) 154.6 32.6 ...... 28.5 ......
10 (C-D) 231.2 41.8 41.4 22.3 36.5 39.3 18.7
11 (C-E) 264.8 41.0 31.0 33.9 38.9 32.5 29.0
12 (C-F) 166.7 31.8 ...... 31.5 ......
13 (D-E) 61.2 19.9 21.8 24.8 18.6 23.1 29.0
14 (D-F) 68.1 21.8 ...... 18.7 ......
15 (E-F) 100.2 21.2 ...... 23.3 ......
The power law fittings of the 3C279 values are shown in Figure 3a.
regarded as a cylinder with a diameter equal to the
telescope's aperture, the measured atmospheric fluc-
tuations are spatially averaged over the aperture. The
NRSM antennas are more sensitive to the spatial
pattern of the water vapor distribution than the NMA
antennas because the aperture of the NRSM anten-
nas is smaller than that of the NMA antennas. In the
following analyses, both the fringe phases were ob-
tained by means of a 10-s accumulation. If the wind
velocity aloft is 10 m s -1 the procedure of 10-s
accumulation averages the spatial pattern with the
scale of 100 m. This spatial scale is larger than both
the apertures of the NMA and NRSM antennas. This
procedure allows us to ignore the difference of the
aperture size, although it may cause a coherence loss
during the accumulation period due to the atmo-
spheric phase fluctuations. The validity of this as-
sumption of the wind aloft will be evident in the later
discussion.
The CS is located at 184.2 ø in azimuth and 48.3 ø in
elevation at Nobeyama. The quasar 3C279 passes the
CS position with a minimum separation angle of less
than 0.1 ø. The time variation of the separation angle
between 3C279 and CS was basically the same as
Figure 3 of Asaki et al. [1996]. The time when the
separation angle reached its minimum was about 0430
LT. This time is used as "zero-separation time" in this
paper.
The contribution of thermal noise to the 10-s
accumulated fringe phase of 3C279 could not be
appropriately estimated because the precise parame-
ters of the system noise temperature and the corre-
lated source flux density were not available. In the
season of the experiment the system noise tempera-
ture of each of the NMA antennas was 300-500 K.
For example, adopting the system noise temperature
of 400 K and a typical value of the flux density of 6 x
10 -26 W m -2 Hz -1 for 3C279 obtained from a single
antenna observations at 150 GHz [Stevens et al.,
1994], the estimated thermal noise is 6.4 ø where the
aperture efficiency is 0.3 at 146 GHz, and an effi-
ciency factor for quantized correlation processing
with the spectrocorrelator is nearly equal to 1. Al-
though this value can only be roughly estimated, an
averaged closure phase error of 3C279 is well consis-
tent with the above value. Hereinafter we assume that
the contribution of the thermal noise to the fringe
phase of 3C279 is 6.4 ø.
The CS signal is so strong that the thermal noise in
the 10-s accumulated CS fringe phase must be much
smaller than the atmospheric effect. Therefore we do
not attempt to estimate the thermal noise in the CS
fringe phase, regarding it as negligible. However, the
contribution of the instrumental phase fluctuation
might exist and be different among the baselines:
Different performance in the antennas might happen
due to the very cold weather at the time of the
experiment because the receiver systems were not
thermostabilized. In the following analyses the anom-
alous phase fluctuations of certain baselines are seen.
1302 ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2
4. Data Analysis
4.1. Preprocessing
The major steps to produce the fringe phase dif-
ference from the millimeter- and centimeter-wave
fringe phases are the following:
1. The 27r jumps in the CS fringe phase at 19.45
GHz were corrected first. This procedure was carried
out almost automatically because the fringe phase
varied very smoothly with time. The CS fringe phases
measured at 19.45 GHz were then effectively con-
verted to those at 146.81 GHz by multiplying by the
nondispersive scaling factor (146.81/19.45). The ob-
tained CS fringe phase showed slow drifts due mainly
to the slight motion of the satellite. Therefore we
used high-pass filtering in which slow drift compo-
nents, calculated by a running mean process for the
time interval of 500 s, were removed.
2. The CS fringe phases were measured for the
four baselines involving the reference NRSM antenna
(letter E in Figure 2a) only because of the limited
number of the available vector voltmeters. The CS
fringe phases of the other baselines were calculated
using the measured fringe phase in the "closure
relation" [Rogers et al., 1974].
3. Since the CS fringe phase data were stored in
the accumulation time of 1 s, the time series of the CS
fringe phase were low-pass filtered by a running mean
process for the time interval of 10 s.
4. Spurious 27r changes in the fringe phase of
3C279 had to be removed. This procedure was carried
out graphically, and the results were confirmed by
visual inspection referring to the corrected CS fringe
phase. This procedure was repeated until we made
sure by the "closure ,test" [Marcaide and Shapiro,
1983] that 27r spurious phase changes were com-
pletely removed.
5. We also applied the high-pass filtering with a
time interval of 500 s to the fringe phase of 3C279 to
suppress the effects of baseline errors, source position
errors, instrumental phase drifts, and source struc-
ture.
6. Fringe phase differences were obtained by
subtracting the CS fringe phase converted to 146.81
GHz from the fringe phase of 3C279 of the corre-
sponding parallel baseline.
4.2. Estimation of the Spatial Structure Function
at the Observatory
The structure function [Tatarskii, 1961] is one of
several useful tools for estimating the universal char-
acteristics of the tropospheric fluctuations. The spa-
tial structure function (SSF) D(p) is defined as the
mean square difference in the phase fluctuations at
two sites separated by a displacement vector p'
D(O) = 4yr2v2({•'air(r + p) - •'air(r)} 2), (6)
where angle brackets mean an ensemble average, q'air
is the excess path delay due to the water vapor, v is
the observing radio frequency, and r is a position
vector. According to the Kolmogorov theory of iso-
tropic turbulence, the excess path SSF is well approx-
imated by a simple power law:
= (7)
where C l is the structure coefficient, a is the structure
exponent, and ,X is wavelength. Kolmogorov theory
predicts that the exponent a tends toward 5/3 when p
is smaller than the scale height h, whereas it tends
toward 2/3 when p is much larger than h [Dravskikh
and Finkelstein, 1979; Treuhaft and Lanyi, 1987].
