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