The Art and Technique of VLBI
5 km of VLBI tape (value $1000) on Onsala
control room floor due to incorrectly mounted
tape on drive while pre-passing tape in
preparation for a VLBI experiment.
VLBI Principle
Basic observable: time difference of signal arrival
Global VLBI Stations
Geodetic VLBI network + some astronomical stations
(GSFC VLBI group)
VLBA Station Electronics
At Antenna:
● Select right or left circular polarization
● Add calibration signals
● Amplify
● Mix with local oscillator signal to
translate frequency band down to
500 – 1000 MHz for transmission
In building:
● Distribute copies of signal to 8
baseband converters
● Mix with local oscillator in BBC to translate band to baseband (0.062 – 16 MHz)
● Sample (1 or 2 bit)
● Format for tape
● Record
● Keep time and stable frequency
Walker (2002)
Station Electronics: Feed Horn
1. Want linear field shape in aperture
for high polarization purity, but modes in
circular waveguide are not linear.
So, introduce a step to excite two special
modes that sum to give a linear field shape
2. Want broad bandwidth, but
step 1. works for only one
frequency since the two modes
propagate at different speeds at
different frequencies.
So, corrugate the surface to make
modes propagate at same speed.
3. Want beamwidth matched to
size of telescope, so make aperture
as broad as needed.
Johnson & Jasik (1984)
Station Electronics: Polarizer
Orthomode transducer
(separates polarizations)
One linear
comes out here
Other linear
comes out here
Send orthogonal linear
polarizations in here
Chattopadhyay et al. (1998)
90◦ hybrid junction
(converts linear to circular polarization)
Signal 1
Signal 1 + e-i π/4 Signal 2
Signal 2
Signal 2 + e-i π/4 Signal 1
James & Hall (1989)
Station Electronics: Low-Noise Amplifier
Metal mounting block
indium phosphide
MMIC
Input waveguide
Dipole probe into waveguide
couples to electric field
Impedance matching network
Transistor junctions
(amplification happens here)
DC voltage supply for
transistors
Output waveguide
4 stage 100 GHz InP MMIC amplifier
(MMIC = monolithic microwave integrated circuit)
Station Electronics: Receiver
Feed horns
Copper straps for heat
transport to refrigerator
Thermal gap in waveguide
Polarizer
Low-noise amplifiers
15 K stage
77 K stage
Stirling-cycle refrigerator
ATNF multi-band mm-wave receiver
Station Electronics: Downconversion
Why?
For RG 58 coaxial cable:
Loss at 1 GHz = 66 dB / 100 m
Dielectric loss ~ frequency
8.4 GHz and 400 m: 10-222 of signal comes out
a: Outer plastic sheath
b: Copper shield (outer conductor; cylindrical)
c: Dielectric insulator
d: Copper core (inner conductor)
Best cables: air dielectric + bigger diameter -> 2.3 dB / 100 m.
But they don't bend much and are expensive.
How?
Multiply signal by sinusoid at a known, stable frequency ωLO.
Generates sum and difference frequencies:
A(t) . sin(ωt) . cos(ωLO t) = 2 . A(t) . [sin(ω + ωLO) + sin(ω - ωLO)]
Filter off the sum (too high frequency) -> A(t) . sin(ω - ωLO)
Send this intermediate frequency (IF) signal down the cable.
Station Electronics: Baseband Converter
Sampler and Formatter
IF Distributor:
make multiple copies of the IF signal
send each to a baseband converter
Baseband Converter (BBC):
Amplify further
Downconvert from intermediate frequency
to zero frequency
Filter to selectable bandwidth of
16 MHz, 8 MHz, 4 MHz, ... 0.0625 MHz
Samplers:
Convert analogue to 1 bit or 2 bit digital
at Nyquist rate (ie 2 x BBC filter bandwidth)
One sampler per BBC
Formatter:
Receive digital streams from samplers
Receive time from the station clock
Prepare frames with time and data
Distribute to tracks of recorder
Station Electronics: Recorder
Mark 5 disk-based recorder
Records 1 Gbps for 12 h unattended
Commercial off-the-shelf PC components
Prototype worked after 3 months of project start
Developed starting 2001.
Station Electronics: Recorder: A Paradox
Burke (1969) Nature
Two element interferometer is a Young's double slit
Each photon passes through both antennas (slits)
The Paradox:
VLBI records signal for later playback
So, play back once and get fringes
play back a second time and count photon arrivals at slit
The Resolution: Amplifier must add noise > hv/k (>> signal)
Signal phase preserved and can't count signal photons
Station Electronics: Recorder
Station Electronics: Time and Frequency
Standard
hydrogen maser – hydrogen maser
hydrogen maser – rubidium
EVN June 2005, project EI008
Torun H-maser failed and was away for repair
Station Clock
A commercial rubidium standard
An EFOS hydrogen maser with covers removed (Neuchatel)
Stability:
Cost:
3x10-15 over 1000 s (1 s in 107 yr)
~ 200 kEUR (!)
