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
For RG 58 coaxial cable:
Loss at 1 GHz = 66 dB / 100 m
Why?
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: Cable Compensation
Cable loss is frequency dependent
-> high frequencies have low amplitude
Solution: pass signal through a filter with the inverse
characteristic, ie large attenuation at low frequencies.
Result: relatively flat spectrum for later stages of processing
Station Electronics: IF Distributor
IF Distributor:
make multiple copies of the IF signal
send each to a baseband converter
Resistive power splitter:
matches impedance on all ports
compact
broad band (DC to GHz)
But: factor-of-two loss
(ok for IF processing, not ok
for RF phasing of antennas)
Hybrid power splitter:
matches impedance on all ports
low loss
But: narrow-band
Station Electronics: Baseband Converter
Baseband converter (BBC):
amplify further
downconvert from intermediate frequency (500-1000 MHZ) to zero frequency
filter to selectable bandwidth of 16 MHz, 8 MHz, 4 MHz, … 0.0625 MHz
Input IF spectrum
Effect:
0
500
1000 MHz
Output spectrum
0
500
1000 MHz
band of interest
Why downconvert from IF to baseband?
●narrow filters are easier at baseband since fractional bandwidth larger
eg 16 MHz filter at 750 MHz = 2 % fractional bandwidth
16 MHz filter at 0 MHz = 200 % fractional bandwidth
●filter centre frequency can be tuned simply by tuning the LO in the BBC
●sampling at baseband is easier
Station Electronics: Baseband Converter
Recall filters:
A simple example
(Horowitz & Hill 1989)
More complex filter gives steep flanks,
excellent stop-band rejection
(Horowitz & Hill 1989; telephone filter)
For small fractional bandwidth need high Q
-> large energy stored in filter -> sensitive to temperature
-> better to downconvert to baseband to get large fractional
bandwidth
(Filter design is beyond the scope here; a large and mature field)
Station Electronics: Baseband Converter
Standard downconversion:
Input IF spectrum
0
500
LO
1000 MHz
lower
upper
sideband sideband
Output spectrum
0
500
1000 MHz
sidebands overlapped -> degrades SNR
Single-sideband downconversion:
(used in BBC)
Uses two mixers driven by one LO
One mixer has 90º phase shift in LO
followed by another 90º shift after mix.
Result: 180º phase shift of one sideband
Summing cancels one sideband.
Differencing cancels other sideband.
Horowitz & Hill (1989)
Station Electronics: Sampler
1-bit sampler:
Comparator: Vout = 105 ( V1 – V2) is saturated most of the time
Multi-level flash sampler:
Horowitz & Hill (1989)
Uses multiple comparators, each
with its own threshold voltage,
looking at the same input signal.
Ladder of
resistors gives
successively
increasing
voltages for
comparison with
the input signal
Sampler statistics tell whether
the thresholds are set correctly.
(for 1-bit, want 50% 1’s, 50% 0’s
Can servo the thresholds to give the
correct statistics, provided input power is
within the range of adjustment of
Input signal
thresholds. If not, must change attenuation
of input power; routine during setup)
Station Electronics: Formatter
Inputs:
bit streams from all samplers from all BBCs
5 MHz from maser
1 pulse per second from maser
Output:
VLBA Tape Frame Format (Whitney 1995)
Station Electronics: Digital BBC
Analogue
replaced
by digital
Heart of the DBBC: stacked
ADC cards and FPGA cards
Analogue VLBA terminal (> 20 yr old)
Key spectacular development in last few years:
field-programmable gate array (FPGA)
FPGA = a VLSI chip with huge numbers of logic gates and softwareprogrammable switches to connect them together as you wish.
(eg Xilinx Virtex 5: 200 000 flip-flops, 200 000 LUTs, 2 MB RAM,
384 DSPs containing a multiplier, and adder and an accumulator,
clock rate 550 MHz. Up to 1200 pins on the package (!) )
Capacity and speed has grown such that analogue radio or TV
receivers can now be implemented digitally up to ~ 1 GHz.
