1. Radio Interferometry
Jeff Kenney

2. Outline of talk Differences between optical & radio interferometry
Basics of radio interferometry
Connected interferometers & VLBI
How radio interferometers are used

3. Differences between radio and optical interferometry
Wavelength – larger in radio by factors of
Resolution poorer than optical for given D, but very large D’s (~earth!) are used in radio VLBI, so best resolution very good ~0.1-1 mas
Effect of atmosphere: Spatial scale of atmospheric coherence length larger than antenna for radio, smaller than telescope for optical, timescale for variation minutes (radio) vs. millisec (optical) – can measure and calibrate phases in radio (by observing nearby source of known phase) but not in optical
Type of detection & beam combination:
Radio – signal (amplitude & phase) detected at antenna, digitized, then combined in correlator
Optical – light beams propagated to lab, forms interference pattern before being detected
Signal processing: Much easier to do complex signal processing at low frequencies

4. Basics of radio interferometry

5. Point Source and a Single Dish
f = hour angle
R = dish radius
l = wavelength f
q = angular resolution

6. A Simple Interferometer
Note improved resolution!

7. Signal delays
Problem: signal arrives at different antennae at different times – would yield no correlation
Solution: add a signal delay by sending signal from one antenna through one of “delay lines”
Set of cables of various specific lengths, giving specific time delays
Maximum cable length comparable to maximum baseline in interferometer, delay times in ’s nanosec

8. correlation

9. “Downconversion”
Signal from source is often “downconverted” to lower frequency before correlation
Easier to handle electronic signals at lower frequencies

10. Cross-correlation Correlation reduces noise!
(most of noise is uncorrelated)

11. Other important details:
Radio interferometers are used in radio astronomy for aperture synthesis imaging. This technique allows radio telescopes with resolution equivalent to very large effective apertures to be built using an array of widely spaced, smaller antennas. Many variations on the technique are possible, but all rely on collecting samples in the Fourier transform plane (u-v plane) of the image, taking advantage of the fact that the interference pattern (fringes) performs a similar mathematical operation to doing a Fourier transform. Each point in the u-v plane corresponds to a particular orientation and physical separation of the antennas (baselines) in the interferometer. Many samples in the u-v plane are required. These can be collected using an array of antennas (thus forming many interferometers at once, each with different baselines) or by motion of the interferometers relative to the source. Such motion is usually provided by the rotation of the earth ("earth rotation synthesis") or in the case of Space VLBI by the motion of an orbiting antenna. The results of such measurements can yield an image of the intensity of the radio emission at each frequency in the band (i.e. a 3-dimensional data-set, where one of the dimensions is frequency).
If the array of antennas is compact, phase-synchronized local oscillators can be distributed to the antennas and the signals from the antennas can be directly connected to the correlator. If the antennas are widely separated, connecting them in real time is impractical. The technique of Very Long Baseline Interferometry (VLBI) was developed to overcome this problem -- stable (atomic hydrogen) maser "clocks" are used for synchronization and the signals from the antennas are recorded on magnetic tape. Although this technique requires a more complex recording and correlator system, the antennas can be any distance apart, and very high resolution images (typically 10 milliarcsec) can be made.
For Space VLBI the synchronization and the data are handled by a telemetry station where recording also takes place. The separation of the antennas is sufficient to achieve microarcsec resolutions. The time it takes to adequately fill the aperture depends on the number of antennas and their spacing in the array, as well as the size and quality of the image. The number of independent points in the image depends on the number of independent points in the synthesized aperture. A large, complex image will require more coverage of the u-v plane than a small image. Long observing time can partially compensate for a small number of antennas. If many antennas are used, then many spacings get filled in simultaneously and it takes less time to fill the aperture. In VLBI, where antennas can be separated by continents (or are in space) it is generally not possible to entirely fill the aperture. In these cases, images of the small, bright components of the radio sources are the objects of interest.

