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Phase Referencing Optimization

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

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Phase Referencing Optimization

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  1. Phase Referencing Optimization Ed Fomalont National Radio Astronomy Observatory Charlottesville, VA USA

  2. 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

  3. 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:qf~l/D ~ 400 mas • goal of 10 as relative position accuracy • for one 8-hour experiment How VLBI Attains 10 as Accuracy (1)

  4. Three astrometric limits: • 1. Signal to noise: • Target must have SNR >20 in image at 23 GHz • position accuracy (p) = 0.5 qf / SNR ~ 10 mas • 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 (~15oto~0.5 cm (~150oand isweather 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 (2)

  5. 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 mas (residual 0.2 mm delay) per antenna --> 10 mas averaging all antenna How VLBI Attains 10 as Accuracy (3)

  6. 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 mas (residual 0.2 mm delay) per antenna --> 10 mas averaging all antenna CONGRATULATIONS: YOU HAVE DONE IT! BUT you were probably a little bit lucky How VLBI Attains 10 as Accuracy (3)

  7. Typical VLBA Observing Sequence Use accurate correlator model Proper sampling, temporal, frequency sampling of visibility Apply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys)

  8. Typical VLBA Observing Sequence Use accurate correlator model Proper sampling, temporal, frequency sampling of visibility Apply apriori corrections (GPS ion tropo, EOP, Pcal, Tsys) 3 steps to processing (VLBA specific) Atmospheric + Electronic Cal + Phase referencing Source rising Source setting 40 min Phase Referencing Phase Referencing Electronic Cal Atmospheric Cal Time From Mark Reid

  9. 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

  10. 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)

  11. 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

  12. Typical VLBI Temporal Phase Behavior

  13. Typical VLBI Temporal Phase Behavior =23 GHz 1= 360o = 1.3 cm 3C279 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

  14. Phase Referencing Editing for Temporal Noise 23 GHz: 3C279 20-min of data Antenna-based phases LA as reference 40-sec cal, 40-sec target 3C279 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 data Subjective BUT Images/positions are much better! ? ? ? !! ? ? !! ?

  15. Comparison with Target Phases (strong target) Target sources strong enough to be detected and checked. Position offsets removed All sources should define a continuous phase #

  16. 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?

  17. The Angular Coherence Problem Cal & target Cal - Target Nod Cal - target

  18. The Angular Coherence Problem Cal & target Cal - Target Nod Cal - target Cal - Target Simultaneous (offset 30o) Cal-target phase Cal-target phase Nodding observations Simultaneous 8 GHz simulations, 2.0o separation,20-s nodding [Asaki et al]

  19. The Angular Coherence Effects Calibrator - Source separation is critical astrometric parameter Cal & target coherence Cal - Target Nod simultaneous nodding Cal - target Cal - Target Simultaneous (offset 30o) Astrometric precision Simultaneity versus nodding does not make a big difference Simultaneity increases SNR! Feed arrays in future

  20. 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 Nod coherence Cal - target Cal - Target Simultaneous (offset 30o)

  21. 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 Nod coherence • 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? Cal - target Cal - Target Simultaneous (offset 30o)

  22. 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+GBT23 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

  23. Tricks: Multi-Source Calibration Observe several calibrators around target to remove angular phase dependence. Cal & target LA-MK baseline 8 GHz Sep 8, 2002 Cal - Target Nod J0839-top J0842-middle J0854-bottom Cal - target Cal - Target (offset 30o) =7mm 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

  24. More Complicated Observing Scheme 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 coherence C is closest calibrator to target C1 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? A(t1, ) B(t1, )

  25. 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).

  26. Calibrator Source Structure 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 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.

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  28. Source Position vs Frequency How will the frequency dependence of source positions be found in general? Chris Jacobs talk about an ICRF at 23-43 GHz Compare with ICRF2 at 8 GHz Obtain requency offset for many strong calibrators A few sources having jets with very bright ejecta cannot be used.

  29. 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.

  30. Calibrator Catalog Goal A catalog of thousands of calibrators Perhaps, 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

  31. 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

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