ALMA Long Baseline Campaigns: Phase Characteristics of Atmosphere at Long Baselines in the Millimeter and Submillimeter Wavelengths

0.44 MB·

by  Satoki Matsushita

Draftversion January12,2017
PreprinttypesetusingLATEXstyleemulateapjv.5/2/11
ALMA LONG BASELINE CAMPAIGNS: PHASE CHARACTERISTICS OF ATMOSPHERE AT LONG
BASELINES IN THE MILLIMETER AND SUBMILLIMETER WAVELENGTHS
Satoki Matsushita1, [email protected] Yoshiharu Asaki2,3, Edward B. Fomalont2,4, Koh-Ichiro
Morita2,3, Denis Barkats5, Richard E. Hills6, Ryohei Kawabe7,8,9, Luke T. Maud10, Bojan Nikolic6, Remo P. J.
Tilanus10, Catherine Vlahakis4, Nicholas D. Whyborn2
Draft version January 12, 2017
7 ABSTRACT
1
We present millimeter- and submillimeter-wave phase characteristics measured between 2012 and
0
2014ofAtacamaLargeMillimeter/submillimeterArray(ALMA)longbaselinecampaigns. Thispaper
2
presentsthefirstdetailedinvestigationofthecharacteristicsofphasefluctuationandphasecorrection

n methods obtained with baseline lengths up to ∼ 15 km. The basic phase fluctuation characteristics
a can be expressed with the spatial structure function (SSF). Most of the SSFs show that the phase
J
fluctuation increases as a function of baseline length, with a power-law slope of ∼ 0.6. In many

1 cases, we find that the slope becomes shallower (average of ∼ 0.2−0.3) at baseline lengths longer
1 than ∼ 1 km, namely showing a turn-over in SSF. These power law slopes do not change with the

amount of precipitable water vapor (PWV), but the fitted constants have a weak correlation with
]
PWV, so that the phase fluctuation at a baseline length of 10 km also increases as a function of
M
PWV. The phase correction method using water vapor radiometers (WVRs) works well, especially
I for the cases where PWV >1 mm, which reduces the degree of phase fluctuations by a factor of two
.
h in many cases. However, phase fluctuations still remain after the WVR phase correction, suggesting
p the existence of other turbulent constituent that cause the phase fluctuation. This is supported by
- occasional SSFs that do not exhibit any turn-over; these are only seen when the PWV is low (i.e.,
o
when the WVR phase correction works less effectively) or after WVR phase correction. This means
r
t thatthe phase fluctuationcausedby this turbulentconstituent is inherently smallerthanthat caused
s bywatervapor. Sinceintheserarecasesthereisnoturn-overintheSSFuptothemaximumbaseline
a
length of ∼ 15 km, this turbulent constituent must have scale height of 10 km or more, and thus
[
cannot be water vapor, whose scale height is around 1 km. Based on the characteristics, this large

1 scale height turbulent constituent is likely to be water ice or a dry component. Excess path length
v fluctuation after the WVR phase correction at a baseline length of 10 km is large (&200 µm), which
2 is significant for high frequency (> 450 GHz or < 700 µm) observations. These results suggest the
3 needforanadditionalphasecorrectionmethodto reducethe degreeofphasefluctuation,suchasfast
0
switching,inadditiontotheWVRphasecorrection. Wesimulatedthefastswitchingphasecorrection
3
method using observations of single quasars, and the result suggests that it works well, with shorter
0
cycle times linearly improving the coherence.
.
1 Subject headings: atmospheric effects; site testing; techniques: high angular resolution; techniques:
0 interferometric
7
1
: 1. INTRODUCTION ter/submillimeter (mm/submm) interferometer. One of
v
the most important technical developments for ALMA
i The Atacama Large Millimeter/submillimeter Array
X (ALMA; Hills et al. 2010) is the world’s largest millime- full operation has been making the longest (∼ 15 km)
baselineobservationspossible,whichwasachievedforthe
r
a 1Academia Sinica Institute of Astronomy and Astrophysics, first time at the end of 2014 (ALMA Partnershipet al.
P.O.Box23-141,Taipei10617,Taiwan,R.O.C. 2015a).
2JointALMAObservatory,AlonsodeCo´rdova3107,Vitacura Prior to that, the longest baseline observations for
7630355,Santiago, Chile
3Chile Observatory, National Astronomical Observatory of mm/submm linked arrays had been much shorter, only
Japan, National Institutes of Natural Sciences, Joaquin Mon- ∼2 km at 230 GHz with the Berkeley-Illinois-Maryland
tero3000Oficina702,Vitacura,Santiago, C.P.7630409,Chile Association(BIMA)ortheCombinedArrayforResearch
4NationalRadioAstronomyObservatory,520EdgemontRd, in Millimeter-wave Astronomy (CARMA), and several
Charlottesville,VA22903, USA
5Harvard-Smithsonian Center for Astrophysics, 60 Garden hundred meters at 345 GHz or higher frequencies with
St.,MS-78,Cambridge,MA02138, USA the Submillimeter Array (SMA) or the NOrthern Ex-
6Astrophysics Group, Cavendish Laboratory, University of tended Millimeter Array (NOEMA), although there are
Cambridge,JJThomsonAvenue,CambridgeCB30HE,UK
7NationalAstronomicalObservatoryofJapan,2-21-1Osawa, some very long baseline interferometry (VLBI) obser-
vations with the frequency up to 230 GHz and with
Mitaka,Tokyo181-8588,Japan
8Department of Astronomy, School of Science, University of baseline lengths up to ∼ 4000 km (e.g., Doeleman et al.
Tokyo, Bunkyo,Tokyo113-0033,Japan 2008, 2012). The longest baseline length currently pos-
9SOKENDAI (The Graduate University for Advanced Stud-
sible with ALMA (∼ 15 km), together with a signif-
ies),2-21-1Osawa,Mitaka,Tokyo181-8588, Japan
10LeidenObservatory,LeidenUniversity,P.O.Box9513,2300 icant increase of the number of baselines (1225 base-
RALeiden,TheNetherlands lines with 50 antennas) compared with the aforemen-
2 Matsushita et al.
tioned mm/submm arrays, is therefore a revolutionary utes (usually 10−40 minutes, depending on the longest
improvement for mm/submm linked arrays. This 15 km baseline length) with ∼ 1 s integration time per data
baseline length with good uv coverage provides milli- point. Hereafterwerefertotheseobservationsas“single
arcsecond resolution; such high sensitivity and high fi- source stares.” For each measurement, ten or more an-
delity at these wavelengths cannot be obtained with tennaswithvariousbaselinelengthshavebeenused. We
any other current facilities. Indeed, in the ALMA long only used 12 m diameter antenna data and did not use
baseline campaign in 2014, science verification images datatakenwith7mdiameterantennasinordertomake
revealed extraordinally detailed features of an asteroid the thermal noise contribution uniform over the data as
(ALMA Partnership et al.2015b),aprotoplanetarydisk much as possible.
