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
Walker (2002)
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 trans-
late band to baseband (0.062 – 16 MHz)
● Sample (1 or 2 bit)
● Format for tape
● Record
● Keep time and stable frequency
Station Electronics: Feed Horn
Johnson & Jasik (1984)
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.
Station Electronics: Polarizer
Chattopadhyay et al. (1998)
James & Hall (1989)
90◦ hybrid junction
(converts linear to circular polarization)
Orthomode transducer
(separates polarizations)
Signal 1
Other linear
comes out here
Send orthogonal linear
polarizations in here
One linear
comes out here
Signal 2 Signal 2 + e-i π/4 Signal 1
Signal 1 + e-i π/4 Signal 2
Station Electronics: Low-Noise Amplifier
4 stage 100 GHz InP MMIC amplifier
(MMIC = monolithic microwave integrated circuit)
Input waveguide
DC voltage supply for
transistors
Transistor junctions
(amplification happens here)
Impedance matching network
Dipole probe into waveguide
couples to electric field
Output waveguide
indium phosphide
MMIC
Metal mounting block
Station Electronics: Receiver
ATNF multi-band mm-wave receiver
Stirling-cycle refrigerator
Polarizer
Low-noise amplifiers
Thermal gap in waveguide
Feed horns
Copper straps for heat
transport to refrigerator
15 K stage
77 K stage
Station Electronics: Downconversion
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.
a: Outer plastic sheath
b: Copper shield (outer conductor; cylindrical)
c: Dielectric insulator
d: Copper core (inner conductor)
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
Why?
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 furtherdownconvert from intermediate frequency (500-1000 MHZ) to zero frequencyfilter to selectable bandwidth of 16 MHz, 8 MHz, 4 MHz, … 0.0625 MHz
Effect:
500 1000 MHz
Input IF spectrum
500 1000 MHz
Output spectrum
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
0 0
Station Electronics: Baseband Converter
For small fractional bandwidth need high Q-> large energy stored in filter -> sensitive to temperature-> better to downconvert to baseband to get large fractionalbandwidth
(Filter design is beyond the scope here; a large and mature field)
Recall filters:
A simple example
(Horowitz & Hill 1989)
More complex filter gives steep flanks,excellent stop-band rejection (Horowitz & Hill 1989; telephone filter)
Station Electronics: Baseband ConverterStandard downconversion:
500 1000 MHz
Input IF spectrum
500 1000 MHz
Output spectrum
0 0LO
lower sideband
upper sideband sidebands overlapped -> degrades SNR
Single-sideband downconversion:
(used in BBC)
Uses two mixers driven by one LO One mixer has 90º phase shift in LOfollowed by another 90º shift after mix.Result: 180º phase shift of one sidebandSumming 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:
Uses multiple comparators, eachwith its own threshold voltage,looking at the same input signal.
Sampler statistics tell whetherthe 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
thresholds. If not, must change attenuation
of input power; routine during setup)
Ladder ofresistors givessuccessivelyincreasing voltages forcomparison withthe input signal
Input signal
Horowitz & Hill (1989)
Station Electronics: Formatter
VLBA Tape Frame Format (Whitney 1995)
Inputs: bit streams from all samplers from all BBCs 5 MHz from maser 1 pulse per second from maser
Output:
Station Electronics: Digital BBC
Analoguereplacedby digital
Heart of the DBBC: stackedADC 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 software- programmable 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 TVreceivers can now be implemented digitally up to ~ 1 GHz.
Station Electronics: Digital BBC
IF input (eg 500-1000 MHz)
ADC board v1 and v2 developed at MPIfR, core board at Noto14 layersStripline transmission lines, impedance matched and equal lengths
analogue-to-digitalconverter card v1outputs 8 bits/sample, 1 Gsample/s
Digital data flow8 Gbps per IF (!)
FPGA core board v1 (circa 2005)1 core board = 1 BBCSingle-sideband conversion to baseband,filters (perfect bandpass shape)Bit-reduction to 1 or 2 bit for recording(no formatter function since newest recordersMark 5B do not need a formatter)
torecorder
Station Electronics: Recorder
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
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.