Station Electronics: Digital BBC
IF input (eg 500-1000 MHz)
Digital data flow
8 Gbps per IF (!)
analogue-to-digital
converter card v1
outputs 8 bits/sample,
1 Gsample/s
to
recorder
FPGA core board v1 (circa 2005)
1 core board = 1 BBC
Single-sideband conversion to baseband,
filters (perfect bandpass shape)
Bit-reduction to 1 or 2 bit for recording
(no formatter function since newest recorders
Mark 5B do not need a formatter)
ADC board v1 and v2 developed at MPIfR, core board at Noto
14 layers
Stripline transmission lines, impedance matched and equal lengths
Station Electronics: Recorder
Mark 5 disk-based recorder
Records 1 Gbps for 18 h unattended
Commercial off-the-shelf PC components
Prototype worked 3 months from project start
Developed starting 2001.
2003
Mark 5A:
Direct replacement for tape recorders, time is in headers from formatter.
Data input via same connector as used for tape drives,
Records tracks from formatter,up to 1 Gbps
2006
Mark 5B:
Introduced VSI-H connector, 32 bit parallel data in. Formatterless.
Time comes from external 1 pps input, high-order time from PC clock.
Disk frame headers are inserted by Mark 5B every 104 bytes,
containing time calculated by counting samples since latest 1 pps
2008
Mark 5C:
Data I/O via 10 Gbps ethernet at 4 Gbps; a packet recorder
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
Station Electronics: LO Generation
Problem: maser outputs a sinusoid at 5 MHz
mixer requires a sinusoid at, eg, 1000 MHz, tunable, phase locked to maser.
Solution:
phase-locked loop synthesizer.
Principle:
5 MHz ref.
from maser
phase
detector
low-pass
filter
divide by
n
gain
voltagecontrolled
oscillator
n x 5 MHz
output
Station Electronics: LO Generation
Phase detector:
Horowitz & Hill (1989)
VCO: eg, yttrium iron garnet (YIG) oscillator
Oscillator drives Larmor precession
at a frequency dependent on applied
magnetic field (2.8 MHz/gauss)
(electron spin resonance)
RF coupling
coil
garnet
sphere
Applied magnetic field aligns electron
spins, causes Zeeman splitting.
Kaa (2004)
Oscillator frequency is tuned via
the magnetic field strength
Q = thousands; spectrally pure;
octave tuning ranges
Divide by n: eg, a binary counter, reset to zero when reaching n.
Many variants: offset loops, locking to harmonic of reference
Key performance: phase noise, capture and lock range, lock speed
Station Electronics: Cable Length Calibration
Problem: maser is in control room but LO and mixer are in receiver room
Cable joining the two is stretched during antenna motion and is heated by
sun, both changing the electrical length, hence adding phase noise to LO.
Solution: Measure the cable length by sending up a tone and reflecting some back
and measure the round-trip phase (aka ‘Cable Cal’)
Station Electronics: Amplitude Calibration
Problem: How can you measure source amplitudes when 1 bit sampling
throws away ampitude information !?
Hint 1:
Hint 2:
Hint 3:
Correlation coefficient from correlator measures degree of similarity of signals from the two antennas.
Signal from a point source is 100 % correlated at the two stations.
Noise from the receivers is completely uncorrelated.
Solution: Measure the system noise and the SNR (correlation coefficient) and you’ve
got enough to derive the signal strength.