system(ALMA Partnership et al. 2015c), anda gravita- The single source stares were taken for the purpose
tionallylensedsystem(ALMA Partnership et al.2015d). of statistical phase analysis beyond the wind crossing
Inordertocontinuetoimproveonthequalityofthedata, time of the longest baseline. For example, assuming (1)
it is important to characterize the atmospheric phase a longest baseline length of 10 km, (2) a wind speed
fluctuation,andtotestphasecorrectionmethodsatthese along a given baseline of 10 m s−1, and (3) that the
long baselines. phasescreendoesnotchangewithtime(i.e.,frozenphase
Characterization of the atmospheric phase fluctuation screen;Taylor1938;Dravskikh & Finkelstein1979),then
so far has mainly been carried out at low frequencies; the crossing time can be calculated as 1000 s (∼ 17
Very Large Array (VLA) was often used to character- minutes). To have statistically significant data for the
izetheatmosphericphasefluctuationatcentimeter-wave longestbaselinedata,abouttwicethemeasurementtime
(cm-wave) with baseline lengths up to a few tens of is needed (see Asaki et al. 1996 for the detailed discus-
km (Sramek 1990; Carilli & Holdaway 1999). At higher sion)11. We used Bands 3 (100GHz band), 6 (200 GHz
frequencies, studies with 80 − 230 GHz (1 − 3 mm) band), and 7 (300 GHz band) for all the campaigns, ex-
are available with baseline lengths up to only about 1 ceptforBand8(400GHz band),whichwasonlyusedin
km (Wright 1996; Asaki et al. 1998; Matsushita & Chen the 2014 campaign.
2010). These previous cm-/mm-wave studies displayed The data were reducedusing the CommonAstronomy
similarresultsforcaseswheretheatmosphericphasefluc- SoftwareApplications(CASA) package(McMullin et al.
tuation is caused by water vapor in the atmosphere. 2007), using a standard ALMA calibration prescrip-
Since 2010, as a part of ALMA Commissioning and tion. Below we give a brief overview. The WVR phase
ScienceVerification(CSV), andmostrecently,aspartof correction12 was applied using the program wvrgcal
the Extension and Optimization of Capabilities (EOC; (Nikolic et al. 2012) installed inside CASA. The precip-
seeALMA Partnership et al.2015a), wehaveconducted itable water vapor (PWV) values calculated by wvrgcal
severalALMAlongbaselinecampaigns,startingfromthe is used as a measure of the water vapor content in front
longest baseline length of 600 m in 2010 and 2011, 2 km of the array of each data set.
in 2012, 3 km in 2013, and finally 10−15 km in 2014. Linear phase drift, which is mostly caused by the
In the earlier long baseline campaigns, we mainly con- antenna position determination error (main reason for
ducted basic tests, such as characterizingthe phase fluc- this error is due to poor knowledge of the dry air de-
tuationandcheckingtheeffectivenessoftheWVRphase lay term for each antenna, which can be very differ-
correction; in the later phase, we mainly concentrated ent from each other due to the height difference; see
on the coherence time calculation and the evaluation of ALMA Partnership et al.2015afordetails),hasbeenre-
the fastswtiching phase correctionmethod. Some ofthe movedfromeachdataset(theantennapositionerrorsare
earlytestresultshavebeenreportedinMatsushita et al. generallysmallenoughthatthey onlycauselinearphase
(2012, 2014, 2016) and Asaki et al. (2012, 2014, 2016), drift on timescales of tens of minutes or more). After
and the overview of the latest 10−15 km baseline test this, we averaged the data points for 10 s to take out
has been reported in ALMA Partnership et al. (2015a). phase errors due to thermal noise. With this 10 s time
In this paper, we presentthe detailed characterization averaging, and assume the source flux density is 1 Jy
of phase fluctuation, improvement of phase fluctuation and the system temperature is a typical value for each
after the water vapor radiometer (WVR) phase correc- ALMA Band (Remijan et al. 2015), root mean square
tion method (Wiedner et al. 2001; Nikolic et al. 2013), (rms) phase errors due to thermal noise are calculated
coherence time calculation, and the cycle time analy- as 3.4, 2.0, 2.4, and 4.5 µm for Bands 3, 6, 7, and 8,
sis for the fast switching phase correction method us- respectively. In our observations, the minimum source
ing the data obtained in the ALMA long baseline cam- flux densities are 1.7,1.1, 1.2,and 3.7 Jy for Bands 3, 6,
paigns. Theresultspresentedinthispaperreplacethose 7, and 8, respectively, so that the maximum rms phase
reported previously by Matsushita et al. (2012, 2014, errors can be calculated as 2.0, 1.8, 2.0, and 1.2 µm for
2016). Note that the relation between phase fluctuation Bands 3, 6, 7, and 8, respectively. The smallest mea-
and the weather parameters (wind speed, wind direc- sured phase fluctuation at very short baseline lengths of
tion, temperature, pressure, etc.) will be discussed in about 15 m before the WVR phase correction, but af-
the forthcoming paper (Maud et al., in prep.), so that ter the 10 s averaging, is about 6 µm (Matsushita et al.
we do not discuss here.
11 Longermeasurementtimeof90minuteshasalsobeentested;
2. OBSERVATIONSANDDATAREDUCTION seeSect.3.2.2.
In this paper, we use the data taken in the long base- 12 WVR phase correction method isto estimate the amount of
water vapor in front of each antenna using the 183 GHz WVR
line campaigns between 2012 and 2014 (see Sect. A).
(Nikolicetal. 2013), calculate the excess path length and phase
All the data were taken with observations of a strong difference between antennas, then correct the phase fluctuation
point source (i.e., radio-loud quasars) for tens of min- causedbywater vapor(Wiedneretal.2001;Nikolicetal.2013).
Atmospheric Phase Characteristics of ALMA Long Baseline 3
104 3. RESULTSANDDISCUSSION
km (a) 3.1. Improvement Factor of the WVR Phase Correction
1
>
L WVR phase correction often improves the data qual-
B
at 103 ity (Matsushita et al. 2012, 2014; Nikolic et al. 2013;
h
Lengtcron] AticLaMl sAtuPdayrthnoewrsmhiupchetitali.m2p0r1o5vae)s,fbourtshthoerrtetoislonnogstbaatsies--
h mi
at[ lines. In this subsection, we present the statistical study
MS P 102 results for this method.
