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Phase Referencing Optimization. Ed Fomalont National Radio Astronomy Observatory Charlottesville, VA USA. Phase Referencing used for years. Used for virtually all arrays VLA, ATCA, WSRT as well as VLBI Mainly for instrumental temporal errors - PowerPoint PPT Presentation
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Phase Referencing Optimization
Ed FomalontNational Radio Astronomy Observatory Charlottesville, VA USA
Phase Referencing used for years
Used for virtually all arrays VLA, ATCA, WSRT as well as VLBI Mainly for instrumental temporal errors Data flagging (scan beginning quack) Quality checking of antenna sensitivity, stability
But for VLBI Above functions Most important to remove the effects of troposphere and ionosphere refraction above each VLBI antenna
How VLBI Attains 10 as Accuracy (1)• Introductory Statements: Deal with troposphere delay errors only. Shami - At low frequency find an in-beam calibrator to deal with ionosphere! SKA below 22 GHz has so much sensitivity, there will always be in-beam calibrators.
Imaging versus Astrometry. No difference in techniques. position accuracy 1% of resolution means 100:1 dynamic range images can be obtained.
Example to be used: 5000 km at 23 GHz (=1.3 cm): resolution: f~/D ~ 400 as goal of 10 as relative position accuracy for one 8-hour experiment
How VLBI Attains 10 as Accuracy (2)
Three astrometric limits:
1. Signal to noise: Target must have SNR >20 in image at 23 GHz position accuracy (p) = 0.5 f / SNR ~ 10 as SNR limit is frequency dependent because of resolution. SNR > 60 needed for 8.4 GHz; SNR> 300 at 1.4 GHz
2. Semi-random small-scale delay errors: r~0.05 cm (~15oto~0.5 cm (~150oand isweather related ‘pray for good weather’. Dynamic scheduling especially if one large telescope for sensitivity is needed (mega-masers)
3. Systematic large-scale (angle and time) delay error (a) Apriori a>5cm. Must reduce to ~1 cm (GPS, special observations) Error still one wavelength which is why group delays are used for all-sky astrometry. Phases are ambiguous!
2. And 3. Accuracy is NOT frequency dependent
How VLBI Attains 10 as Accuracy (3)
Solution:
Phase reference target to calibrator do away from target
p ~ (d/57) a / D + decrease in r (random)
for d = 1o, a=1 cm, D=5000 km; p ~ 15 as (residual 0.2 mm delay) per antenna --> 10 as averaging all antenna
How VLBI Attains 10 as Accuracy (3)
Solution:
Phase reference target to calibrator do away from target
p ~ (d/57) a / D + decrease in r (random)
for d = 1o, a=1 cm, D=5000 km; p ~ 15 as (residual 0.2 mm delay) per antenna --> 10 as averaging all antenna
CONGRATULATIONS: YOU HAVE DONE IT! BUT you were probably a little bit lucky
Typical VLBA Observing Sequence
Use accurate correlator modelProper sampling, temporal, frequency sampling of visibilityApply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys)
Typical VLBA Observing Sequence
Atm
ospheric Cal
Electronic C
al
40 min
Source rising Source setting
Time
Phase Referencing Phase Referencing
Use accurate correlator modelProper sampling, temporal, frequency sampling of visibilityApply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys)
3 steps to processing (VLBA specific) Atmospheric + Electronic Cal + Phase referencing
From Mark Reid
Electronic Frequency Calibration
Phase versus Frequency Calibration
Several short observations of a strong calibrator, not too far from the calibrator-target (20o okay). Or use phase calibrator if strong enough.
Although the phase is changing quickly with time, the phase versus frequency is stabile in most instruments
For phase referencing on weak calibrators when all frequency channels must be coherently added for scan detection, this calibration is crucial. Also crucial for spectral line astrometry and spacecraft astrometry when sources are at different frequencies. Watch out for ionosphere calibration (GPS models) since this produces a phase/frequency slope versus position
Residual Troposphere Calibration
Typical zenith path delay error a>5 cm, after best apriori and GPS calibration. Error is somewhat stable over hours.
