Post on 01-Jun-2020
VLBIVery Long Baseline Interferometry
Yasuhiro KoyamaSpace-Time Standards Group, NICT
Kashima Space Research Center
34-m antenna
VLBI Network of NICT
What is VLBI?Very Long Baseline Interferometry
Measure time delay
Receivingradio signalsat 2 stations
VLBI stands for,
• Very Long Baseline Interferometry= Technique
• Very Long Baseline Interferometer= Instrument
VLBIRadioTelescopeConnected
Array
GeodesyAstronomyAstrometry
Hubble Space Telescope(2.4m)
~0.05 arcsec6cm Telescope~1.93 arcsec
Naked Eyes~1arcmin
Principle of ResolutionResolution = Ability to see fine features.
∝ λ/D
http://ja.wikipedia.org/wiki/%E3%83%95%E3%82%A1%E3%82%A4%E3%83%AB:Moon.jpg
Radio Telescopes
Arecibo Telescope : D = 305mλ/D = 28 arcsec (λ=4cm)
Very Large Array : D = 21kmλ/D = 0.07 arcsec (λ=7mm)
Interferometry
http://www.aoc.nrao.edu/intro/vlapix/vlaoverall.html
Precise determination of time delay between two separated antennas was made possible by atomic clocks and high volume data recorders.
Time Delay
Baseline
Correlator
H-maserH-maser
RecorderRecorder
Baseline
Time Delay
Signals from a Quasar
PreciselySynchronized
Time Delay
A/DA/D
Invention of Atomic Clocks Enabled VLBI
Interferometry
Laser
Interferometric Pattern = Fringe
Thin slits
Geometry of Radio Interferometry
θ
Station X Station Y
Additional Path Length (D cosθ = − D· is)
cgsiD ⋅−=τ
Geometrical Delay
D
si
D si c: Baseline Vector : Unit Vector to the Source : Speed of Light
= (D cosθ) / c
相関処理
相関係数X局
Y局
(似ている度合い)
少しずつずらす
Determination of Geometrical Time Delay
Cross Correlation Function
Station X (Reference)
Station Y
AdjustingShifts
Correlation Factor
Simplified Model of Interferometry
X局での受信信号
Y局での受信信号
雑音信号
雑音信号電波星からの信号 遅延回路
τ
x(t)
y(t)
s(t)
s'(t)
n (t)x
n (t)y
s(t)
Spectrum Domain
)()()()()()(
fNfSfYfNfSfX
y
x
+′=+=
=s(t-τg)
gfiefSfS τπ2)()( −=′
g
Signal from the radio source
Delay
Received signalat station X
Received signalat station Y
NoiseNoise
Expressions with equivalent temperature
)()()(
)()()(
fnTfsTfY
fnTfsTfX
ynyay
xnxax
+′=
+=
nynx
ayax
TT
TT
,
, Equivalent Temperature of Received Signal
Equivalent Temperature of Noise at Stations
where,
Cross Correlation FunctionIn the case of no frequency conversion, cross correlation spectrum is
)()()()(
)()()()(
)()()(
**
**
*
fnfnTTfsfnTT
fnfsTTfsfsTT
fYfXfC
yxnynxxaynx
ynyaxayax
xy
+′+
+′=
=
Three terms from the second term decrease with integration time.