R
e Fig.1(a)showsthermsexcesspathlengthbefore(filled
g
era symbols) and after (open symbols) the WVR phase cor-
Av 101 rection for the data with baseline length longer than 1
7 km(dataforbaselinelength>1kmineahcdatasethave
(b) beenaveragedintoonedatapoint). Itisobviousthatthe
6
WVR phase correction reduces all the rms excess path
ctor5 lengths to less than 1000 µm.
a
F The improvementfactor of the WVR phase correction
ent 4 methodhasbeencalculatedastheratioofthermsexcess
m
ove3 path length for each baseline without the WVR phase
pr correction to that with the correction. Higher values
m
R I2 mean that the WVR phase correction works better (im-
V
W provedmore)thancaseswithlowervalues(lessimprove-
1
ment). Values of less than unity means that the WVR
0 phase correction made the phase fluctuation worse than
7 theoriginaldata. Calculatedvaluesareaveragedoverall
(c)
baselines, and plotted as a function of PWV (Fig. 1b).
6
In addition, we plotted the data divided into baseline
ctor5 lengths shorter and longer than 1 km (Fig. 1c). For the
a
F
nt 4 former, we used data from all campaigns; for the latter,
me weuseonlydatafromthe2014campaign,sincetheolder
e
ov3 data contain very few long baselines.
pr
m The mean improvement factor over all PWV con-
VR I2 ditions is 2.1 ± 0.7. This result is consistent with
W
1 what is reported previously (Matsushita et al. 2012;
ALMA Partnership et al.2015a),butthisisthefirststa-
0
0.0 0.5 1.0 1.5 2.0 2.5 3.0 tistical result. However, from Fig. 1(b), it is obvious
PWV [mm]
that the improvement factor is often larger when PWV
Fig.1.—(a)Averagedrmsexcesspathlengthatbaselinelengths is larger than 1 mm, with a mean improvement factor
longer than 1 km. This plot only uses the 2014 data, since only of 2.4±0.7. In the case of PWV < 1 mm, however, the
the2014datahavestatisticallysignificantdatapointsatbaselines
ratiois1.7±0.4. ThusitisclearthatalthoughtheWVR
longer than 1 km. Symbols are differentiated with the frequency
bands; diamond, triangle, square, and circle symbols indicate the phase correctionin most cases provides an improvement
datatakenwithBands3,6,7,and8,respectively. Filledandopen in the amount of phase fluctuation, the amount of im-
symbols are before and after the WVR phase correction, respec- provementcan be significantly largerfor PWV > 1 mm.
tively. (b)ImprovementfactoroftheWVRphasecorrection(ratio
This result can be explained because at low PWV, the
of the rms excess path length without WVR phase correction to
thatwiththecorrection)asafunctionofPWV.Eachdatapointis differenceintheamountofwatervaporalongthelinesof
averagedoverallbaselines. Thisplotusesallthe2012−2014data. sight of two antennas is small compared to the thermal
(c)Datapointshavebeenseparatedfortheoneaveragedoverthe noiseoftheWVRsof∼0.1Krms(whichcorrespondsto
baseline length shorter (filled) or longer (open) than 1 km. The
aboutafew tensmicronrms;Nikolic et al.2013). Inad-
open symbol data points are calculated from the data shown in
(a). dition,scatterofthedatapointsisalsodifferentbetween
low and high PWV cases, which is obvious in Fig. 1(b)
2012), which is larger than the upper limit of the phase and also from the error values of about twice difference
error. We can therefore conclude that we successfully (±0.7 vs ±0.4) as mentioned above. This means that
suppressed the effect of instrumental noise in our data not all the data show significant improvement in phase
with 10 s averaging. fluctuation in the case of PWV > 1 mm after the WVR
We then calculated the rms phase fluctuation for each phase correction.
baseline. For the unit of phase, we express in path Fig. 1(c) shows that the improvement factor for the
length13. This allows us to directly compare the re- baseline length shorter than 1 km is 2.3±0.9, and that
sults from various frequencies in the same unit without for the baseline length longer than 1 km is 2.0 ± 0.7.
any frequency dependence, and is often referred to as Thelongerbaselinedatatendtohavelowerimprovement
excess path length. factor than the shorter ones, although the difference is
statistically not significant.
an1d3inΦde=gre3e6sθ0,◦re×speνcc,tiwvehleyr,ecΦisatnhde sθpeaerde pofhalisgehtin, apnadthνliesngththe wiItnh dbiofftehrepnltotssy,mdbiffolesr,ebnuttfrweequfienndcynobasingdnsifiacraentpdloitffteerd-
observationfrequency. enceintheimprovementfactorasafunctionoffrequency
4 Matsushita et al.
band.
(a)
n]
o1000
cr
mi
3.2. Spatial Structure Function of Phase Fluctuation h [
gt
In this subsection, we first define the spatial structure en
function(SSF)ofphase(Sect.3.2.1),andderivetheSSF h L 100
at
slopes(Sect. 3.2.2)andconstants(Sect.3.2.4)forallthe P
S
pastlongbaselinesinglesourcestaredata. Statisticalre- M
R
sult for the slopes is compared with the previously pub-
10
lished studies (Sect. 3.2.2). We then estimate the rms 101 102 103 104
phasefluctuationfora10kmbaseline,andderiveaweak Baseline Length [m]
correlation with PWV (Sect. 3.2.4). After WVR phase
correction, there is a significant residual phase fluctu- n] (b)
ation, suggesting that there may be other constituents cro 1000
than water vapor that cause the phase fluctuation exist mi
in the atmosphere; we discuss the possibilities for liquid gth [
n
water,ice,anddrycomponents,andalsoanyinstrumen- e
tal causes (Sect. 3.2.5). h L 100
at
P
S
3.2.1. Definition of Spatial Structure Function RM
The SSF of phase is defined as 10
101 102 103 104
Baseline Length [m]
Dθ(d)=<{θ(x)−θ(x−d)}2 >, (1)
Fig. 2.—Tworepresentativeplots ofthespatialstructurefunc-
where θ(x) and θ(x−d) are phases at positions x and tion(SSF) with(open diamond)and without (cross)WVR phase
x−d, and the angle brackets mean an ensemble average correction. Solid and dashed lines are the fitting results of slopes
usingbaselines shorter than 500m and longer than 1km, respec-
(Tatarskii 1961; Thompson et al. 2001). Since θ(x) − tively. (a)ExampleofSSFwithaclearturn-over. Thedatafilefor
θ(x−d)isaninterferometerphasewithabaselinelength this plot is “uid A002 X8bd3e8 Xa59” in Table 5. (b) Example
of SSF without any clear turn-over. The data file for this plot is
d, Dθ(d) isapproximatedtothe rms phasefluctuation “uid A002 X8e1004 Xf04”inTable5.
ofpa baseline over the entire observationtime. SSF plots
inthispaperhavethereforebeenmadebycalculatingthe SSFwithaconstantslopeisinherentlymorestablethan
rms phase for each projected baseline in the direction of that with a turn-over (see also the end of Sect. 3.2.2).
atargetsourceusingtensofminutesofobservationtime, The baseline length of the turn-over roughly corre-
and plotted as a function of baseline length. spondstothescaleheightofthethree-dimensionalatmo-
Slopes for rms phase fluctuation are well studied the- spheric turbulence (Treuhaft & Lanyi 1987; Lay 1997).