Measurements of the SSF with a spatial size compa-
rable to or less than a scale height of the water vapor
indicate that the exponent distributes between 2/3
and 5/3 [e.g., Sramek, 1990].
We estimated the time variation of the structure
coefficient and exponent by means of the power law
fittings of the rms fringe phase of 3C279 estimated for
the time interval of 1000 s. The thermal noise contri-
bution 6.4 ø was eliminated from the rms phase of
3C279. The calculated rms phases of CS and 3C279
centered on the zero-separation time are listed in
Table 2. The results of the power law fittings at the
zero-separation time are shown in Figure 3a.
The SSF obtained from the CS data is in general
agreement with that from the data of 3C279 through
the experiment if we neglect the thirteenth baseline
(D-E, 61 m), which shows slightly larger phase fluc-
tuations. It indicates ,that there might be something
wrong in the instrument of the NRSM due to the very
cold weather and the temporary configuration during
this experiment. Since five more baselines of the
NMA (15 baselines total) are available in the power
law fittings, we adopt the SSF obtained from the data
of 3C279 for further discussion.
The obtained time variations of the SSF exponent
are shown in Figure 3b. They range from 1.2-1.9 to
1.0-1.7 for January 28 and 29, respectively. These
values are roughly consistent with the theoretical
prediction from the Kolmogorov law (5/3 = 1.667) for
the spatial scale smaller than the scale height of the
ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2 1303
water vapor in the troposphere. The averaged excess
path length for the 100-m baseline estimated from the
SSF is 0.172 mm and 0.148 mm for January 28 and 29,
respectively. These values are very good ones and
slightly higher than the median value of the measured
rms excess path length of site candidates for the
LMSA or the MMA [e.g., Masson, 1994; M. Saito,
private communication, 1997]. Then, from the aver-
aged rms excess path length for the 100-m baseline,
the mean structure coefficients are calculated as C l =
0.798 x 10 -5 cm 1/6 and C l = 0.687 x 10 -5 cm 1/6
for January 28 and 29, respectively, where the spatial
frequency spectrum of the tropospheric fluctuations is
assumed to have the Kolmogorov power law (a =
1.667). The structure coefficient values are much
smaller than those obtained in the previous PAM
experiments [Asaki et al., 1996] held in October 1994
at Nobeyama, since the present experiment was car-
ried out in the extremely good (dry) weather condi-
tions in the wintertime.
4.3. Standard Deviations of the Differential
Fringe Phase
The obtained time series of the fringe phase differ-
ence are shown in Figure 4 for the second baseline
(A-C, 256 m) with the original fringe phases and in
Figure 5 for the other baselines. Although we ana-
lyzed all the data obtained in the experiment, we show
here the fringe phase difference for the range of
separation angle from -20 ø to +20 ø for January 28
and from -30 ø to + 10 ø for January 29, because the
correlation between the fringe phases of 3C279 and
CS was barely seen beyond the above ranges. A
significant decrease of the fluctuations in the fringe
phase difference is evident when the separation angle
approaches the minimum value. The calculated stan-
dard deviations of the fringe phase difference cen-
tered on the zero-separation time are estimated for
the time interval of 1000 s and are listed in Table 2
with that of the fringe phase of 3C279 and the CS.
The angular separation was within 2 ø in the 1000-s
interval centered on the zero-separation time. For the
baselines longer than 200 m the standard deviations
reach the level of 20 ø , while the standard deviations of
3C279 are at the level of 400-50 ø. These results show
the effectiveness of the PAM even in the case where
the reference fringe phase at centimeter-wave fringe
phase is used for the compensation of the millimeter-
wave fringe phase.
The time variations of the standard deviations of
the fringe phase difference estimated for the time
i , .i- i i i.
', o ...-
....... 1995/1/29 •c•.O'"
.0 0
ß
i- [ i i i i i i i i
100 1000
baseline length [m]
1995/1/28
...... 1995/1/29
I
1 4 6
time (JST) [hour]
Figure 3. Estimation of the spatial structure function
(SSF) in the phase compensation experiment. (a) The
power law fittings of the rms phases estimated from the
3C279 fringe phase time series for the time interval of
1000 s centered on the time when the separation angle was
minimum. (b) The time variation of the structure exponent
of the SSF.
interval of 1000 s are shown in Figures 6 and 7 with
solid circles. Again, it is evident from the results for
all the baselines except for the thirteenth baseline
that the standard deviation is small when the separa-
tion angle is near the minimum and increases as the
separation angle increases up to a certain critical
value. The critical separation angle depends on the
baseline length and the scale height of the atmo-
spheric turbulent layer, as discussed by Asaki et al.
[1996]. Specifically, the longer the baseline length is
and/or the lower the phase screen is, the larger the
critical separation angle is.
5. Discussion
It is worth noting that the phase compensation in
the PAM experiment at Nobeyama reached the rms
1304 ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2
1995/1/28 baseline ID' 2(A-C)
4 5
time (JST)[hour]
995/1/29 baseline ID' 2(A-C)
, , , , , I • , , , , I
4 5
(ST)[nou]
Figure 4. Fringe-phase time series for baseline 2 (A-C). Each set includes four time series and shows
the fringe phase of 3C279, the Japanese communication satellite, their simple phase difference, and the
difference considering the time-lag-inserted phase correction (see section 5.4). The abscissa is JST
(Japan standard time) in hours, and the ordinate is fringe phase in degrees at the frequency of 146.81
GHz. One data point corresponds to a 10-s accumulated value.
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1305
1995/1/•8 baseUne ID: I(A-B)
separation angle Idesreel
•0 . . .-•0 • . , O, • • • 1Q • : . 2i
• ...... ß i ,' ß ,. , i ,' , ß ,.
.•: : .1 • • i ß • .....
.: ;' : '.,, i,
........
........