This error produces a systematic delay difference , c-t, between cal and target as a function of zenith angle z
c-t = a sec(z) tan(z) zc-t
sec(z) tan(z) = 0.0 at z=0o; 3.5 at z=60o; 8.0 at z=70o]
This is why low elevation observations should be avoided
c-t = for 1o cal-sources separation at z=40o for a~5 cm = 1 mm
Need to reduce this error to 0.2 mm, otherwise >50 as accuracy
Reid, Kogan, Mioduszewski (DELZN) Simplified astrometric observations to determine zenith-path delay (mentioned by Andreas yesterday)
Global Troposphere Residual Delay (DELZN)
•Observe ~15 ICRF sources over the sky for about 40 min.• Spanned a bandwidth of about 500 MHz and measure group delays (phase slope with frequency)•Each ‘blue’ box’ is the result of a 1-minute scan. •Fit delay to a using AIPS task DELZN. In this case a = 7.0 cm, error of ~1 cm.
•Yellow crosses are the group delay after correcting for the tropospheric error. Typical total troposphere is 500 cm
100 psec=3 cm
<- 40 min ->
Strongly recommend observations every 4 hours
Typical VLBI Temporal Phase Behavior
Typical VLBI Temporal Phase Behavior
=23 GHz1= 360o = 1.3 cm3C279 at z=40o
LA as reference
Long-term variations: 3 over hours
Medium term: 0.5 over 10 min
Short term: 0.1 to 0.5 over 10 sec to 10 min sporadic
Closer inspection at 19 h data
1800 km
3000 km
5.5000 km
1100 km
4500 km
Phase Referencing Editing for Temporal Noise
23 GHz: 3C27920-min of dataAntenna-based phases LA as reference40-sec cal, 40-sec target3C279 strong so that 10-sec solution okay to see shorter fluctuations
Question: Can you interpolate accurately between scans?? = Ambiguous!! = No phase stability
DELETE relevant target dataSubjectiveBUT Images/positions are much better!
? ? ?
!! ?
!!?
?
Comparison with Target Phases (strong target)
Target sources strong enough to be detected and checked. Position offsets removedAll sources should definea continuous phase
#
Time Coherence Editing
•Don’t be afraid to edit regions where phase coherence looks doubtful.•Some automatic software available.•Typical editing: 8 GHz 5% 23 GHz 20% 43 GHz 40% (usually SC)•Images and astrometric precision are usually significantly better, even for weak targets.
•The main reason phase referencing pipelines are difficult to make
•For in-beam and VERA, can be more casual But, if phase is changing by 100o in a minute, who knows what is happening only 2o away?
The Angular Coherence Problem
Cal &target
Cal -target
Cal -TargetNod
The Angular Coherence Problem
Cal-target phase Cal-target phase Nodding observations Simultaneous
8 GHz simulations, 2.0o separation,20-s nodding [Asaki et al]
Cal &target
Cal -target
Cal -TargetNod
Cal -TargetSimultaneous(offset 30o)
The Angular Coherence Effects
Cal &target
Cal -target
Cal -TargetNod
Cal -TargetSimultaneous(offset 30o)
Calibrator - Source separation is critical astrometric parameter
coherence
Astrometric precision
Simultaneity versus nodding does not make a big differenceSimultaneity increases SNR! Feed arrays in future
simultaneous
nodding
Cal &target
Cal -target
Cal -TargetNod
Cal -TargetSimultaneous(offset 30o)
coherence
The Bottom Line
What we knew all along: The closer the calibrator is to the target, the higher the astrometric precision.
Cal &target
Cal -target
Cal -TargetNod
Cal -TargetSimultaneous(offset 30o)
coherence
The Bottom Line
What we knew all along: The closer the calibrator is to the target, the higher the astrometric precision.