oretically, and in the case of 3-dimensional (3-D) Kol- Ourresultssuggestthatthescaleheightofthe waterva-
mogolov turbulence of the Earth’s atmosphere, it is porconstituent atthe ALMA site is about 1km inmost
expected to have a slope of 0.83; for the 2-D turbu- cases, which is a typical value of the turn-over baseline
lence case, the slope is expected to be 0.33. In the length measured with astronomical radio arrays (e.g.,
case of no correlation in the atmospheric turbulence be- Carilli & Holdaway 1999). It is highly possible that the
tween two antennas, the slope is expected to be zero mainturbulentconstituentattheALMAsiteiswaterva-
(Thompson et al. 2001). por, which is consistent with the improvement of phase
Fig. 2 shows two example plots of SSFs we obtained fluctuation by the WVR phase correction in most cases
using the ALMA data. In these plots, both the WVR (Sect. 3.1). On the other hand, no turn-overmeans that
phase corrected and uncorrectedSSFs are displayed. As the scale height of the turbulent constituent is higher
mentionedabove,phaseisconvertedintotheunitofpath than 10 km. This scale height is much higher than that
length. Fig. 2(a) displays a typical SSF plot; there is a ofwatervapor,suggestingthattheturbulentconstituent
clear turn-over in the SSF at baseline lengths of ∼ 1 for the SSF with no turn-over is caused by some other
km in both plots with and without the WVR phase cor- constituent (see Sect. 3.2.5 for further discussion).
rection. Shorter baselines, before the turn-over, show a
steeper slope, while longer baselines show a shallow or 3.2.2. Slopes for the Spatial Structure Functions
almost flat slope. In general, for the ‘typical’ data sets,
Wefirstfittedtheslopesforthedatapointswithbase-
onlyone turn-overisevidentwith the currentdataanal-
line lengths shorter than 500 m and longer than 1 km
ysis method, and is usually observed between baseline
for each SSF plot, namely shorter and longer than the
lengths of several hundred meters to ∼1 km. Fig. 2(b),
turn-oversin the plots. The fitting function is expressed
ontheotherhand,exhibitsnoclearturn-over;phasefluc-
as
tuationincreasesconstantlyevenatlongbaselines. Such
log (∆L)=a×log (d)+b, (2)
a constant slope SSF is not common, but is sometimes 10 10
observedin the data (see Sect. 3.2.2for statistics). Note where ∆L is the rms excess path length in micron, d is
thatthesenoturn-overdatagenerallyhaveamuchlower the baseline length in meter, and a and b are the slope,
excess path length value compared to the ‘typical’ data namely the structure exponent, and the structure con-
atparticularbaselinelengths(especiallyatshorterbase- stant, respectively. Examples of the fitting are shown in
lines), which can be seen in Fig. 2. This means that the Fig. 2, and the fitted slopes as a function of PWV are
Atmospheric Phase Characteristics of ALMA Long Baseline 5
TABLE 1
Fitted slopes ofthe spatialstructure functions (SSFs).
WithoutWVRphasecorrection WithWVRphasecorrection
BaselineLength All PWV<1mm PWV>1mm All PWV<1mm PWV>1mm
<500m 0.65±0.06 0.65±0.06 0.66±0.06 0.62±0.09 0.64±0.08 0.60±0.09
>1km 0.22±0.15 0.27±0.20 0.17±0.07 0.29±0.13 0.31±0.15 0.26±0.11
1.2 are 0.22±0.15 and 0.29±0.13 for the data before and
(a) aftertheWVRphasecorrection,respectively. Theseval-
1.0
ues are significantly smaller than those for the baseline
)
em 0.8 length shorter than 500 m, indicating that most of the
p
o0 0.6 data have a turn-over at a baseline length between 500
Sl50 m and 1 km.
F < 0.4 For almost all the cases, the slopes for shorter base-
SL 0.2 lines are in the middle of theoretical 3-D and 2-D Kol-
SB
mogorov turbulence, which are 0.83 and 0.33, respec-
( 0.0
tively. This suggests the existence of undeveloped tur-
−0.2 bulence or multi-layer turbulence with different heights
intheatmosphere. Theslopesforlongerbaselines(slopes
1.2
aftertheturn-over),ontheotherhand,exhibitthevalues
(b)
1.0 between the 2-D Kolmogorov turbulence (slope = 0.33)
em) 0.8 and no correlation between two antennas (slope = 0) in
opk most cases.
Sl1 0.6 Our result is very similar to the result from the sta-
F > 0.4 tistical study of the SSF slope at the VLA site; the
SL slope of 0.59 at short (< 1 km) baselines, and 0.3 at
SB 0.2 longerbaselines(Sramek1990). Ontheotherhand,later
(
0.0 SSF study with long measurement time of 90 minutes
(Carilli & Holdaway1999) exhibits two clear turn-overs,
−0.2
one from the 3-D Kolmogorovturbulence (slope = 0.83)
0.0 0.5 1.0 1.5 2.0 2.5 3.0
tothe2-Done(slope=0.33),andtheotherfromthe2-D
PWV [mm]
one to the no-correlation regime (slope = 0). SSFs with
two turn-overshas never been obtainedin the statistical
Fig.3.—Fitted slopesof thespatial structurefunctions (SSFs)
as afunction of PWV.(a) Slopes forthe data points ineach SSF study by Sramek (1990), suggesting that SSFs with two
withthebaselinelengthsshorterthan500m,and(b)longerthan1 turn-overs are statistically rare, the coverage of the ar-
km. Symbolsaredifferentiatedwiththefrequencybands;diamond, rayconfigurationwasnotwideenoughtoinvestigatethe
triangle, square, and circle symbols indicate the data taken with
fullrangeoftheatmosphericturbulence,orthemeasure-
Bands 3, 6, 7, and 8, respectively. Filled symbols are the data
before the WVR phase correction, and open symbols after. Note ment time was not long enough. Note that we took one
that (a) includes the 2012−2014 data, but (b) only includes the 90minuteslongdata(see“uid A002 X8e1004 Xfe5”in
2014data, forthereasonsameasinSect. 3.1.