,• , .... i ........ • ,, ß ....
4time (.IS'T) [hour]
1995/I/•8 baseline [D:
4ti.me (JST) [hour] $
1995/1/28 baseline ID: 10{C-D)
[hour]
1995/1/28 baseline ID: 3(A-D)
o o
4Ume (Js'r) (hour) •
1996/1/28 baseline ID: ?(B-D)
4Ume (JST) [hour] 5
1995/1/28 baseline ID: 11(C-E)
i?,0 , , ,-10 s , , 0, , , 1Q
, ,, . .. ! ...............
1995/1/26 baseline ID:
4t•e {•s'r) [hour) 5
1995/1/28 baseline ID: 8(B-E)
4ttme Us'r) [hour] 5
1995/1/28 b&sell•e ID: 13(D-E)
•.•.•.-•, .... •.-.,,.r-•l•,.,,[i, I.-
i
'W.m,e (JST) [ho,.u-) 5
Figure 5. Fringe phase time series in the phase compensation experiment.
1306 ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2
1995/1/29 b,,seUne IJ): 1(A-B) 1995/1/29 bmaeUne ID: 3(A-D) 1996/i/29 bueltne ID: 4(k-•.)
o o
T T T
.
4-00. . . -,•0. . . -.t0. , , ,0 , , , •t•
.... , ,. , I ........ I, ß '- . I ........
3 time (lb"T) [hdlar] 5 3 t. lme (IST) [ha•'] 5 3 ttme (JST) [laa•ar] 5
1995/1/2g be, sellne il): 8(B-C) 1995/1/29 baseline ID: 7(B-D) 1995/1/29 baseline IJ): 8(B-E)
3 t. Lme (lb'T) (hdlar] 6
1995/1/29 baJeltne ll): 10(C-D)
(,rs'r) [ho•r] S
baseline ID: It(C-E)
3 Ume (JST) [ha•ar] S
1995/1/29 baseline ID: 13(D-E)
', : : : ' ' I , , , • , t
;o .... :.,•o. , : .o. , , •]
'.i ,• ........ i. i ,, , ,,
3 tLme (JST) (hcAa, r] S
Figure 5. (continued)
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1307
1995/1/28 baseline ID: 2(A-C)
o-30 -20 - 10 0 10 20
ß m
•....... ..... .•:: .............................. o...o.: .... .o
....... o ........ • -e ....... • .........................
c• o ß 'e ee
o ß •t e ,
øoe. ß o .e . , ' ee
o
......... o; ....... , ...... . .... ;oo • ..........
0 _ ooo ß e•e e ß
CO ,
o 0% o 0
......................... %•-..,.. - - - •oOO ...............
, Ooo•oofO
time (JST) [hour]
0 I I I , • , , 0
3 4 5
1995/1/29 baseline ID: 2(A-C)
-30 -20 - 10 0 10 20
' ;;•a:r r;;i .............................
[, ' * ' ' ' . o '• eee ß
time (JST)[hour]
3 4 •
o TM
ß
Figure 6. The standard deviations of the fringe phase difference calculated for the time interval of
1000 s for baseline 2 (A-C). Note that the right ordinate is the excess path length, in millimeters. Solid
circles represent the results of the simple phase difference, and open circles represent the results of
time-lag-inserted phase correction (see section 5.4). The gradual increase of the standard deviations
with the growing separation angle is evident. The solid and dashed lines show the result of a simulation
based on a statistical model, which is described in section 5.2.
level of 0.1 mm or smaller in terms of the excess path
length. This value is almost at the level required for
observations at a frequency of around 500 GHz.
Therefore the present experiment shows that the
future large-millimeter or submillimeter arrays are
indeed feasible, at least when one uses the PAM or
another method with equivalent performance for the
compensation of the atmospheric phase fluctuations.
In this section we discuss the baseline dependence of
the phase compensation, the relation between the
critical separation angle and the height of the as-
sumed phase screen, the scaling factor multiplied by
the reference fringe phase, and reference source
counts in the PAM.
5.1. Critical Baseline Length for the Paired
Antennas Method
The standard deviations of the fringe phase differ-
ence for the time interval of 1000 s centered on the
zero-separation time are plotted in Figure 8, com-
pared with the SSF shown in Figure 3a. We note that
all the standard deviations except for that of the
thirteenth baseline are smaller than the SSF and that
they are separated into two groups: those that are
smaller than the 20 ø level and those that are larger.
The latter group consists mainly of the data whose
baseline involves the E antenna (baseline ID of 4, 8,
11, and 13 in Figure 8), probably because the CS
fringe phases of those baselines were contaminated
1308 ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2
1995/1/28 baseline ID' I(A-B) 1995/1/28 baseline ID: 3(A-D) 1995/1/28 baseline ID: 4(A-E)
oF30 -20 -10 0 10 20 if30 -20 -10 0 10 20 30 -20 -10 0 10 20
separ•ti0n 0ngle [degree] : : ; ø•2' '.. i i ', i i ', ', ' ø' ........ ' " '
i i i ', ] ', ', ', ', : ', • ........... ß , ' ' ' ' , .... ß ß ' '
........... o ' o. . ,. .... .', .o ß . . : ; ', '. i. ';, . '.o
,•,OL ........ • .i - e, , , ß o
•l: : : ,, : : : : ;,..:•:1.o• •, •, ,.,.,, ,•,.j , , .,/:, ,., :.,., , .
,...._ : . . .,.. •., . .,.., , q,o , , O
' ',' ' : ' ',' ',' ' ', - ',' ' . .....
......... n' "' •"•' : ' "':•
, ß , , , , • , , ,' o ø , , :' : ': : :co
:•': ',- ;. : : : : , :. : •' ! : ,,-%/o..,•v I ,, ,:4,,!_;, , ,I
, , , ., ..... .• , • , , , i ....
