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: Baseband Converter

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

Sampler and Formatter

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

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)

Optical Clock: Schematic and Resonance Signal

Physikalisch-Technisch Bundesanstalt (PTB) - Germany

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

(435.5 nm = 6.9x1014 Hz)

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

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

Correlator

Mark IV Correlator Block Diagram

Correlator: Delay Model (CALC)

Adapted from Sovers et al. (1998) by Walker (1998)

BKG Sonderheft “Earth Rotation” (1998)

Correlator

Mark IV Correlator Board: 1 of 16 (total is equal to 1000 Pentiums at 3 GHz)

Correlator: The Fundamental Operation

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 (= 6) N (= 1.0)

Telescope 1 -> 1 0 1 1 0 0

Telescope 2 -> 0 1 0 0 1 1

(= -1.0)(same processing as above)

Telescope 1 -> 1 0 1 1 0 0

Telescope 2 -> 0 0 1 0 1 0

(= 0.0)(same processing as above)

Case 3: Uncorrelated signals

Case 2: Perfectly anti-correlated signals

Case 1: Perfectly correlated signals

-0.5 (= 0.5) *2 (=1.0)

(normalization)

A Single Correlator

Romney (1998)

Antenna 1 ->

Antenna 2 ->

Single-sample delays (shift register)

XOR Σ

A Single Correlator: Typical Output

Lag Spectrum:

correlation

coefficient

x 106

Fourier Transform

Frequency Spectrum:

Frequency (channels)

phase

amplitude

Time lag (channels)

Mark IV Correlator

Mark IV Correlator Board BlockSchematic Whitney et al. (2004)

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

Fringe Fitting: Basics

V(frequency)

V(time)

1D FFTV(time delay)

1D FFTV(fringe frequency)

V(time delay, fringe frequency)2. V(frequency, time)2D FFT

Fringe Fitting: (self calibration with first derivatives in time and frequency)

3. Find location of peak amplitude in the tranform -> gives delay & rate

Astronomy: correct the visibility data for measured delay and rate.

4. Geodesy: stop here. Measured delay is the observable. Add this

to the correlator model delay to obtain the total delay.

1. Divide visibilities by source model to remove source structure phase

Fringe Fitting: High SNR Case: EB-SC

Source is easily seen in a single integration time-frequency channel

Movies by Moellenbrock (2002) ; layout Walker (2002)

Time

Frequency Delay

Fringe rateAmplitude of Fourier transformInput phases

2D FFT

Fringe Fitting: Low SNR Case: HN-Halca

Source cannot be seen in a single integration time-frequency channel

Time

Frequency Delay

Fringe rateAmplitude of Fourier transformInput phases

2D FFT

Movies by Moellenbrock (2002) ; layout Walker (2002)

Fringe Fitting: The Result

Frequency

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

Will arrive 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 will give Mars Reconnaissance Orbiter position

Spacecraft Navigation

105 +/- 15 km

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

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