Table 5), but this data set did not show two turn-overs
asCarilli & Holdaway(1999),butshowedsimilarfeature
plotted in Fig. 3; (a) is for the shorter baseline slopes, as the 30 minutes long data taken in the same day.
and (b) for the longer baseline slopes. For PWV < 1 mm, the average of the slope at longer
In Fig. 3(a), there is no significant trend either as a baselines is much smaller than that for the shorter base-
function of PWV, frequency, or the effect of the WVR lines, but the scatter of the slope is large (Table 1), and
phase correction. The fitted slopes before and after the the highest values of the slope are almost the same as
WVR phase correction with averaging all the data, and that of the shorter baselines. This means that there are
that with PWV lower and higher than 1 mm are shown somecasesthatdonothaveanyturn-over;anexampleis
inthetoprowofTable1. Allthosevaluesarearound0.6, showninFig.2(b). AsmentionedinSect.3.1,atthislow
indicatingthattheWVRphasecorrectionortheamount PWV range, the improvement factor of the WVR phase
of water vapor in the atmosphere does not change the correction is not high, suggesting that the phase fluctu-
shorter baseline slopes of SSFs. The averageslope with- ation is not due to water vapor but caused by another
outtheWVRphasecorrectionof0.65±0.06isconsistent constituent, the same conclusion as above (Sect. 3.2.1).
with the 50% quartile slope for the 3-year (1996 July – For PWV > 1 mm and without the WVR phase cor-
1999 March) statistical data using the site testing 11.2 rection, the slopes are always small (small values with
GHz radio seeing monitor of 0.63 (Butler et al. 2001). small scatter; Table 1), but after the WVR phase cor-
This indicates that the data we took are typical phase rection, both the slope and the scatter are large. This,
fluctuation characteristics at the ALMA site. togetherwiththeimprovementfactoroftheWVRphase
Fig. 3(b) clearly shows that the slopes at longer base- correctionmentioned above (Sect. 3.1), indicates that in
lines (baseline length > 1 km) are shallower than the many of the casesthe slopes turn to be steeper after the
shorter baselines (baseline length < 500 m; Fig. 3a) in WVR phase correction for the longer (> 1 km) base-
most cases. Similar to the above, the fitted slopes are lines. For some cases, the slopes become similar to the
shownin the bottom rowof Table 1. The averageslopes
6 Matsushita et al.
n]104 hn]104
o (a) atro
nticr103 s Pmic
F Consta500 m) [m111000012 RMS ExcesL = 10 km [110023
SS(BL < 1100−−21 Estimated ength at B1010.0 0.5 1.0 1.5 2.0 2.5 3.0
]104 L PWV [mm]
n
(b)
tro103 Fig.5.— Estimated rms excess path length of each data set
nc
tami102 mtaeknetnioinne2d01in4Saetcat.b3a.s2e.l2i,newlheinchgthrooufgh10lykrmepuressinengttshtehfietrtmedsreexscuelstss
onsm) [101 pfiatttihnglernegstuhltesvfeonrltohnegeersttihmaante1d0rkmms.eSxocleidssapnadthdalsehnegdthlinbeesfoarreeatnhde
F C1 k100 acoftleorrsthareeWthVeRsapmheasaescinorFreigct.i3o.n, respectively. Symbols and their
S
S >10−1 3.2.4. Phase Fluctuation on 10 km Baselines
L
B10−2 Tounderstandquantitativelyhowmuchphasefluctua-
( 0.0 0.5 1.0 1.5 2.0 2.5 3.0 tion exists at long baselines, we calculate the rms excess
PWV [mm] path length for the baseline length at 10 km. Although
the averaged slope at baseline lengths longer than 1 km
Fig.4.— Fitted structure constants of SSFs as a function of is around 0.2−0.3 (see Sect. 3.2.2), the slope at base-
PWV. Symbols and their colors are the same as in Fig. 3. (a) line lengths longerthan 10 km is expected to be close to
StructureconstantsforthedatapointsineachSSFwiththebase-
linelengthsshorterthan500m. Solid[braw=(0.3±0.1)×PWV+ zero, namely no increase of the rms excess path length
(0.1±0.1)] and dashed [bwvr =(0.3±0.1)×PWV−(0.2±0.1)] (Carilli & Holdaway1999). Thereforeitisexpectedthat
linesarethefittingresultsforthedatabeforeandaftertheWVR the rms excess path length at 10 km is roughly equal to
phase correction, respectively. (b) Structure constants for the the rms excess path length longer than 10 km. Here, we
data points in each SSF with the baseline lengths longer than 1
km. Solid [braw = (0.9±0.3)×PWV+(0.8±0.4)] and dashed estimate the rms excess path length at 10 km using the
[bwvr =(0.5±0.2)×PWV+(0.8±0.3)]linesarethefittingresults fittingresultsderivedintheprevioussubsection. Thisin-
for the data before and after the WVR phase correction, respec- formationwill be useful for high frequency observations,
tively. or future extended-ALMA (Kameno et al. 2013), which
slope at shorter (< 500 m) baselines, namely SSF being is to extend the maximum baseline lengths longer than
similarto the one with no turn-over,suggestingthat the thecurrentALMA(>16km),orVeryLongBaselineIn-
WVRphasecorrectiontookoutallthephasefluctuation terferometry(VLBI) observations,whichwillhavemuch
caused by water vapor, and that causedby another con- longer baseline lengths (>100 km).
stituent remains. This means that if we can completely Using Eq. (2) to fit the data with baseline lengths
remove the phase fluctuation due to water vapor in the longer than 1 km, we estimated the rms excess path
atmosphere,alarge-scaleturbulentcomponentthatcov- length at a baseline length of 10 km. Fig. 5 displays the
ers the longest baseline lengths is revealed. This also estimated rms excess path length at a baseline length of
means that phase fluctuation due to the large-scale tur- 10 km as a function of PWV for both before and after
bulent component is inherently smaller than that due to the WVR phase correction. As expected from a weak
water vapor. correlation between the structure constant b and PWV,
both data set show a weak correlation with PWV (see
3.2.3. Constants for the Spatial Structure Functions
the solid and dashed lines for the fitting results); lower
Figs. 4(a) and (b) display the derived structure con- PWV conditions tend to have smaller rms excess path
stantsbinEq.2asafunctionofPWVforbaselinelengths length,andoppositefor higherPWVconditions. This is
shorter than 500 m and longer than 1 km, respectively. understandable since a larger amount of water vapor in
For both cases, there is a weak correlation between the the atmosphere provides a greater possibility for larger
structure constants and PWV for both before and after phase fluctuations caused by increased differences in the
the WVR phase correction (the solid and dashed lines, water vapor content over the array. On the other hand,
respectively in Fig. 4). the scatter is large, almost an order of magnitude at a
With the average slope a in Table 1 and the fitted given PWV ranges, which makes the correlation weak.
resultsofthe structure constantbin Fig.4,it is possible This indicates that the phase fluctuation cannot only be
to estimate the rms excess path length on any baseline the fucntion of the total water vapor content in the at-
length for the current ALMA (i.e., baseline length up mosphere.
to 15 km). Note that the scatter is large so that this Foralmostallthedata,thereisasignificantrmsexcess
estimationisusefulonlytotellthetendencyofthephase pathlengthaftertheWVRphasecorrection,withamean
fluctuation. value of 206 µm even at PWV < 1 mm. This result in-
Atmospheric Phase Characteristics of ALMA Long Baseline 7
dicates that evenafter the WVR phase correctionunder sphere absorbs the amplitude of electromagnetic waves
goodweatherconditions,peak-to-peakphasefluctuation significantly(Ray1972;Liebe1989;Liebe et al.1991)at
reaches around 2π or more at the high frequency bands continuum level. This changes the line profile of the wa-
(i.e.,Bands9&10;600−1000GHzor300−500µm)over ter vapor in the atmosphere, so that the WVR phase
∼10minutetimescales. Thisphasefluctuationblursthe correction, which uses the liquid water-free line profile
final synthesized image, with the blurring size around model, will no longer be appropriate (Matsushita et al.