..,7:;;0': ' I :": .... ,,o
•, , ,•, ? :•/:o: : : i "•"i•:.h.'"•'":/'7"i ...... I •
' .
o' ..... ' ........ ' ........ ' ....... 'o o'-' "-' ':' ':' ,:, ': ..... :' ':' ':' ':'o :' ':' ':' ':' ".' ". ..... :, ':. ,:, ,',lo
3 4 5 3 4 5 3 4 5
1995/1/28 baseline ID: 6(B-C) 1995/1/28 baseline ID: 7(B-D) 1995/1/28 baseline ID: 8(B-E)
cy30 -20 -10 0 10 20 off30 -20 -10 0 10 20 cy30 -20 -10 0 10 20
o•, ß ....... .•, , ,i ø o•t ........................... •...i. ø o• ........................ ..-. .... I.ø
;-:.• : : : : :o ..:..i..:_.:..i..:..i.;:'.:.'.io ,'.-,. ........ :o
•' ':' :-" •i' '"' "' '"':' I'*' :1 • .......... x , ':'' :" ::' ':'' ',' ':'"' '.
: :• :•"" : : :'"' : :l • i i-i,,i i i •
'•,"o ø ß '' : . ' ....
oo. i ' • ., ...... .. , •o ,
•: o::: ; , . :70 -:--,--,--.:--,-- -:•
,,., 0:, ,. ..... i i;: i i'".'! :!"::i !1
::" ":':"':: :1 . ....,..,,......o
:::: :,,,-: : :o •..!--;..!--',:•:;..i..!..,:l• ....... _-
I',' '•ime•JST)EBo•]' ' '1 f : :UeiJS)ior]: : :r ,: i ! :1
I:' ':' ':' ':' ':' ': ..... '-' "-' ':' ':'o o I" '" •" '" ' ' •': ':/':' ':' •:' ':' '"o
• • • o,., ; • ; ,o • • •..
1995/1/28 baseline [D: 10(C-D) 1995/1/28 baseline ID: 11(C-E) 1995/1/28 baseline ID: 13(D-E)
cy30 -20 -10 0 10 20 cy30 -20 -10 0 10 20 off30 -20 -10 0 10 20
O•.T..• .... <. ................. : . ß
o • ,.. , .. , , , ' ., , .., ',. , , , : , ,
':.••::":A'"'"":'-•,/'!":"iIK •-,"¾",''"',""":,,":"%'•,• --,--•--,--.--,--,--•--,--,-- :
'::•o: : ! ? • •' : :':: ", : ," :•:ø:
........ , ..... . ,.., ..... •, ,o :....'" '_.:...:,..:..•..•.: .
. o . ß .. .... . ....... :•.. * . .•
" ' 'o ß',, : ', 0,' : :o :' :",' : ',, ' ....... "f' '
o l'_•:-- :--:-.:.-•--:..', .'•,.;•- .•
':'": ":":• oI:":'-':":%',"1:"/;/:i":":":1• o•.., ,•. .... .,,•,,,,', •
I', : :t• kJs•> i•o•]: : :1 I'/. :u em,, •JST)[ho,•rl: :
o I:' ':' ':' ':' ".' ': ..... :' ':' "-' ':'o o I" '" '' ' "' ':' '-': ' .... [:' ':' ' o
3 4 5 3 4 5 3 4 5
Figure 7. The standard deviations of the fringe phase difference calculated for the time interval of
1000 s in the phase compensation experiment.
ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2 1309
1995/1/29 baseline ID: i(A-B) 1995/1/29 baseline ID: 3(A-D) 1995/1/29 baseline ID' 4(A-E)
cy30 -20 -10 0 10 20 •30 -20 -10 0 10 20 cr30 -20 -10 0 10 20
•[i:•;•r;•_;•';•/•;'i•_;• ;•'•"•1 • • :;'::'. , : •
: : :•g ':-':--:'-:-':--; .:-•j-:-.:..
'.:::
, , , •.-'•• ]
i •. s o[l, r..:, :..:..:. ,: ..... :. ,:..:. o
3 4 5 3 4 5 3 4 5
1995/1/29 baseline ID: 0(B-C)
cy30 -20 -10 0 10 20
.• ,,.._o:...,,. • ,,: ¾,..,.. ,:. _:_.,,_. o
o:•. .,.. : : : : •
.e...,• .,.. ,.•.. .... ,e..,. _,.. O
' ' •) 'o •' ß •'• ' '
o ............. '•1 '" :;':'"," •
time ,(JST) [ho,ar]
, ,. , I. , •. ! •. • I ..... ,. • I. • 1. • •
3 4 5
1995/1/29 baseline ID' 7(B-D)
Cy30 -20 -10 0 10 200
;- .... •., . :'T.--. , . .T .... -.,-. . ,. ." ß .
-:'•---.,?••--:-- •:-:-- :-!1 •
: :u•. iJs/') iho•d: : :,1
' ':' ':' ':' ':' ': ..... :' ':' ':'
3 4 5
1995/1/29 baseline ID: 8(B-E)
Off30 -20 -10 0 10 20
:- -:--- •:-- :- -?-: --7 -:- -': •
:, ' ',' ' :' ',' ',' ' :, [o
[' /,, ,', ,,. • .', ,.', m' :: :, ,:, t'., ,:, ,:1 o
3 4 5
1995/1/29 baseline ID: 11(C-E)
30 -20 -10 0 10 20
o oø•.,, ':. : .....
;:•; ':.•. , j• , ,
--,-o:--,-•,•--,--,--..r.-','',''
: i ;•J': : ::.: :
' ',' ': '•'.' ' ,' '. ' ','4•, ' '.' ',' '
' :__•. '_•l.' •' ' ' o
- ',- - , - -,- ' ,' ' o ',? ,• ', ' ',' '
ß : : : : •.':•, : :
: :time '.(JS•) iho•r]:
3 4 5
1995/1/29 baseline ID: 13(D-E)
Cy30 -20 -10 0 10 2,00
r'T'. .... •., .--. ::.--. , . .W" .... -.,--. . ,. ." ,
•- -,- - : - -,- -,- - ; ß -,- - r - -.- -,- - :-•
C•_ o. o .........
CO,o . • .........