g
g
fiayax
fiayaxxy
eTT
efsTTfCτπ
τπ
2
22)()(
=
=
∫∞
∞−= dfefCc fixyxy
τπτ 2)()(
By Inverse Fourier Transform, the cross correlation function becomes
If we limit integration of frequency to certain band (f0~f0+B),
)()(sin
)})(2cos{(2
)(2cos2
}2sin2sin
2cos2{cos2)(
0
0
0
0
0
g
g
gayax
Bf
f gayax
g
Bf
f gayaxxy
BB
BfTTB
dffTT
dfff
ffTTc
ττπττπ
ττππ
ττπ
τπτπ
τπτπτ
+
+⋅
++=
+=
⋅−
⋅=
∫
∫
+
+
-τg
By assuming f0 = 0,
B1cosπB(τ+τg)
sinπB(τ+τg)πB(τ+τg)
Radio Source : 0059+581Flux Density : 3.4 JyIntegration Time : 90 sec. SNR : 20.2BW : 2MHzStation 1 : Kashima(34m)Station 2 : Westford (18m)
SNR= 2B t Ts1Ts2
Ta1Ta2π
2
Wider bandwidth(B) leads to
Sharp Peak ⇒ Precise Delay
Large SNR ⇒ High Sensitivity(ability to detect faint objects)
Improvement of delay precision by using multiple frequency channels
Frequency
Phase
derivative = delay
Example of frequency assignments(better to assign channels near edges)
S-Band(MHz)2154.992164.992234.992294.992384.992414.99
X-Band(MHz)7714.997724.997754.997814.998034.998234.998414.998524.998564.998584.99 Spacing = 10 30 60 120 200 180 110 40 20 MHz
Spacing = 10 70 60 90 30 MHz
Fine Correlation Function after Bandwidth Synthesis (X-band)
Fine Resolution Correlation Function
Evaluation of various errorsSignal to Noise Ratio BTSNR 20ρ=
SNR1
=φσFringe Phase Error
SNRBs ⋅=
πστ
3Error of Coarse Delay
Error of Bandwidth Synthesis Delay SNRf
m ⋅=
πσστ 2
1
∑=
−=N
nnf ffNN 1
2)(1σEquivalent Bandwidth
SNRfT ⋅=
πστ
3&Error of Delay Rate
Reference point of Geodetic VLBI= Az Axis & El Axis Intersection
Station X Station YD
rx ry
τ1
θ1
Source 1
Source 2
Source 1cτ1 = D cos θ1 +rx−rycτ2 = D cos θ2 +rx−ry
Source 2
τ2
θ2
c (τ1−τ2 )D =cos θ1 − cos θ2
Least Square Estimate (Parameter Estimations)
τ1τ2τ3
τi
Observables
τ1τ2τ3
τi
Calculations
Theoretical Model
Δτ1Δτ2Δτ3
Δτi
min Σ (Δτi)2i
p1, p2, p3,・・・,pi , ・・・
Estimated Parameters (Coordinates of position, clock offset, atmospheric delay, ...)
Time Transfer by VLBI and GPS
VLBI
GPS
Space-VLBI
HALCA(Muses-B)Quasar 0637-752
NGC4261
High Angular Resolution VLBI Astronomy with Satellite VLBI Telescope HALCA
VLBI for Geophysics
鹿島
ハワイ
アラスカ
5700km5700km
5400km5400km
4700km4700km
鹿島-ハワイの基線長変化
-400
-200
0
200
400
1984 1986 1988 1990 1992 1994
年
基線
長(m
m)
アラスカ-ハワイの基線長変化
-400
-200
0
200
400
1984 1986 1988 1990 1992 1994
年
基線
長(m
m)
鹿島-アラスカの基線長変化
-400
-200
0
200
400
1984 1986 1988 1990 1992 1994
年
基線
長(m
m)
-63.5 ± 0.5 mm/year
-46.1 ± 0.3 mm/year
1.3 ± 0.5 mm/year
Kauai
Fairbanks
Kashima
Kashima-Kauai Baseline Length
Fairbanks-Kauai Baseline Length
Kashima-Fairbanks Baseline Length
VLBI at Opening Ceremony of International Year of Astronomy
(January 15, 2009)
30
China-Japan Collaboration for VLBI• The first China-Japan VLBI experiment was
performed with Shanghai-Kashima Baseline in Sep. 1985
• Kashima is one of the most precisely determined positions in Japan : used as the reference point to establish Japan Geodetic Datum 2000 (JGD2000)
• Seshan (Shanghai) is the most precisely determined position in China
• Chinese Academy of Sciences and NICT are both active members of IVS*
余山(Seshan, Shanghai)
烏魯木斉 (Urumqi)
鹿島(Kashima)
* IVS=International VLBI Service for Geodesy and Astrometry
31
Eurasian Plate
Pacific Plate
North American Plate
Philippine Sea Plate
上海鹿島1876km
Measuring Earth with VLBI
Parameter Type VLBI GPS/GLON.
DORIS/PRARE
SLR LLR Alti-metry
Quasar Coord. (ICRF) XNutation X (X) X
Polar Motion
XUT1XLength of Day (LOD)
X X X XCoord.+Veloc.(ITRF) X X X X X (X)
Geocenter X X X XGravity Field X X X (X) X
Orbits X X X X XLEO Orbits X X X XIonosphere X X X X
Troposphere X X X XTime/Freq.; Clocks X X (X)
(X)
Gravity Field
XX X X X
Capabilities of Space Geodetic Techniques
ICRF
EOP
ITRF
IERS International Earth Rotation Service (1987~2000)
International Earth Rotation and Reference Systems Service (2001~)
• One of the services established under the IAG (International Association of Geodesy). There are other services including IVS and IGS.