Where we are now:
•ICRF forms basic quasi-inertial frame-work of calibrators now accurate position to <0.1 mas (ICRF2)•VLBA Calibrator Survey (Petrov, Kovalev, Gordon, Fomalont) increased number to >2000 good quality calibrators > 80 mJy•LBA Calibrator Survey + ICRF work in the South (Phillips + others)
•BUT----Average separation is 3o in north. Need a increased factor of at least 5, especially near galactic plane.
The best plan to find the calibrators?
Arrays have plenty of sensitivity
Detection Level of Calibrator: Calibrator must also be detected in coherence time to be useful. Phase error ~ 50o / antenna solution SNR SNR > 5.0 recommended (assumed all frequencies added)
VLBA 23 GHz in 30 sec @ 256 Mb/s 6.0 mJy VLBA 8 GHz in 120 sec @ 256 Mb/s 2.0 mJy
VLBA+GBT 23 GHz in 30 sec @ 256 Mb/s 2.6 mJy
VLBA+GBT 8 GHz in 30 sec @ 256 Mb/s 1.0 mJy
EVN 8 GHz in 120 sec @ 256 Mb/s 1.4 mJy
Potentially many calibrators are available. You ‘just’ have to find them
Until then, use more complicated schemes
Tricks: Multi-Source Calibration
Cal &target
Cal -target
Cal -TargetNod
Cal -Target(offset 30o)
Observe several calibrators around target to remove angular phase dependence.
J0839-topJ0842-middleJ0854-bottom
LA-MK baseline 8 GHzSep 8, 2002
Pc0842 = 0.75*P0839 + 0.25*P0854 - P0842
In general, you need three calibrators.Hard to find, must be strong enough, fast cycling, position uncertainties
Guirado’s talk on Polar cap surveys
=7mm
More Complicated Observing Scheme
A(t1, ) B(t1, )
Scan sequence:
C-T-C-T-C-T-C-C1-C-T-C-T-C-T-C-C1-C-T-… C = Cal, T = target, C1 = Secondary cal
Switching time consistent with temporal coherenceC is closest calibrator to targetC1 another calibrator within about 4o (Check source)
Analysis: Use C as main calibrator Image C1: It will probably be offset What are non-positional errors?
Example at 8 GHz
A(t1, ) B(t1, )
C1 after phase referencing C1 after position correction Image has offset -0.7, -0.3 mas Phase residual ~ delay errors Poor quality data indicated. Should remove this time perioid from target source as well since similar residuals occuring (but not seen).
Calibrator Source Structure
1. As the phase calibrator for a target: Okay as long as detectable at longest spacings Self-cal methods will provide image to compensate for non-closed phase problems in antenna solutions
2. Alignment for different frequencies important for spectral line comparisons, spectral index Definitely a problem since core shift with frequency is now well documented for most AGN calibrators
Next page shows alignment of four sources they were phase-referenced together.
s
Source Position vs Frequency
How will the frequency dependence of sourcepositions be found in general?
Chris Jacobs talk about an ICRF at 23-43 GHzCompare with ICRF2 at 8 GHzObtain requency offset for many strong calibrators
A few sources having jets with very bright ejecta cannot be used.
3. Source Position vs Time
Most astrometric problems deals with changes with time.Calibrator changes add uncertainties to proper motion and parallax determinations.
“Weak sources seems better behaved than strong sources.” Less structure and variability?Not sure this is true. Harder to determine if weak.
Another reason to use more than one calibrator. If one goes ‘crazy’ you can recognize it.
Dave Boboltz described pilot project to define methods for determining changes with time at several frequencies.
Calibrator Catalog Goal A catalog of thousands of calibratorsPerhaps, many found specifically for certain targets
Need Images/astrometric tie to ICRF that are made at several frequencies
Catalog information: Position of ‘stationary’ location of each source core position at 43 or 86 GHz (~50 as) Position offset versus frequency Simple position motion down jet (~20 as) Anomalous sources noted
Summary
•We can reach 10 as now with good fortune
•Good apriori and supporting observations are important
•We need a much higher density of calibrators
•We are subject to the weather. Edit, dynamic schedule
•Frequency/time dependence of calibration positions needed