•,- :•,•-.- -.- -: - -.- -: - -.- -.- - •
::. :':.-I i•. i_•_ '_.•. ;.. i.;•..':..i..
:,.-.
3 4 5
Figure 7. (continued)
1310 ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2
SSF 1995/1/28)
@
i ß ! i i i i i i I i
Ioo
baseline length [m]
i i I s i
1000
' ' ' ' I
....... SSF ( 1995/1/29)
.
ß
1, i
o
! ! i ! i I
IOO
• i i i lll
•10 '1'000
baseline length [m]
Figure 8. Standard deviations of the fringe phase differ-
ence for the time interval of 1000 s centered on the time
when the separation angle was minimum, compared with
the spatial structure function in the phase compensation
experiment. The open circles are the standard deviations of
the fringe phase difference with the baseline identification
listed in Table 2. The dashed lines represent the spatial
structure function shown in Figure 3a.
by instrumental troubles of the E antenna. On Janu-
ary 28 the standard deviations of the third and tenth
baselines (A-D and C-D) are higher than the 20 ø
level because there is spiky phase noise in their fringe
phase differences around the zero-separation time, as
shown in Figure 5. These values are greatly improved
after extraction of the spiky noises or by phase
compensation considering a time lag discussed in
section 5.4, so that the standard deviations of the
fringe phase difference of the third and tenth base-
lines will fall below the 20 ø level.
The former group suggests that the phase compen-
sation with the PAM is independent of the baseline
length and that the PAM phase compensation is able
to calibrate the atmospheric phase fluctuations to a
certain level when the separation angle is within a few
degrees. From Figure 8, if the desired compensation
level was 20 ø in the present PAM experiment, the
PAM phase compensation was successful for baseline
lengths longer than 70 m. The phase compensation
was not effective for the thirteenth baseline because
(1) the amplitudes of the tropospheric fluctuations
were originally small because of the shortness of the
baseline and (2) uncalibrated instrumental effects
larger than the atmospheric ones were included in the
CS fringe phase of the baseline.
5.2. Statistical Model of the Paired Antennas
Method Experiments
Asaki et al. [1996] showed a simple statistical model
for the PAM observations based on the "Kolmogorov
turbulence and phase screen and frozen flow" hypoth-
esis. They also demonstrated that the simulated series
of the standard deviations of the differential fringe
phase was in good agreement with the experimental
results. We used this model to generate a simulated
series of the standard deviations of the differential
fringe phase in the present PAM experiment and
compared them with those derived from our experi-
ment.
In the case of the present experiment we used the
time series of the SSF parameters (the structure
coefficient and exponent) estimated from the data of
3C279 as described in section 4.2. As mentioned by
Asaki et al. [1996] in the discussion of the critical
separation angle, the standard deviations of the fringe
phase difference are sensitive to the horizontal dis-
tance between the beams of the paired antennas in
the moist air, which means that the standard devia-
tions strongly depend on the height of the screen.
Consequently, the height can be estimated by com-
paring the whole shape of the simulated time series
with those obtained in the experiment. If the height is
assumed too high/low, the shape of the simulated
standard deviations becomes narrower/wider than the
experimental results. Thus we estimated the height of
the phase screen as 1500 m.
The parameters used in the simulation are listed in
Table 3, and the results of the simulated standard
deviations are shown as solid lines in Figures 6 and 7
along with the experimental results. The results of the
simulated standard deviations adopting the constant
SSF parameters are also shown as dashed lines in
Figures 6 and 7, which are useful to estimate the
critical separation angle. The peaks at the zero-
separation time are not very sharp in the curves of the
experimental and simulated standard deviations due
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1311
to the time variation of the separation angle within
the averaging time. Figures 6 and 7 show that the
simulation results trace the experimental results
much more finely than in the previous experiments
[Asaki e! al., 1996], especially when the separation
angle is smaller than several degrees. The agreement
worsens as the separation angle becomes larger. This
is because the SSF of the CS is less consistent with
that of 3C279 for a larger separation angle. In the
present PAM experiment the wider the separation
angle, the larger the difference in elevation between
the two sources. Atmospheric phase fluctuations
would vary when the observing elevation is different
[Holdaway and Ishiguro, 1995].
Note that the fringe phase at 146.81 GHz in the
present experiment is almost one order of magnitude
more sensitive to the excess path fluctuation than that
at 19.45 GHz in the previous ones [Asaki et al., 1996].
The results suggest that the hypotheses on the atmo-
spheric structure are good enough at least for the
spatial scale of the NMA. The model analyses dis-
cussed here suggest that it is important to choose
carefully suitable SSF parameters for a precise esti-
mation of the rms phase error of the compensated
fringe phase in the PAM.
5.3. Coherence Factor of the Differential Fringe
Phase
Figures 9 and 10 show the lag, which maximizes
the coherence factor •c
T•C •
exp {j[cI)^(t) - (I)B(t + z)]) dt
(8)
introduced by Asaki et al. [1996] for the two time
series of the fringe phases: •A for 3C279 and •B for
CS. Here the integration time T is set to 200 s. The
remarkably linear relationship between the lag r
maximizing the coherence factor and the separation
angle is evident for all baselines except the thirteenth.
The linear trend is demonstrated in the present
experiment much more clearly than in the previous
ones [Asaki et al., 1996]. The results show the general
validity of the "phase screen and frozen flow" hypoth-
esis [see, for example, Dravskikh and Finkelstein,
1979]. The time lag data for the range of the separa-
tion angle between -10 ø and + 10 ø were fitted to the
linear function of time:
•'c(t) = u x (t - to), (9)
Table 3. Parameters Adopted in the Simulation Series
Based on a Statistical Model
January 28, 1995 January 29, 1995
Scale height, m
Integration duration, s
Wind velocity, m s-1
Wind direction
Cl (for constant SSF)
(for constant SSF)
!/2
100 m, mm
(for constant SSF)
1500 1500
1000 1000
18 11
west to east west to east
0.665 x 10 -5 0.574 x 10 -5
1 - a/2 1 - a/2
cm cm
1.667 1.667
0.175 0.151
The structure coefficient and exponent of the spatial structure
function (SSF) in the list are averaged during each observing time.
ignoring three rr outliers. The results are shown in
Figures 9 and 10. Since the two sources are separated
along the almost east-west direction on the phase
screen parallel to the ground, we can estimate the
east-west component of the wind velocity assuming
the height of the phase screen. In Table 4, we list
values of the rate u' of the change of *c per separa-
tion angle in radians and to. The velocity component
is expressed by an equation h x sec(elevation angle)/
u'. Assuming 1500 m for the height of the phase
screen, we obtained -17.9 _+ 1.2 m/s and -10.8 +_ 1.0
m/s for January 28 and 29, respectively, which are in
a reasonable range of the geostrophic wind velocity in
the lower troposphere.