Station Electronics: Recorder: A Paradox
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
Burke (1969) Nature
Station Electronics: Recorder
hydrogen maser – hydrogen maser hydrogen maser – rubidium
Station Electronics: Time and FrequencyStandard
EVN June 2005, project EI008
Torun H-maser failed and was away for repair
Station Clock
Stability: 3x10-15 over 1000 s (1 s in 107 yr) 1x10-12 over 1000 s
Cost: ~ 200 kEUR (!) ~ 5 kEUR
Manufacturers: Smithsonian Astrophysical Observatory (USA)
Observatoire de Neuchatel (Switzerland)
Sigma Tau (now Symmetricom) (USA)
Communications Research Lab (Japan)
Vremya-CH (Russia)
KVARTZ (Russia)
A commercial rubidium standard
An EFOS hydrogen maser with covers removed (Neuchatel)
Station Clock: Hydrogen Maser
(TE011 cavity tuned to 1420 MHz)
(H2 -> H + H)
Humphrey et al. (2003)
Output is extremely stable due to:
●long atomic storage time (1 s)
gives narrow resonance line
●no wall relaxation (teflon coating)
Station Clock: Stability is not Accuracy
eg: H maser Rubidium Caesium Optical (?)eg: H maser Rubidium Caesium Optical (?)
(Illustration from Percival, Applied Microwave & Wireless, 1999)
Station Clock: Rate and Drift
(EFOS hydrogen maser from Obs. Neuchatel)
0.5 μs
1 month (= 3x1012 μs)
Rate = 0.5 μs / 3x1012 μs = 1.7x10-13 s/sCompare to correlator delay window: ~ 1 μs
Drift due to cavity frequency change (due temperature, ...)
Effelsberg maser – GPS time, April 2005
Future: Optical Time & Frequency Standards?
Gill & Margolis
Physics World May 2005
Optical Clock: Ion Trap
Physikalisch-Technisch Bundesanstalt (PTB) - Germany
Paul trap: ring electrode, 1.3 mm diameter
and end caps
Crystal of five stored 172Yb+ ions
(fluorescence emission)
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:
Station Electronics: LO Generation
phase detector
5 MHz ref.from maser low-pass
filter gain
voltage-controlledoscillator
divide by n
n x 5 MHz output
Station Electronics: LO Generation
Phase detector:
Divide by n: eg, a binary counter, reset to zero when reaching n.
Many variants: offset loops, locking to harmonic of referenceKey performance: phase noise, capture and lock range, lock speed
Horowitz & Hill (1989)
VCO: eg, yttrium iron garnet (YIG) oscillator
Kaa (2004)
garnetsphere
RF coupling coil
Applied magnetic field aligns electronspins, causes Zeeman splitting.
Oscillator drives Larmor precessionat a frequency dependent on appliedmagnetic field (2.8 MHz/gauss)(electron spin resonance)
Oscillator frequency is tuned viathe magnetic field strength
Q = thousands; spectrally pure;octave tuning ranges
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: Cable Length Calibration
Problem: How can you measure source amplitudes when 1 bit sampling throws away ampitude information !?
Hint 1: Correlation coefficient from correlator measures degree of similarity of signals from the two antennas.Hint 2: Signal from a point source is 100 % correlated at the two stations.Hint 3: 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.
Station Electronics: Amplitude Calibration
Method: monitor total power in IF (written in station log)inject known noise from a noise diode into front endcompare resulting step in IF power to the system noiseratio of step sizes = Tcal/TsysIf 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
Mitaka Correlator, Japan
LBA Correlator, Sydney, Australia
Penticton Correlator, Canada
● 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
(Covered earlier by Walter Alef)
Correlator: Delay Model (CALC)
Adapted from Sovers et al. (1998) by Walker (1998)
BKG Sonderheft “Earth Rotation” (1998)
A Single Correlator
Romney (1998)
Antenna 1 ->
Antenna 2 ->
Single-sample delays (shift register)
XOR Σ
Time lag (channels)
Lag Spectrum: correlation
coefficient
x 106
Post Processing: Transform from Lag to Frequency
Lag Spectrum:
correlation
coefficient
x 106
Fourier Transform
Frequency Spectrum:
Frequency (channels)
phase
amplitude
Time lag (channels)
Post Processing: Raw Residual Data
Walker (2002)
Frequency channel Frequency channel
Phase slope in time
is “fringe rate”
Phase slope in
frequency is delay
Post Processing: Effect of a Delay Error
Path length = L
Delay τ = L / c
phase: φ1 = 2π τ v
phase: φ2 = φ1+ dφ = 2π τ (v + dv)
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
Two components:
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.)