Method: monitor total power in IF (written in station log)
inject known noise from a noise diode into front end
compare resulting step in IF power to the system noise
ratio of step sizes = Tcal/Tsys
If Tcal is known, this gives Tsys
To measure Tcal: perform on-off on primary calibrator
switch noise diode on/off
ratio of step sizes gives Tcal / Tsource
Ship Data to Correlator
2000 GB / 3 days = 60 Mbps
Price: ~ 50 EUR to 150 EUR
Correlator
JIVE Correlator, Dwingeloo, NL
For EVN production correlation
MPIfR/BKG Correlator, Bonn
VLBA Correlator, Socorro, USA
USNO Correlator, Washington
Haystack Correlator
● 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
Mitaka Correlator, Japan
LBA Correlator, Sydney, Australia
Penticton Correlator, Canada
(Covered earlier by Walter Alef)
Correlator: Delay Model (CALC)
BKG Sonderheft “Earth Rotation” (1998)
Adapted from Sovers et al. (1998) by Walker (1998)
A Single Correlator
Single-sample delays (shift register)
Antenna 1 ->
Antenna 2 ->
XOR
Σ
Lag Spectrum:
correlation
coefficient
x 106
Time lag (channels)
Romney (1998)
Post Processing: Transform from Lag to Frequency
Lag Spectrum:
correlation
coefficient
x 106
Time lag (channels)
Fourier Transform
Frequency Spectrum:
phase
amplitude
Frequency (channels)
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
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
Length of day and atmospheric angular
momentum are highly correlated:
LoD is affected by wind
Atmospheric angular momentum
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
Arrived at Mars March, 2006
Earth Orientation Parameter Errors and
Spacecraft Navigation
1.6 x 109 km
This angle gives 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
1 to 5 days without measuring LOD
-> error > altitude tolerance
-> Mars Reconnaissance Orbiter would
Altitude for mars orbit insertion = 300 km
Altitude for aerobraking = 105 +/- 15 km
burn up or miss Mars
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
Astrometry: Galactic Centre
VLBA, 43 GHz
inverse-phase referencing
to nearby weak calibrator
15 s source changes
Galactic rotation: 219 km/s
Mass Sgr A*: > 10 % of 4x106 Msun
No binary companion > 104 Msun
Reid & Brunthaler (2004)
Astrometry: Local Group Motions
VLBA, 22 GHz, water masers,
phase referencing 1 min cycle,
tropospheric delay calibration
M33/19 proper motion
Brunthaler, Rector, Thilker, Braun (2006)
Brunthaler (2006)
Astrometry: Local Group Motions
Astrometry: Extragalactic Distance Scale
Water masers in NGC 4258
Argon et al. (2007)
Miyoshi et al. (1995)
Astrometry: Extragalactic Distance Scale
Herrnstein et al. (1999)
D = 7.2 +- 0.3 Mpc
Astrometry: GR Test: Deflection due to Gravity
Einstein 1916: solved propagation of light in static gravitational field.
Shapiro 1964: delay measurable with radar or VLBI
Shapiro et al. (1971) measured delay using radar to Venus
Counselmann et al. 1974: measued delay with VLBI deflection
during occultation by sun of 3C 279 wrt 3C 273
Shapiro et al. (1971)
Astrometry: Speed of Gravity
Einstein 1916: solved propagation of light in static gravitational field.
Shapiro 1964: confirmed with VLBI gravitational deflection by sun
Kopeikin 2001: generalized solution to moving bodies
2002 Sep 8th: Jupiter passed 0.82 deg from J0839+1802
Shapiro delay: 115 ps (1.190 mas)
Retarded potential: 4.8 ps (51 uas)
Observe VLBA + Effelsberg, 8.4 GHz, 5 days around closes approach
Phase reference to two nearby quasars, 10 uas astrometric precision
Result: retarded deflection is 0.98 +/- 0.19
times that predicted by GR.
Kopeikin & Fomalont (2003)
Astrometry: Winds of Titan
Witasse et al. (2007)
Bird et al. (2005)
Avruch et al. (2006)
Astrometry: Lunar Gravity Map
Earth gravity map
GRACE: two spacecraft, 270 km
apart, measure separation, leading
spacecraft falls into gravity anomaly
first, increasing separation
Lunar gravity map: VLBI tracking of lunar orbiters happening now
Orbit perturbations will yield lunar gravity map
China: Chang-E spacecraft being tracked with Chinese VLBI array
Japan: Kaguya: differential VLBI using VERA to measure separation between two orbiters
Active Galactic Nuclei: Superluminal Motion
3C 111, VLBA
3.7 yr
17 lyr
Kadler et al. (2008)
Image courtesy NRAO/AUI and C. Fromm MPIfR
Active Galactic Nuclei: Jet Collimation
M 87
VLBA
15 GHz
NRAO/AUI and Y.Y. Kovalev and ASC Lebedev
Edge-brightened jet due to fast jet core beaming radiation away from observer
3 light-month resolution (0.6 mas)
(Covered by C.S. Chang earlier in this school)