5.4. Phase Compensation With Account of
Hypothesis of the Simple Frozen Screen
It is interesting to examine how well the PAM
phase compensation is improved if we take account of
the time lag between the two fringe phase time series,
which maximizes the coherence factor. For this pur-
pose we generated new time series of the CS fringe
phase in terms of shifting the original time series by
the time lag determined in the least squares fittings as
described in the previous section. The fringe phase
differences between the time series of 3C279 and the
new time series of the CS are shown in Figures 4 and
5, and the standard deviations of the fringe phase
difference are shown in Figures 6 and 7 by open
circles. It is evident that the PAM phase compensa-
tion is remarkably improved. This again shows the
appropriateness of the "phase screen and frozen
flow" model in the present experiment.
5.5. Scaling Factor for Frequency Conversion
of Fringe Phase
Although the effectiveness of the PAM phase
compensation using different observing frequencies
1312 ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2
1995/1/28 baseline ID: 3(A-D)
-30 -20 -10 0
separa•:ion angle [degree] t
ß ' , ß
lO
.
• I I , ' ' '•l• ß
,, ....... . .... .-:-.:.:: .... ........
. - ';'. : : . ' . :
[' ' time (JST) [hour]
,'•-•_ ' , =l: , , ,• , , I , , , , , I , , , ,l
3 4 5
-40
%sepTation.
,
1995/1/29 baseline ID' 3(A-D)
-30 -20 - 10
ang•e [degree]
, ß
ß
2 3 4
Figure 9. The time lag maximizing the coherence factor of the fringe phase difference for the second
baseline (A-C). The lag is almost 0 s at the minimum separation angle and increases with increasing
time. The solid lines represent the results of least squares fittings of the time lag with separation angle
between - 10 ø and + 10 ø ignoring 30- outliers.
for the target and reference source is clearly demon-
strated in the above results, the following important
question is yet to be answered: Is the refractivity of
the water vapor in the troposphere strictly nondisper-
sive? In order to answer the question we calculated
the standard deviations of the fringe phase difference
introducing two scaling factors/x and •<. Factor/x is to
be multiplied by the CS fringe phase in calculating the
standard deviations of the fringe phase difference,
whereas •< is the scaling factor which minimizes the
contribution of the atmosphere commonly included
in both of the fringe phases of 3C279 and CS. The
fringe phase of 3C279 •3C279 and the CS fringe phase
CP[s multiplied by an arbitrary scaling factor/x are
(I)3c279 -- 4)3C279 q- 4)atm
(10)
(I)•s = /.t X (/)CS + -- (•atm , (11)
where (b½s and 4)3C279 are phase fluctuations due to
the independent noises such as thermal noise or
instrumental phase noise at each observing frequency
and 4)atm is the fluctuation due to the common
ASAKI ET AL.' PHASE COMPENSATION EXPERIMENTS, 2 1313
1995/1/28 baseline ID: I(A-B)
0-30 -20 -10 0 10
ø• i ,• .... . .....
sel•r•ti•n •lgl• [degree]
'•: . '.A"
• ,.
, ,
1995/1/28 baseline ID: 3(A-D) 1995/1/28 baseline ID: 4(A-E)
0-30 -20 -10 0 10 o-30 -20 -10 0 10
- se•a tiOn,½l•g)e[degre•l
.e ,
$' ß ,
ß
•',,' 'tim• (JST) [hour] ß ' ".t•r•.• ('.JST)[hour] ' : •}n4v. ('JST) [ho•.•]
oø ,'., a:., '.,:, '. .... ,'. ....... ,..' .... ' .....
7 3 4 5 7 3 4 5 7 3 4 5
ID:
1995/1/28 baseline ID: 6(B-C) 1995/1/28 baseline ID: 7(B-D) 1995/1/28 baseline 8(B-E)
0-30 -20 -10 0 lO 0-30 -20 -10 0 10 0-30 -20 -10 0 10
o..: .. I" ,. ,_ ......
o | .... . ........ : •.•l•r.a•iO.n .ans.le [degre.•]' ;
' ['sep,•r.•L• •xgl',e [,deg•'ee] •'. fseq•ar.•tid, n lSmg,le [degre,e] ,: :t _o ,._ _%.:,: .......
'e , • ß , ß , , ß ....
f',', ',"• ', : : : :•' •"•" ':*: :: ": : :• Li'., ,., ,:, , , . '
, , *, ...... ß , ", , %,, ....... ,, , , ......
•-..s ...., .... , ,=1-:,.,...., .... ..-I
,.. "'""" "'"' ...... '
.... ,. 7 ::':,;:: ::' 7 [....s., . ,.....•1'•
.', I '. .... ' • • '.' . .* . .
o .. .. o .....
17.:., •'.,,•: :1::
. ::1 ..
g :"'.': : ,; : i ! '='' ' :
oß ' [hou'r] ' o [!}; '" •'•e ("3S•)
..- o I:,;.!,•.'. ...... '., ,'., ,'., ,'., ,;, , ,
I 3 4 5 I 3 4 5 I 3 4 5
1995/1/28 baseline ID' 10(C-D) 1995/1/28 baseline ID: 11(C-E) 1995/1/28 baseline ID: 13(D-E)
0-30 -20 -10 0 tO
q--4 ß
sep, l• .r•,t•o• •ngl,e [degree]
' $ '
*
..... ,..., .......