Manufacturers:
Smithsonian Astrophysical Observatory (USA)
Observatoire de Neuchatel (Switzerland)
Sigma Tau (now Symmetricom) (USA)
Communications Research Lab (Japan)
Vremya-CH (Russia)
KVARTZ (Russia)
1x10-12 over 1000 s
~ 5 kEUR
Station Clock: Hydrogen Maser
(H2 -> H + H)
(TE011 cavity tuned to 1420 MHz)
Output is extremely stable due to:
●long atomic storage time (1 s)
gives narrow resonance line
Humphrey et al. (2003)
●no wall relaxation (teflon coating)
Station Clock: Stability is not Accuracy
eg: H maser
Rubidium
Caesium
Optical (?)
(Illustration from Percival, Applied Microwave & Wireless, 1999)
Station Clock: Rate and Drift
Effelsberg maser – GPS time, April 2005
0.5 µs
(EFOS hydrogen maser from Obs. Neuchatel)
1 month (= 3x1012 µs)
Rate = 0.5 µs / 3x1012 µs = 1.7x10-13 s/s
Compare to correlator delay window: ~ 1 µs
Drift due to cavity frequency change (due temperature, ...)
Future: Optical Time & Frequency Standards?
Gill & Margolis
Physics World May 2005
Optical Clock: Ion Trap
Paul trap: ring electrode, 1.3 mm diameter
and end caps
Crystal of five stored 172Yb+ ions
(fluorescence emission)
Physikalisch-Technisch Bundesanstalt (PTB) - Germany
Optical Clock: Schematic and Resonance Signal
(435.5 nm = 6.9x1014 Hz)
Cooling laser and interrogation laser are applied alternately
In each cycle, interrogation frequency is increased or decreased
Fluorescence signal during subsequent cooling tells of deviation from line resonance
Physikalisch-Technisch Bundesanstalt (PTB) - Germany
Stability Measurement: Allan Variance
Thompson, Moran & Swenson (1986)
Hydrogen Maser: Stability for mm-VLBI
For VLBI at wavelength of 1 mm (300 GHz):
integration time 100 s -> coherence 0.9
integration time 1000 s -> coherence 0.6
Thompson, Moran & Swenson (1986)
Ship Data to Correlator
2000 GB / 3 days = 60 Mbps
Price: ~ 50 EUR to 150 EUR
Correlator
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JIVE Correlator, Dwingeloo, NL
For EVN production correlation
MPIfR/BKG Correlator, Bonn
VLBA Correlator, Socorro, USA
USNO Correlator, Washington
Haystack Correlator
Mitaka Correlator, Japan
LBA Correlator, Sydney, Australia
Penticton Correlator, Canada
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Play back disks or tapes
Synchronize data to ns level
Delay the signals according to model
Correct Doppler shift due Earth
rotation
Cross correlate (-> lag spectrum)
Fourier transform
(lag spectrum -> frequency spectrum)
Average many spectra for 0.1 s to 10 s
Write data to output data file for
post processing
Correlator
Mark IV Correlator Block Diagram
Correlator: Delay Model (CALC)
BKG Sonderheft “Earth Rotation” (1998)
Adapted from Sovers et al. (1998) by Walker (1998)
Correlator
Mark IV Correlator Board: 1 of 16 (total is equal to 1000 Pentiums at 3 GHz)
Correlator: The Fundamental Operation
Case 1: Perfectly correlated signals
Telescope 1 -> 1 0 1 1 0 0
Telescope 2 -> 1 0 1 1 0 0
XOR 0 1
0 1 0
1 0 1
Σ
⁄ N (= 1.0)
(= 6)
(normalization)
-0.5
(= 0.5)
*2
(=1.0)
Case 2: Perfectly anti-correlated signals
Telescope 1 -> 1 0 1 1 0 0
(same processing as above)
(= -1.0)
Telescope 2 -> 0 1 0 0 1 1
Case 3: Uncorrelated signals
Telescope 1 -> 1 0 1 1 0 0
Telescope 2 -> 0 0 1 0 1 0
(same processing as above)
(= 0.0)
A Single Correlator
Single-sample delays (shift register)
Antenna 1 ->
Antenna 2 ->
XOR
Σ
Romney (1998)
A Single Correlator: Typical Output
Lag Spectrum:
correlation
coefficient
x 106
Time lag (channels)
Fourier Transform
Frequency Spectrum:
phase
amplitude
Frequency (channels)
Mark IV Correlator
Mark IV Correlator Board BlockSchematic
Whitney et al. (2004)
Post Processing: Raw Residual Data
Phase slope in time
is “fringe rate”
Phase slope in
frequency is delay
Frequency channel
Frequency channel
Walker (2002)
Post Processing: Effect of a Delay Error
phase: φ1 = 2π τ v
phase: φ2 = φ1+ dφ = 2π τ (v + dv)
Path length = L
Delay τ = L / c
Phase difference: φ2 – φ1 = dφ = 2 π τ dν
dφ / dν = 2 π τ
A gradient of phase with frequency indicates a delay error
Fringe Fitting: Basics
V(frequency)
V(time)
1D FFT
1D FFT
V(time delay)
V(fringe frequency)
Fringe Fitting: (self calibration with first derivatives in time and frequency)
1. Divide visibilities by source model to remove source structure phase
2. V(frequency, time)
2D FFT
V(time delay, fringe frequency)
3. Find location of peak amplitude in the tranform -> gives delay & rate
4. Geodesy:
stop here. Measured delay is the observable. Add this
to the correlator model delay to obtain the total delay.