twicethe synthesizedbeamsizeormore,significantlyaf- 2000; Matsushita & Matsuo 2003). Therefore if liquid
fectstheimagingquality,ifwecalibratethephaseatthe water dominates the atmosphere, then the rms phase
same frequency. One way to mitigate the 2π ambigu- after WVR phase correction will not improve or will
ityprobleminthephasecalibrationistouseacalibrator even be worse. Since we are looking for the cause of
phaseatlowerfrequencyandtoapplythesolutionstothe the remaining phase fluctuation after successful WVR
targetathigher frequency, i.e., band-to-bandphase cali- phase correction, liquid water cannot be the cause. Wa-
brationand/or using the fast switching phase correction ter ice in the atmosphere, which is not detected by the
method. The formerphasecalibrationtechnique hasan- WVR,caninducesimilarphasefluctuationstowaterva-
other advantage in ALMA; because the arraysensitivity por (Hufford 1991; Liebe et al. 1993). Density fluctua-
is higher at lower frequencies, fainter phase calibrators tions of a dry component (i.e., N and O ) in the at-
2 2
are available at lower frequency even though the ther- mosphere could also be the cause of phase fluctuations
mal noise in phase is scaled up with the frequency ratio. (Nikolic et al. 2013). Both water ice and a dry compo-
This leads another advantage of the availability of the nent have a high scale height of around 10 km or more,
phase calibrator;it becomes easierto find a closer phase so that the SSFs with no turn-over can be explained by
calibrator to a science target source. The fast switching these constituents. Although it is not clear whether the
phase correction is further discussed in Sect. 3.4. water ice always exists in the atmosphere, and the den-
sity fluctuations are still not confirmed observationally,
3.2.5. Why Does the WVR Phase Correction Not Take Out
those two atmospheric components could potentially be
All the Phase Fluctuation?
the causes.
In most cases, the main difference between SSFs with Instrumentation problems could also be a possibility;
and without the WVR phase correction is the reduc- since the SSF is baseline-based, instruments that could
tion in the absolute rms phase (rms path length) val- cause baseline-based problems needed to be considered.
ues (Fig. 1a), whereas the overall shapes and slopes do The correlator is one of the baseline-base instruments,
not change significantly with the WVR phase correc- but it is very unlikely that this could produce larger
tion (Fig. 2a) andare only weakly correlatedwith PWV phase fluctuation selectively at longer baselines all the
(Fig. 5). The WVR phase correction improves the rms time, because the correlation process after analog-to-
path lengths by a factor of 2 on average (Sect. 3.1). If digitalconversionofthe receivedsignalsateachantenna
the WVR phase correction takes out all the phase fluc- is highly digitized. The Line Length Corrector (LLC;
tuation, the resultant spatial structure function should round-tripphasecorrector)isaninstrumentthatcancre-
exhibitanalmostflatfeature;sincethe WVRphasecor- ate phase noise as a function of baseline length; noise in
rectionis applied to the data every1 second, if the wind thisinstrumentalcomponentcausesantenna-basedphase
blows along a baseline with a velocity of 10 m s−1 and noise, but the atmospheric phase fluctuation is baseline-
assuming a frozen phase screen, then the phase at the based, so that the relative effect of LLC phase noise is
baselines longer than 10 m should show random phase larger for shorter baselines and smaller for longer base-
that correspondsto the thermalnoise of the WVRs. We lines, namely it appears as baseline-based. However,the
haveneverobservedsuchaSSFinthe last5yearsofthe variation of the LLC in each antenna is always moni-
longbaselinecampaigns(seealsoMatsushita et al.2012, tored, and the timescale of the variation is much longer
2014, 2016). The overall similarity between the SSFs thanthe observedphase fluctuation. This indicates that
with and without the WVR phase correction suggests the LLCs are unlikely to cause the phase fluctuation.
that the origin of the phase fluctuation is not only due
3.3. Coherence Time
tothewatervaporbutalsootherturbulentconstituents.
Furthermore, SSFs without any turn-over also suggests The temporal coherence function is defined as
the existence of other turbulent constituents with scale
T
height larger than the longest baseline length of ∼ 10 1
C(T)=(cid:12) exp{−iθ(t)}dt(cid:12), (3)
km, as mentioned above (Sect. 3.2.1, 3.2.2). (cid:12)T Z (cid:12)
The cause of this remaining phase fluctuation is still (cid:12) 0 (cid:12)
(cid:12) (cid:12)
unclear: Turbulent eddies excited by wind blowing over where θ(t) is phase(cid:12)at a time t and T is(cid:12) an arbitrary
the mountains can cause additional phase fluctuation. integration time (Thompson et al. 2001). This equation
Indeed, some raw data show this effect, especially data isnamelyavectoraveragingofphaseinthetimedomain.
fromantennasnearmountains,butthephasefluctuation A coherence of unity means no loss in coherence (i.e.,
causedbythiseffectcanbecleanlyremovedbytheWVR amplitude)duetothephasefluctuation,andthatofzero
phase correction (Asaki et al. 2016). Therefore this ef- meansnocoherenceatalldue tohugephasefluctuation.
fect cannot be the cause of the remaining phase fluctua- Coherencetime is a maximum T at which the coherence
tion. Theremainingphasefluctuationcanalsobedueto is not smaller than a certain critical value; since phase
wind speed or its direction parallel or perpendicular to fluctuation increases as time passes from a certain time,
baseline directions. This will be discussed in the forth- coherence decreases.
coming paper (Maud et al., in prep.), so that we do not Coherence time is closely connected with an integra-
discuss here. Liquid water (fog or clouds) in the atmo- tion time for one data point for radio arrays; if one can
8 Matsushita et al.
1000 a median value of the coherence time derived from the
(a)
data at baseline lengths longer than 1 km. Here, we cal-
]
s culatethecoherencetimethatdegradesthecoherenceto
[
me 100 0.9 (i.e., coherence loss of 10%). The calculation results
Ti are shown in Fig. 6 as a function of PWV. Each calcu-
e lationstops at the time rangeof 400s, since ALMA will
c
n not calibrate phase on such long timescales. So the data
e 10
r points located at 400 s means that these did not reach
e
h the coherence loss of 10% even after 400 s. It is obvi-
o
C ous that the data after the WVR phase correction have
1 longer coherence time than that without. The average
1000 of the coherence time after the WVR phase correction
(b) is 184 s, about twice longer than that without (101 s).