,
, ,
'time •) [hour]
4 5
0-30 -20 -10 0 10
':" '1 time (:/ST) ß [hour].
•,,,t_'., ,•,'.•,i., ..i. ,' ......
4 5
0-30 -20 -10 0 10
. Figure 10. The time lag maximizing the coherence factor of the fringe phase difference.
1314 ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2
1995/1/29 baseline ID: I(A-B) 1995/1/29 baseline ID: 3(A-D) 1995/1/29 baseline ID: 4(A-E)
-40 -30 -20 -10 0 o -40 -30 -20 -10 0 • -40 -30 -20 -10 0
[ 0ep0ra,tto•t •gle •.[degr, ee] :" - ' ...... ' • .....
•.: : : : : :.: : • ½, ';'t • [.......h .... ß ....
,...,...., ..... .
ß
x' :,: .: .:.•:': : : : •,.• ß i •h :'½: ::.:•: : : :O
,.,.,',',,-,,, ...... ....
......... ffi ß e .... e
,.. .... g ß •[-: :. :2.•': : : '.4
• •, , ,,• ;...; ;' , , • •
: : .: i : : : ß • .
•. :. ,: = .:. ,:, ',', ,:, , g • •. •z, ,' ,•: •': ,',:, ,:7 ,:, ,:, • ...
2 3 4 I 2 3 4 • 2 3 4
'
t '
o [,e (J, •T) [hour]
o
• 2 3 4
1995/1/29 baseline ID' 7(B-D) 1995/1/29 baseline ID: 8(B-E)
-40 -30 -20 -10 0
" '"• :i•
[ !. •' •.,
,. •!:.. -. :
e, ß l'
:1'.
. . :,$
', .'}. ;... : '
, ,., , , :
, ,. , : . : ,.
."' : :'
2 3 4
-40 -30 -20 -10 0
2 3 4
1995/1/29 baseline [D: 10(C-D) 1995/1/29 baseline ID: It(C-E) 1995/1/29 baseline ID: I3(D-E)
-40 -30 -20 -10 0
['• . •. , -: ....
•, ep•ra.t•og ,• [degree]
• ' ' • I• .
, •', 0, !
• .... ; .... ,.. •- -,-
o
o
e ,
e©e
,
•: |
ß
3 4
0 -40 -30 -20 -tO 0
o• ' ,t-, ' I•'- ....
-q, ep•ralkiog •ng.]• •?:leKre•]
:,•" ! "' 't
: :,: '
•o :,.,.. : . ,
•, •, * . -,
' " ' i' b, "
• ' ,
,t ::
i"
'ST [hour]
• 2 3 4
0 -40 -30 -20 -10 0
3 4
Figure 10. (continued)
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1315
atmosphere at the observing frequency of 3C279
(note that the phase term due to the geometrical
delay is absent here because we have largely elimi-
nated the effects of the geometrical delay and other
slowly variable terms in the process of high-pass
filtering; see section 4.1). If we denote O-•c279 --
2 2 ,1 2 2
{(I)3c279} , O'CS = {(I)•s}, and O'at m = {q•atm}, the
variance o'32C279_C• of the fringe phase difference is
calculated by {A(I)•c279_CS}, that is,
2
O'3C279_CS = {(CI)3c279 -- CI)•s) 2}
( 2t2m/2 4
O'a 2 O'atm
= O'•S • + O'3C279 ß
/<trCS/ /< 2o.• S (12)
2
According to the (12), we can treat O'3C279_CS as a
second-order polynomial of /z. Thus the minimum
standard deviation of the fringe phase difference is
obtained when
Table 5. Scaling Factors Which Give the Minimum
Standard Deviation of the Fringe Phase Difference/z and
the Atmospheric Fluctuations/<
January 28, 1995
January 29, 1995
/-z 0 • /-z 0 •
1 (A-B) 0.887 1.43 0.918 1.33
2 (A-C) 0.969 1.02 0.905 0.969
3 (A-D) 0.900 1.07 0.848 1.15
4 (A-E) 0.943 1.39 0.831 1.29
6 (B-C) 0.884 1.03 0.919 1.00
7 (B-D) 0.795 0.867 0.821 1.14
8 (B-E) 0.988 1.71 0.716 1.75
10 (C-D) 0.859 1.36 0.797 0.845
11 (C-E) 0.877 3.56 1.08 1.92
13 (D-E) 0.463 0.517 0.484 0.414
All the listed values are normalized by a ratio of the observing
frequencies of 146.81/19.45.
2
O'at m
2 ß (13)
/<O'cs
We calculated the variances of the fringe phase
difference with the averaging interval of 1000 s vary-
ing/z. Those variances were fitted to a second-order
polynomial in order to evaluate/z0, which minimizes
the fitted curve for each baseline. Since the residual
atmospheric fluctuations must be made as small as
possible, the fringe phase differences considering the
time lag were used, and the center of the 1000-s time
series was set to the moment when the time lag is zero
for each baseline. The calculated results of/z 0, nor-
malized by the nondispersive value of 146.81/19.45,
Table 4. Results of the Least Squares Fittings of the
Lag Maximizing the Coherence Factors
January 28, 1995 January 29, 1995
Baseline u ', t o , u', t o ,
Identification s rad -1 LT s rad -1 LT
1 (A-B) 97.5 0417:11 146.3 0417:50
2 (A-C) 115.6 0420:51 183.6 0419:21
3 (A-D) 115.7 0421:10 182.9 0420:19
4 (A-E) 114.2 0414:57 171.5 0411:14
6 (B-C) 116.8 0420:20 185.1 0419:18
7 (B-D) 103.3 0419:5 176.5 0420:50
8 (B-E) 107.6 0412:32 184.3 0409:5
10 (C-D) 118.0 0421:5 190.8 0419:47
11 (C-E) 120.2 0413:34 197.1 0411:57
13 (D-E) - 102.9 0441:29 72.6 0358:53
Results of the Least Squares Fittings of the Lag Maximizing the
Coherence Factors
are listed for all the available baselines in Table 5.