Astronomy: correct the visibility data for measured delay and rate.
Fringe Fitting: High SNR Case: EB-SC
Input phases
2D FFT
Amplitude of Fourier transform
Fringe rate
Time
Frequency
Delay
Source is easily seen in a single integration time-frequency channel
Movies by Moellenbrock (2002) ; layout Walker (2002)
Fringe Fitting: Low SNR Case: HN-Halca
Input phases
2D FFT
Amplitude of Fourier transform
Fringe rate
Time
Frequency
Delay
Source cannot be seen in a single integration time-frequency channel
Movies by Moellenbrock (2002) ; layout Walker (2002)
Fringe Fitting: The Result
Frequency
Geodetic VLBI: The Measurement Principle
Geodetic VLBI: Polar Motion
3m
1.1.1991
17.7.1995
500 mas
Two components:
BKG Sonderheft “Earth Rotation” (1998)
1.0 yr period
“annual component”
1.18 yr period “Chandler wobble” discovered in 1891, explained in 2000:
Fluctuating pressure at ocean bottom due to temperature and salinity
changes, wind-driven change in ocean circulation and atmospheric
pressure fluctuations
(Gross 2000, Geophys. Res. Lett.)
Geodetic VLBI: Polar Motion
Pole y coordinate after subtracting the Chandler component
Equatorial component of the atmospheric angular momentum
BKG Sonderheft “Earth Rotation” (1998)
Polar motion is affected by distribution of atmosphere
in addition to oceans
Geodetic VLBI: Length of Day Variations
1 ms/day = 0.46 m/day
= 15 mas/day
(Vrotation = 465 m/s at
equator)
Subtract Chandler variation from Length of Day:
Length of day
Atmospheric angular momentum
Length of day and atmospheric angular
momentum are highly correlated:
LoD is affected by wind
BKG Sonderheft “Earth Rotation” (1998)
Earth Orientation Parameter Errors and
Spacecraft Navigation
Mars Reconnaissance Orbiter
Launched 12 Aug, 2005
Cameras & spectrometers for mineral analysis
Ground-penetrating radar for sub-surface water ice
$500 million spacecraft cost
Will arrive at Mars March, 2006
Earth Orientation Parameter Errors and
Spacecraft Navigation
1.6 x 109 km
This angle will give Mars Reconnaissance Orbiter position
Mars
105 +/- 15 km
MRO
Length of Day affects telescope position
1 ms/day = 0.46 m/day at earth equator
= 27 km/day at Mars
Altitude for mars orbit insertion = 300 km
Altitude for aerobraking = 105 +/- 15 km
1 to 5 days without measuring LOD
-> error > altitude tolerance
-> Mars Reconnaissance Orbiter would
burn up or miss Mars
Polar Motion: Wavelet Analysis
Fourier & wavelet spectra of a test signal
Polar motion and its wavelet spectrum
BKG Sonderheft “Earth Rotation” (1998)
EOP and Ocean Tides
Influence of ocean tide on UT1
VLBI measurements
Tide model
1 – 10 January 1995
Influence of ocean tide on pole position
2 mas
0 ms
Ocean tide (O1) and zonal tide (M2)
(periods ~ 12 h)
-2 mas
BKG Sonderheft “Earth Rotation” (1998)
Station Positions and Continental Drift
1999
1984
30 cm
Baseline length Westford-Wettzell
1 – 10 January 1995
Component perpendicular to baseline
20 cm
● Continental drift is clear
● Precision of baseline measurement improves with time
GSFC VLBI group (Jan 2000 solution)
Station Positions and Continental Drift
1 – 10 January 1995