s] This indicates that the WVR phase correction improves
[
e the coherence time by about twice or more (since our
m 100
calculation stops at 400 s, the coherence time is under-
Ti
e estimated, especially for the WVR phase corrected data
c with the time longer than 400 s). The WVR phase cor-
n
e 10 rection is therefore useful for extending integration or
r
he calibration time interval.
o In terms of overall PWV dependency of coherence
C
1 time,thereisaweaktrendforlowerPWVtogiveriseto
0.0 0.5 1.0 1.5 2.0 2.5 3.0 longer coherence time. This can be understood as more
PWV [mm] watervapor inthe atmosphere,causingmorephasefluc-
tuationandthereforelargercoherenceloss. However,the
Fig.6.— Coherence time that lead to a degraded coherence of scatterisverylarge,morethananorderofmagnitudeof
0.9(i.e.,coherence lossof10%) as afunction of PWV.Each data
coherencetime ata certainPWV,suggestingthatphase
pointintheplotisamedianofthecoherencetimeofeachbaseline
with its length longer than 1 km in each data set. (a) The data fluctuationis notasimple functionofthe amountofwa-
before the WVR phase correction, and (b) after. Colors for the ter vapor in the atmosphere. This result is the same
symbolsandthefittedlinesaredifferentinbands;black,blue,red, as Sect. 3.2.4, since we are showing the same data with
andgreenareforBands3,6,7,and8data,respectively. Thereis
different relationship.
no fitted line for Band 8, since there are not enough data points.
SymbolsarethesameasinFig.3. Thetrendappearstodependonfrequencyband;Band
3 has larger scatter with less dependence on PWV, but
tolerate a certain coherence loss, one could define the Bands 6 and 7 have smaller scatter with tight depen-
integration time based on the coherence time. This is dence on PWV (see the fitted lines in Fig. 6). This can
also true for the calibration time interval; for a typical be explained as follows; observations at Band 3 can be
interferometricobservation,aphasecalibratorwillbeob- carried out under a wider range of PWV, but for Bands
served at certain time intervals, and if one can tolerate 6 and 7, the observationconditions are limited to better
a certain coherenceloss, one could define the calibration weather and the phase fluctuation quickly gets worse as
time interval based on the coherence time. weather conditions get worse.
In addition, this is also relevant for the integration
3.4. Fast Switching Simulation
time of VLBI; for detecting interferometric signals (i.e.,
fringes) with VLBI, it is important to have high signal- Thefastswitchingphasecorrectionmethodistoswitch
to-noise ratio within one data point, since it is needed betweenthesciencetargetsourceandanearbycalibrator
to searchthe signalinthe rangesofdelay anddelayrate quickly (faster than a time scale on which the phases of
due to uncertainty in the antenna locations (i.e., fringe boththetargetandthecalibratordifferfromeachother),
search). On the other hand, since the atmosphere will and calibrate the phase fluctuation (Carilli & Holdaway
affect the VLBI phase stability significantly, we should 1999; Morita et al. 2000; Asaki et al. 2014, 2016). The
be careful in selecting the integration time for VLBI ob- importanceofthismethodisnowbetterunderstoodthan
servations, especially in mm/submm wave. The coher- itwasinthepast. Thisisbecausenomatterwhatcauses
ence time is a good indicator of ideal integration time thephasefluctuation,thismethodcanimprovethephase
forthesignaldetectionwithVLBI.Thisinformationwill stability to cancel out not only the atmospheric phase
be useful for VLBI using single dish telescopes close to fluctuations,butalsotheinstrumentalphaseerrors,such
ALMA, namely APEX and ASTE. Furthermore, VLBI as a frequency standard, which the WVR phase correc-
usingALMA(ALMAPhase-UpProject),whichistoadd tion cannot remove. Compared with the WVR phase
signals from the ALMA antennas in phase in real time correction method, which takes out shorter time scale
to produce a single VLBI “station”, or so-called phased phase fluctuation (order of ∼ 1 second to ∼ 1 minute
array, needs stable atmospheric phase to obtain high ef- scale), the fast switching phase correction method takes
ficiency in adding in phase. The coherence time is also outlongertimescalephasefluctuation(tensofsecondor
goodtofindouttheidealdataaddingtimelengthinreal longer). Combiningthose twomethods, it is expectedto
time to have high efficiency for phase-up. take out a significant amount of phase fluctuation, and
Since the phase fluctuation depends on the baseline improve the data quality significantly.
length, but the slope will be significantly shallower at Using the single source stare data taken in 2014, it is
baselinelengthslongerthan1km(seeSect.3.2),wetake possible to simulate the fast switching phase calibration
Atmospheric Phase Characteristics of ALMA Long Baseline 9
1.0
TABLE 2
Time distribution of the cycle time forthe 0.9
fastswitching simulation.
0.8
e
CycleTime Target Calibrator AntennaSlew c
n 0.7
[s] [s] [s] [s] e
r
28 15 5 4 he 0.6
48 30 10 4 o
68 45 15 4 C 0.5
0.4
by separating the data into “target”, “calibrator”, and
“antenna slew time” components, and making an image 0.3
0 20 40 60 80 100 120 140
forthe “target”(calibratedusingthe “calibrator”data).
Comparingthepeakfluxofthecalibrated“target”image Cycle Time [s]
with that of the self-calibrated image, namely calculat-
ing the coherence of the data, it is possible to estimate Fig. 7.— Plot of coherence as a function of fast switching cy-
cle time for the simulated fast switching method using the single
the effect of the fast switching phase correction method
sourcestaredata(opensymbols). Solidlinesshowthelinearfitting
quantitatively by changing the cycle time (i.e., time for resultsofeachdatawithdifferentcycletime. Wealsooverplotted
“calibrator” → “target” → “calibrator,” including the thecoherencetimecalculationresultsusingthesamesinglesource
antenna slew time between the calibrator and the tar- stare data as the fast switching simulation data, but for the data
pointswiththebaselinelengthslongerthan1km(filledsymbols).
get). This simulationis anidealizedcase,since the “tar-
Dashedlinesarethelinearfittingresultsofeachdatawithdifferent
get” and the “calibrator”do have the same atmospheric coherencetime. SymbolsarethesameasinFig.3. Colorsforthe
phasefluctuationinthissimulation,whichisnottruefor symbolsandthefittedlinesarethesameasinFig.6.
the real case; it depends on the separation between the
WealsooverplotinFig.7(filledsymbols)coherenceas
“target” and the “calibrator” (Asaki et al. 1996, 1998).
afunctionofcoherencetime,whichiscalculatedasinthe
Thissimulationisnonethelessusefulfortestingtheeffect
previoussubsection (Sect. 3.3), using the same data sets
of cycle time.
as the fast switching simulation. Here, we set coherence
In this paper, we simulated three cycle times: 28 s,
to be the same as that of the fast switching simulation,
48 s, and 68 s (see Table 2). In all cases, we used an
and estimated coherence time. This will be useful once
integration time for the target of three times the inte-
we know the difference between the coherence time and
gration time for the calibrator and a slew time of 4 s,
the simulated fast switching results, since the coherence
which are reasonable for the actual observational setup.