• Missions of IERS are to determine and maintain – the International Celestial Reference System (ICRS) and its realization,
the International Celestial Reference Frame (ICRF),– the International Terrestrial Reference System (ITRS) and its
realization, the International Terrestrial Reference Frame (ITRF),– Earth orientation parameters required to study earth orientation
variations and to transform between the ICRF and the ITRF,– geophysical data to interpret time/space variations in the ICRF, ITRF
or earth orientation parameters, and model such variations,– standards, constants and models (i.e., conventions) encouraging
international adherence.
IERS Conventions • Published by IERS to define conventions
(standard models and values, procedures for calculations, etc.)
– MERIT Standards : 1983MERIT=Monitoring Earth Rotation and
Intercomparison of Techniques– IERS Standards : 1989, 1992– IERS Conventions : 1996, 2003
• Conforms to recommendations and decisions of international organizations like IAU and IAG(IUGG).
Reference System and Reference FrameReference System : DefinitionReference Frame : Realization
ICRS International Celestial Reference System
ITRS International Terrestrial Reference System
ICRF92
ICRF [WGRF]
ITRF97
ITRF2000WGS84
Japan GeodeticSystem 2000
EOP/ERP
Reference Frames and Earth Orientation Parameters
ICRF International Celestial Reference Frame
ITRF International Terrestrial Reference Frame
EOPEarth Orientation Parameters
VLBI, GPS, SLR
VLBI, (GPS), (SLR)
VLBI
UT1-UTC and LOD (Length Of Day)
UT1-TAI and UTC-TAILOD
LOD : can be determined by GPS, SLR, and VLBIUT1-UTC : can be determined by VLBI
Time ScalesInternational Atomic Time (TAI)Determined by an ensemble of cesium oscillators (>300)SI standard second 9,192,631,770 oscillations of the cesium atomOrigin defined TT + 32.184 s at 0h 1 January 1977Astronomical time (UT1)Measured by angle between zenith meridian at 0° Lon. and “mean” sunDrifts slowly with periodic variations from TAIUT0 = value before polar wobble correctionUT2 = value after seasonal variation correctionUniversal Coordinated Time (UTC)Runs at the same rate as TAIOrigin is 0h 1 January 1972, 10 s behind TAIOccasional insertions of a leapsecond to keep -0.9sec
UT1-UTC estimation from VLBI and GPS
Markus Rothacher, GeoForschungsZentrum Potsdam, IVS General Meeting 2006 (Jan. 2006)
Polar Motion / Wobble
Chandler Wobble : Periodic variation with the period of 435 daysAnnular Wobble : Periodic variation with the period of 1 year
0.1” = 3.09m
Long-time stability of scale determination
VLBI SLR
DORIS
Adjusted scale factors to construct ITRF2005(International Terrestrial Reference Frame).
s (mm) s (mm)
Markus Rothacher, GeoForschungsZentrum Potsdam, IVS General Meeting 2006 (Jan. 2006)
Definition and Realization
Definition RealizationTime TT (Terrestrial Time) TT (BIPMxx)
TAITerrestrial Coordinates ITRS ITRFCelestial Coordinates ICRS ICRF
ITRF(International Terrestrial Reference Frame)
• ITRS : Definition (System)– Geocentric : center of mass of whole earth, including oceans and atmosphere.– Unit of length is SI metre based on TCG time coordinate. – Orientation initially given by BIH orientation at 1984.0.– Time evolution of orientation : no-net-rotation condition with tectonic motions
• ITRF : Realization (Frame)– Latest realization : ITRF2005– Combined from VLBI, SLR, GPS and other space geodetic measurements
ITRF2000Coordinates of Fiducial Sites in Japan(epoch = 1997.0)
KASHIMA -3997892.269 3276581.278 3724118.233 0.002 0.002 0.003
KASHIMA -3997649.227 3276690.754 3724278.825 0.003 0.002 0.003
KASHIMA -3997505.669 3276878.399 3724240.707 0.005 0.005 0.005
MIZUSAWA -3862411.906 3105015.030 4001944.890 0.031 0.027 0.031
