VLBI - techniques p2
Very big data rates (432 TB per day, 4320TB per session), so discarded basebnd data after correlation (Store and distribute correlated data products)
Clocks and timing
All interferometry relies on accurate alignment of signal
To track delay/phase errors to transfer from reference to target, the data recorder time signal must be stable during the cycle time
Nominally need <10 deg waveront phase error in 1000s at 10GHz
This means clock stability of 10/(360x1000x10e9) ~ 2e10-15
Clock differences between station = delay/rate
We need a hydrogen maser at each VLBI antenna
Connected interferometers can use one central clock as a single standard
Correlator delay model
All Radio astronomy correlators use a delay model to correct data:
Accounts for e.g. Earth rotation, the delay on a single baseline towards a sky target chages with time
To track a source in VBI, we need to mode the decay changes
The "delay model" calculates the delay between two telescopes at a particular time to get fringes in a specific direction
Tota delay = geometry + Earth rotation (+tides etc) + clocks + electronics + troposphere + ionosphere + special and general relativity.
Typically schedule periodic observations of a bright fringe finder source where fringes can be found in correlator
good but not perfect
Atmosphere is hard to predict in detail
Calibration work is needed to correct errors after correlation
Use simple point like sources to solve for errors
Transfer correction to the unknown target image
Flux calibration
Short Baseline
Long
Problem
Solution
Antenna gains fluctuate with time (e.g. temperature)
So: How bright is my target source
Also observe a source with known flux density (power)
Compare with "known answer" gain factor
Scale target with the same gain factor
All standard 'stable calibrators' are resolved - can't give reliable gain factor
Remaining compact source are more variable = not good flux calibrators
Before VBI observation: meaure with single dish:
During observations
Antenna gain as a function of altitude "gain curve"
The power of a "noise diode" in the antenna " noise diode profile"
An absolute flux density source "absolute gain factor"
Combine 1,2,3 noise dioe can be used a flux density reference
Fire noise diode periodically and log received power
After observation
Compare noise diode power with known reference values
Derive corrections as function of time (altitude)
Scale correlated target visabilities with noise diode corrections
Typically applied by a Tsys table which comes with data
Fringe fitting delay/rate corrections
Delays close to 0, ok for bright sources, but for faint sources not ok
Largely due to clock problems at the different location - you have clock drift that maybe small but can amount to a problem
Other interferometers only have one clock
Also chages of baseline geometry
Tidal effects (more relevent for larger arrays
Or antenna positions
Or even in connected arrays (stretching of cable
Some atmospheric affects
AIPS - Global fringe fitting
Use all baselines to jointly estimate the antenna phase, delay and rate relative to a reference antenna
Solves the baselines phase error equation, with one of the antennas set to the reference antenna
Delay, rate and phase residuals for reference antenna are set to 0
Hence only measures difference, not absolute errors
Assumes calibrator is a bright point source at phase centre
Similar to self-calibration as source structure is part of the model
Implimented in AIPS (older radio astronomy package - still used for VLBI a lot) but soon to be implemented in CASA
Phase referencing
Similar to what we have seen for our secondary phase calibrator, just need to be close
Fringe fitting requires observations of a bright, compact source -> e.g. phase cal
Cycle time shorter than atmospheric variations
Obtain fringe fitting solutions for phase, delay and rate but applying fringe fitting to calibrator and applying to target
Issues:
High frequencies - wet troposphere and few calibrators
Low frequency - ionosphere
Closure phase
All antennas have different random phase fluctuation -> atmosphere
Closure phase = sum of simultaneously observed phases of a source on 3 baselines forming a triangle
Independent of station based phase errors
Phase errors due to atmospheric variations are cancelled
Fringe fitting (and self-cal) uses this triangle to solve for the residual phases, rates and delay