12. Connected interferometers & VLBI

13. Most Radio telescopes that do cutting edge research are interferometers – need large spacings to get decent resolution
Connected radio interferometers:
cm-m VLA WRST Merlin AAT GMST -> SKA
mm OVRO/BIMA/PdB/Nobeyama -> ALMA

14. Very Long Baseline Interferometry (VLBI)
Widely separated antennae not connected by cables
Data recorded along with very accurate time signals & correlated later

15. VLBI: Uncertainty in correct delay
Delay tracks phase center Q0 (absolute RA+DEC)
If you know absolute positions of antennae AND all atmospheric propogation effects, then you know correct delay to use, and therefore you know the location of phase center (absolute RA+DEC)
If NOT (often the case for VLBI), you search for delay which gives maximum correlation, but know only relative positions Q

16. VLBI
If the position of the antennas is not known to sufficient accuracy or atmospheric effects are significant, fine adjustments to the delays must be made until interference fringes are detected. If the signal from antenna A is taken as the reference, inaccuracies in the delay will lead to errors in the phases of the signals from tapes B and C respectively. As a result of these errors the phase of the complex visibility is difficult to measure with a very long baseline interferometer.
No phase  no absolute positions, only relative positions over small region of sky

17. Except...
By making use of “closure phase” and similar relations for sets of 3 or more telescopes (relations which hold independent of phase shifts caused by atmosphere or instruments), one can partly correct for errors and get more reliable maps and absolute positions
Works best if large number of elements AND good u-v coverage

18. Today’s VLBI arrays
There are several VLBI arrays located in Europe, the US and Japan.
European VLBI Network (EVN)  -- most sensitive VLBI array ; a part-time array with the data being processed at the Joint Institute for VLBI in Europe (JIVE).
US -- Very Long Baseline Array (VLBA) – dedicated VLBI telescope
Combined EVN & VLBA known as Global VLBI. This provides the highest resolution, capable of imaging the sky with a level of detail measured in milliarcseconds.

20. Space VLBI First mission 1997-2003 VSOP (international)
8m dish in elliptical orbit, up to 3X earth diameter
best resolution 90 marcsec (100x HST)
ARISE (proposed ) 25m dish, 10 marcsec at 86 GHz (AGN engines & water masers around AGN)
Moon?? (Roye 2000)
Multi-epoch imaging of the quasar   from
Seven 5 GHz images are shown above, the first made in August 1997, the second in December 1997, and the last in September The horizontal spacing between images is proportional to the time between observations.   Image courtesy : D.W. Murphy (JPL)

21. e-VLBI : The future?
Recently it has become possible to connect the VLBI radio telescopes in real-time.
In Europe, 6 telescopes are now connected to JIVE with optical fibres at 1 Gigabit per second and the first astronomical experiments using this new technique (e-VLBI) have been successfully conducted.
This speeds up and simplifies the observing process significantly.
The data cannot be sent over normal internet connections as the data-rate in a VLBI observation is so high (far higher than the total global internet traffic.)

22. How interferometers are used
If you know where the antennae are, you can measure positions or make maps of astronomical sources, or determine locations of radio transmitters on ground or in space
If you know where the sources are (e.g. distant, “fixed” quasars), positions of antennae can be accurately measured  geodesy – motions of earth

23. VLBI helps define the Celestial Reference Frame
The radio system (positions derived from radio VLBI observations to quasars) has replaced the traditional optical reference system based on star positions to define the International Celestial Reference Frame.
The optical system which was used for the last 200 years had an average accuracy (of star positions) to about 0".01. The current average accuracy of quasar positions observed by radiosystems is about  milliarcseconds ( times better).

24. geodesy
Determine positions of widely-spaced antennae to accuracy of ~1 mm.
In geodetic experiments the correlator output parameter of interest is the interferometer delay. When delay is known for several different radio sources at several different times, it is possible to accurately determine the coordinates of the antennas.
Measure complexities of Earth’s Rotation (“polar motion”): precession, nutation, & Irregular shifts of earth’s axis due to gravitational effects of sun and moon on equatorial bulge of earth
Measure Tectonic motions of continental plates, continental rebound from ice ages (motion 1-10 cm/yr)
In 1970’s first radio programs to monitor universal time and polar motion (USNO, NRL, NASA, National Geodetic Survey)

25. SUMMARY: Radio VLBI science results
Definition of the celestial reference frame
Motion of the Earth's tectonic plates
Regional deformation and local uplift or subsidence.
Variations in the Earth's orientation and length of day.
Maintenance of the terrestrial reference frame
Measurement of gravitational forces of the Sun and Moon on the Earth and the deep structure of the Earth
Improvement of atmospheric models.
Imaging high-energy particles being ejected from black holes at enormous velocities
Measuring H20 masers in gas disks orbiting close to central black holes in active galaxies
Imaging the surfaces of nearby stars at radio wavelengths

26. Signals in phase

27. Signals in phase