MIZUSAWA -3857236.108 3108803.212 4003883.084 0.016 0.014 0.016
KOGANEI -3941937.446 3368150.894 3702235.314 0.009 0.010 0.009
MIYAZAKI -3582767.649 4052033.587 3369020.207 0.415 0.385 0.355
NOBEYAMA -3871168.560 3428274.280 3723697.866 0.244 0.216 0.222
USUDA -3855355.412 3427427.607 3740971.291 0.049 0.043 0.051
TSUKUBA -3957172.928 3310237.958 3737708.948 0.003 0.003 0.003
TSUKUBA -3957408.752 3310229.367 3737494.789 0.004 0.004 0.005
SHINTOTSUKA -3642141.822 2861496.647 4370361.932 0.648 0.550 0.692
SHINTOTSUKA -3642142.114 2861496.632 4370361.722 0.259 0.219 0.276
CHICHIJIMA -4489356.454 3482989.810 2887931.314 0.267 0.236 0.217
CHICHIJIMA -4490618.496 3483908.137 2884899.122 0.081 0.074 0.066
MINAMI TORI -5227446.489 2551379.698 2607604.995 0.036 0.022 0.022
SAGARA -3913437.574 3501122.887 3608593.441 0.708 0.490 0.641
MIURA -3976129.983 3377927.923 3656753.862 0.011 0.018 0.012
TATEYAMA -4000983.406 3375276.019 3632213.230 0.009 0.014 0.009
AIRA -3530219.389 4118797.596 3344015.918 0.137 0.134 0.119
SYOWA 1766194.139 1460410.951 -5932273.371 0.011 0.011 0.022
Site ID X (m) Y (m) Z (m) σx (m) σy (m) σz (m)
ITRF2000Velocities of Fiducial Sites in Japan
Site ID X (m/yr) Y (m/yr) Z (m/yr) σx (m/yr) σy (m/yr) σz (m/yr)
KASHIMA -0.0003 0.0052 -0.0118 0.0004 0.0003 0.0005
KASHIMA -0.0003 0.0052 -0.0118 0.0004 0.0003 0.0005
KASHIMA -0.0003 0.0052 -0.0118 0.0004 0.0003 0.0005
MIZUSAWA 0.0010 0.0038 -0.0027 0.0053 0.0046 0.0054
MIZUSAWA 0.0010 0.0038 -0.0027 0.0053 0.0046 0.0054
KOGANEI -0.0001 0.0061 -0.0111 0.0015 0.0026 0.0019
MIYAZAKI 0.0217 -0.0475 -0.0484 0.0452 0.0414 0.0378
NOBEYAMA -0.0470 0.0515 0.0305 0.0382 0.0339 0.0351
USUDA -0.0043 0.0048 -0.0051 0.0005 0.0005 0.0006
TSUKUBA -0.0012 0.0073 -0.0087 0.0005 0.0005 0.0006
TSUKUBA -0.0012 0.0073 -0.0087 0.0005 0.0005 0.0006
SHINTOTSUKA 0.0082 0.0134 0.0314 0.1007 0.0855 0.1076
SHINTOTSUKA 0.0082 0.0134 0.0314 0.1007 0.0855 0.1076
CHICHIJIMA 0.0306 0.0390 0.0126 0.0332 0.0296 0.0269
CHICHIJIMA 0.0306 0.0390 0.0126 0.0332 0.0296 0.0269
MINAMI TORI 0.0412 0.0612 0.0228 0.0077 0.0050 0.0051
SAGARA 0.0497 0.0228 -0.0348 0.1786 0.1232 0.1611
MIURA 0.0175 -0.0095 -0.0039 0.0026 0.0051 0.0033
TATEYAMA 0.0106 -0.0182 -0.0056 0.0020 0.0041 0.0023
AIRA -0.0011 -0.0161 -0.0417 0.0545 0.0536 0.0475
SYOWA 0.0038 -0.0015 -0.0015 0.0008 0.0008 0.0018
VLBI�Very Long Baseline InterferometryKashima Space Research CenterVLBI Network of NICTWhat is VLBI?�Very Long Baseline InterferometryVLBI stands for, スライド番号 6スライド番号 7スライド番号 8スライド番号 9Geometry of Radio Interferometryスライド番号 11Simplified Model of InterferometryExpressions with equivalent temperatureCross Correlation Functionスライド番号 15スライド番号 16スライド番号 17Improvement of delay precision by using multiple frequency channelsExample of frequency assignments�(better to assign channels near edges)Fine Correlation Function after Bandwidth Synthesis (X-band)Fine Resolution Correlation FunctionEvaluation of various errorsReference point of Geodetic VLBI�= Az Axis & El Axis IntersectionLeast Square Estimate (Parameter Estimations)スライド番号 25スライド番号 26スライド番号 27スライド番号 28スライド番号 29China-Japan Collaboration for VLBIスライド番号 31Measuring Earth with VLBIスライド番号 33IERS � International Earth Rotation Service (1987~2000)�International Earth Rotation and Reference Systems Service (2001~)IERS Conventions Reference System and Reference FrameReference Frames and Earth Orientation ParametersUT1-UTC and LOD (Length Of Day)Time Scalesスライド番号 40Polar Motion / WobbleLong-time stability of scale determinationDefinition and RealizationITRF �(International Terrestrial Reference Frame)ITRF2000�Coordinates of Fiducial Sites in Japan(epoch = 1997.0)ITRF2000�Velocities of Fiducial Sites in Japan