time is easily calculated from the quick-look data (i.e.,
Note that the simulated observations always start from
datatakenforashorttime,aminuteortwo,tocheckthe
and end with the phase calibrator scan.
quality of observationalconditions), and it is possible to
We then calibrated the “target” data with the “cali-
apply to the actual observations. The relation between
brator” data, and imaged the “target” using the CASA
coherence and coherence time is linear, and the fitting
software and a standard interferometric imaging proce-
results are plotted in dashed lines. Comparisonbetween
dure. We alsoproducedthe self-calibratedimage for the
the results of the fast switching calculations (open sym-
“target”, and we used this image as a reference to com-
bols) and that of the coherence time calculations (filled
parethepeakfluxofthesimulatedimage. Thecoherence
symbols)showsthatthecoherencetimeisalmostalways
of the fast switching method is estimated by calculat-
about 40-50% longer than in the fast switching simula-
ing the ratio of the peak flux densities between the fast
tion. This means that if we estimate the coherence time
switching simulation image and the self-calibrated one.
from the quick-look data, then the recommended cycle
The results of the simulation — coherence as a func-
time of an observation with fast switching will be about
tion of cycle time for various frequency bands (Bands 3,
40-50%shorter.
6, 7, and 8) are shown in Fig. 7. We also overplotted
linear fitting results of coherence as a function of cycle 4. SUMMARY
time as solid lines. It is obvious that longer cycle time
UsingsinglesourcestaredatatakenduringtheALMA
lead to lower coherence. In addition, the decrease of
longbaselinecampaignscarriedoutoverthepast6years,
coherenceasa functionof cycletime appearsalmostlin-
with baseline lengths of up to ∼15 km, we derived vari-
ear. Thisindicatesthatfastswitchingwithshortercycle
ous atmospheric phase characteristicsthat will be useful
timescouldleadtohigherqualityimages. Thisistrueir-
for the ALMA long baseline (and high frequency) obser-
respectiveoffrequencybandandweatherconditions. On
vations. The summary of our study is as follows:
the other hand, since we did not consider the separation
between the “target” and the “calibrator” as mentioned • The183GHzWVRphasecorrectionmethodworks
above, this linear increase of the coherence as a shorter wellforreducingthephasefluctuationatlongbase-
cycle time will be non-linear or even stop at some point lines,especiallyforweatherconditionswithprecip-
in the case of a real observation, due to the different itable water vapor (PWV) larger than 1 mm.
atmospheric conditions toward these two sources. The
point at which this happens may highly depends on the • The WVR phase correction lengthens the coher-
separation between the “target” and the “calibrator,” ence time by about a factor of two or more, indi-
and the actual observational testing of the fast switch- cating thatthe WVR phasecorrectionis usefulfor
ing phase correction method using ALMA is currently lengtheningtheintegrationtimeand/orcalibration
ongoing (Asaki et al. 2014, 2016). time interval.
10 Matsushita et al.
• The WVR phase correction, however, could not 1 mm (no large difference for the data before and
take out all the phase fluctuation, suggesting that after the WVR phase correction), and increases as
there are other reasons that cause phase fluctua- afunctionofPWV.Thisvalueissignificantforthe
tion at millimeter and submillimeter wavelengths. high frequency observations, and strongly suggest
Combining other phase correction methods in ad- to use other phase correction method, such as the
dition to the WVR phase correction is important, fast switching and/or band-to-band phase correc-
suchasthefastswitchingphasecorrectionmethod. tion methods.
• Indeed, our simulation of the fast switching phase
correction method shows an improvement in the
coherenceofthedata,especiallywithshortercycle This paper makes use of the following ALMA data:
time than a few minutes. ADS/JAO.ALMA#0000.0.00341.CSV.ALMA is a part-
nership of ESO (representing its member states), NSF
• Most of the spatial structure functions (SSFs) of
(USA) andNINS (Japan),together withNRC (Canada)
the data show one turn-over around a baseline
and NSC and ASIAA (Taiwan), and KASI (Republic
length of 1 km. This result suggests that the scale
of Korea), in cooperation with the Republic of Chile.
heightoftheturbulentconstituentisaround1km,
The Joint ALMA Observatory is operated by ESO,
consistent with the distribution of water vapor.
AUI/NRAO and NAOJ.
Combinedwiththe successofthe WVRphasecor-
We express our gratitude to all the ALMA members
rection, it is obvious that the main turbulent con-
for the support of the long baseline campaigns. SM and
stituent is water vapor in the atmosphere.
YA thank the Joint ALMA Observatory (JAO) for sup-
porting our visit to ALMA as Expert Visitors in 2013
• The fitted slopes indicate that most of the phase
and 2014. SM and YA also expresses their apprecia-
fluctuation at baseline lengths shorter than 1 km
tionstotheNationalAstronomicalObservatoryofJapan
shows the intermediate value of theoretical 3-D
(NAOJ)fortheirsupportsfortheirstaysinChilein2012
and 2-D Kolmogorovturbulence (i.e., around 0.6),
– 2014. SM is supported by the National Science Coun-
and that at baseline lengths longer than 1 km
cil (NSC) and the Ministry of Science and Technology
displays the intermediate value of theoretical 2-
(MoST) of Taiwan, NSC 100-2112-M-001-006-MY3 and
D Kolmogorov turbulence and no correlation (i.e.,
0.2−0.3). MoST 103-2112-M-001-032-MY3. LM and RT are part
oftheDutchALMAARCnode,Allegro,whichisfunded
• There are a few cases that do not show any turn- by the Netherlands Organisation for Scientific Research
over. Such SSFs are only obtained under very low (NWO).
PWV conditions, when the improvement factor of We deeply regret the loss of our colleague, Koh-Ichiro
the WVR phase correction is not high, or after Morita, who lost his life on May 7th, 2012, at Santiago,
the WVR phase correction. This suggests that the Chile. He significantly helped not only this work but
mainturbulentconstituentinthesecasesisnotwa- alsoforvariousworksintheALMAproject,andwithout
ter vapor, and that the phase fluctuation caused him,wecouldnotachievetheseresults. Furthermore,he
by this constituent is inherently smaller than that taught S.M. the basic and application of interferometry,
caused by water vapor. The scale height of this phase correction methods, and site testings since S.M.
constituent is higher than 10 km, suggesting that was a graduate student at the Nobeyama Radio Obser-
water ice or a dry component (N or O ) can be vatory. Without his guidance, S.M. could not be at the
2 2
the cause of the phase fluctuation. current position. Morita-san, we really miss you...
• Excesspath lengthfluctuationat abaseline length
of10kmislarge,∼200µmevenatPWVlessthan
APPENDIX
DATA LIST
Here, we present the list of the data used in this study. Data for the longest baseline lengths of 2 km, 3 km, and
10−15 km are shown in Tables 3, 4, and 5, respectively.
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