BKG Sonderheft “Earth Rotation” (1998)
17.7.1995
3 m
1.1.1991
500 mas
Geodetic VLBI: Polar Motion
Polar motion is affected by distribution of atmosphere
in addition to oceans
BKG Sonderheft “Earth Rotation” (1998)
Pole y coordinate after subtracting the Chandler component
Equatorial component of the atmospheric angular momentum
Geodetic VLBI: Length of Day Variations
Subtract Chandler variation from Length of Day:
BKG Sonderheft “Earth Rotation” (1998)
1 ms/day = 0.46 m/day
= 15 mas/day
(Vrotation = 465 m/s at
equator)
Length of day and atmospheric angular
momentum are highly correlated:
LoD is affected by wind
Length of day
Atmospheric angular momentum
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
1 to 5 days without measuring LOD
-> error > altitude tolerance
-> Mars Reconnaissance Orbiter would
burn up or miss Mars
1.6 x 109 km
Mars
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
This angle gives Mars Reconnaissance Orbiter position
Spacecraft Navigation
105 +/- 15 km
EOP and Ocean Tides
Ocean tide (O1) and zonal tide (M2)
(periods ~ 12 h)
Influence of ocean tide on UT1
Influence of ocean tide on pole position
2 mas
0 ms
-2 mas
1 – 10 January 1995
BKG Sonderheft “Earth Rotation” (1998)
VLBI measurements Tide model
Station Positions and Continental Drift
1 – 10 January 1995
GSFC VLBI group (Jan 2000 solution)
● Continental drift is clear
● Precision of baseline measurement improves with time
1984
Baseline length Westford-Wettzell
30 cm
1999
Component perpendicular to baseline
20 cm
Station Positions and Continental Drift
1 – 10 January 1995
Astrometry: Galactic Centre
Reid & Brunthaler (2004)
VLBA, 43 GHzinverse-phase referencingto nearby weak calibrator15 s source changes
Galactic rotation: 219 km/sMass Sgr A*: > 10 % of 4x106 Msun
No binary companion > 104 Msun
Astrometry: Local Group Motions
Brunthaler, Rector, Thilker, Braun (2006)Brunthaler (2006)
M33/19 proper motion
VLBA, 22 GHz, water masers,phase referencing 1 min cycle,tropospheric delay calibration
Astrometry: Local Group Motions
Astrometry: Extragalactic Distance Scale
Argon et al. (2007)
Miyoshi et al. (1995)Water masers in NGC 4258
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 VLBIShapiro et al. (1971) measured delay using radar to VenusCounselmann 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 GravityEinstein 1916: solved propagation of light in static gravitational field.Shapiro 1964: confirmed with VLBI gravitational deflection by sunKopeikin 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 approachPhase reference to two nearby quasars, 10 uas astrometric precision
Kopeikin & Fomalont (2003)
Result: retarded deflection is 0.98 +/- 0.19times that predicted by GR.
Astrometry: Winds of Titan
Witasse et al. (2007)
Avruch et al. (2006)
Bird et al. (2005)
Astrometry: Lunar Gravity Map
Earth gravity map
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 arrayJapan: Kaguya: differential VLBI using VERA to measure separation between two orbiters
GRACE: two spacecraft, 270 km apart, measure separation, leadingspacecraft falls into gravity anomalyfirst, increasing separation
Active Galactic Nuclei: Superluminal Motion
Kadler et al. (2008)Image courtesy NRAO/AUI and C. Fromm MPIfR
3C 111, VLBA
3.7 yr
17 lyr
Active Galactic Nuclei: Jet Collimation
NRAO/AUI and Y.Y. Kovalev and ASC Lebedev
M 87
VLBA15 GHz
Edge-brightened jet due to fast jet core beaming radiation away from observer3 light-month resolution (0.6 mas)
(Covered by C.S. Chang earlier in this school)