Most of the factors are nearly equal to the nondis-
persive value but tend to be slightly smaller. It does
not necessarily imply that the refractivity of the water
vapor is not nondispersive because the significant
instrumental phase fluctuations in the CS fringe
phase are seen, especially among the baselines involv-
ing the E antenna. The residual atmospheric contri-
bution could also remain in the fringe phase differ-
ence when the separation angle was rather large
during the 1000-s averaging interval.
We estimated •c from/z0 using (13). The standard
deviations of the CS fringe phase O-cs were calculated
from the same 1000-s averaging interval of the CS
fringe phase for each baseline. We estimated Crat m
from the standard deviations of the fringe phase of
3C279 with the same 1000-s averaging interval, from
which the thermal noise 6.4 ø was eliminated for all the
baselines. The calculated results of •c, normalized by
the nondispersive value, are shown in Table 5. The
obtained factors are highly scattered. It must be
caused by the rough estimation of the thermal noise
of the fringe phase of 3C279 and the instrumental
fluctuations in the CS fringe phase. Apparently, the
effects of those phase noises are too large to allow a
sensitive determination of the "true" scaling factor.
The only conclusion we can draw at present is that the
nondispersive scaling factor is good enough to realize
the effective phase compensation with PAM using
millimeter and centimeter waves for observing the
target and reference source.
1316 ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2
5.6. Reference Source Counts
The phase-referencing technique requires astro-
nomical reference sources very close to a scientifically
interesting object. Reference source counts are de-
pendent on the observing frequency. Sasao et al.
[1996] showed that a VLBI source brighter than 0.1 x
10 -26 W m -2 Hz -1 can be found within 1.2 ø around
a target in the arbitrary direction of the sky at 8 GHz.
In the millimeter-wave region, Foster [1994] esti-
mated the reference source counts at 90 GHz using
Monte Carlo simulations based on a 90-GHz source
survey [HoMaway et al., 1994]. He showed that there
is a 70% possibility that a reference with a flux density
of at least 0.1 x 10 -26 W m -2 Hz -1 at millimeter
waves can be found within 2 ø of a random point on
the sky. These results encourage us that simultaneous
observations with centimeter or millimeter reference
sources are successful.
In the submillimeter-wave region it is more difficult
to find a suitable reference within a few degrees of a
target source. Different frequency observations are
very promising for submillimeter-wave phase com-
pensation. In the submillimeter-wave region, how-
ever, the direct phase scaling from the frequency ratio
cannot be applied to compensate the submillimeter-
wave phase because the refractive index of the water
vapor is becoming more dispersive. If the excess path
fluctuations are still almost only dependent on the
quantity of the water vapor along the line of sight, the
scaling factor will be easily obtained for each fre-
quency. In the submillimeter-wave region, more pre-
cise investigation will be needed for applying the
phase scaling.
There are plans to install a dual-band receiver
including a 12-mm band and a shorter-wavelength
band on the Australia telescope compact array [Hall,
1996], to observe, for example, CO sources with the
water vapor maser at 22 GHz. Since such maser
sources can be good references for a target emitting
molecular lines in the same field, it is possible to
achieve a very high level of the phase compensation.
The SiO maser sources at 43 GHz or other frequen-
cies also will be good candidates for the phase-scaling
PAM calibrators.
6. Conclusions
A phase compensation experiment with the PAM
using different observing frequencies for the target
and reference source was successfully carried out. In
the present PAM experiment the nondispersive scal-
ing factor equal to the frequency ratio was used for
converting the lower-frequency fringe phase to the
higher frequency. The calibrated fringe phase with
the separation angle less than 2 ø showed only minute
fluctuations of less than 0.1-mm rms in the excess
path length. This value is good enough for the future
millimeter- or submillimeter-wave radio arrays. Al-
though our experiment was not sensitive enough to
precisely determine the scaling factor which mini-
mizes the atmospheric phase fluctuations and its
possible deviation from the nondispersive value, the
achieved phase correction is good enough to conclude
that the PAM with the different observing frequen-
cies is a promising technique for future ground-based
radio interferometry. Since it becomes increasingly
difficult to find a sufficient number of suitable refer-
ence sources as the observing frequency increases, the
above results should be emphasized from a practical
point of view. This technique also can be applied to
the fast switching method in terms of the phase
connection. The higher the observing frequency is,
the more difficult the correction of the 2rr ambiguity
will be. The phase connection and the interpolation of
the reference phase would be much easier where
reference sources are observed at lower frequency in
order to appropriately infer time variations of the
excess path delay without this ambiguity.
The analyses of the present experiment generally
show that the simple structure of the atmosphere
based on the "Kolmogorov turbulence and phase
screen and frozen flow" hypothesis is a fairly good
representation of the reality for a millimeter array. In
particular, the remarkably linear relationship be-
tween the time lag maximizing the coherence factor
and the separation angle strongly supports the exis-
tence of the fairly stable and strong wind in the lower
troposphere as assumed in the frozen flow hypothesis.
Also, the PAM phase compensation was more suc-
cessful when we inserted the time lag determined by
means of the linear dependence of the time lag on the
separation angle. The above results suggest that if we
are able to measure the speed and the direction of the
wind aloft over a connected radio array by indepen-
dent meteorological means, we will achieve the more
efficient phase compensation with the phase-refer-
encing.
Acknowledgments. We are deeply indebted to the staff
and students of the Nobeyama millimeter array who made
it possible to conduct this experiment. We express special
thanks to T. Takahashi, H. Iwashita, and K. Handa (NAO)
ASAKI ET AL.: PHASE COMPENSATION EXPERIMENTS, 2 1317
for valuable discussions and help in setting up the instru-
ments for the experiment. Y. A. expresses his heartfelt
gratitude to N. Kawano and S. Enome (NAO) for contin-
uous encouragement and helpful suggestions.
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(Received September 22, 1997; revised April 9, 1998;
accepted May 12, 1998.)
