Relative astrometry and phase referencing
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RELATIVE ASTROMETRY AND PHASE REFERENCING. Ed Fomalont National Radio Astronomy Observatory Charlottesville, VA USA. OUTLINE. 1. Group Delays and Phase Delays Comparison and Accuracies VLBA Relative Astrometry with Phase Delay

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Relative astrometry and phase referencing

Ed Fomalont

National Radio Astronomy Observatory

Charlottesville, VA USA


  • 1. Group Delays and Phase Delays

  • Comparison and Accuracies

  • VLBA Relative Astrometry with Phase Delay

  • Many results: Solar bending of 3C279 in October 2005

  • Very accurate relative positions (0.02-0.05 mas)

  • Group delays during unstable periods

  • 3. Source Structure Problems

  • A problem for relative and absolute astrometry at <0.1 mas level

  • Source variations over time/frequency. Registration to 0.1 mas?

  • 4. Combining Techniques

  • Can phase delays be used? Stepwise approach?

  • Imaging and position monitoring into a coherent picture.

  • 5. Use of ALMA for Astrometry

Group versus phase delay 1
Group versus Phase Delay (1)

--For any Source-Baseline-Frequency for a scan of ~2 min

Residual Phase Fr(n)

Fr (n) = (Total phase -2pn (Model delay)): Modulo 360o

Residual Group Delay Gr

Gr =DFr / 2pDn = Total group delay – Model delay

--Both Fr andGr are functions of astrometric/geodetic offsets

Analysis programs determine these offsets

Fr is ambiguous, only defined between -0.5, 0.5 fringe.

Need accurate model delay (<20 psec at 8 GHz)

about 0.5 cm!!

Gr is well-defined even with a relatively poor Model delay

Can be used directly to determine astrometric/geodetic prop.

Group versus phase delay 2
Group versus Phase Delay (2)

Relative Accuracy (at 8 GHz):

Residual Phase Fr accuracy = (50/SNR) psec

Residual Group Delay Gr accuracy = (50/SNR) (Dn / n) psec

Delay scatter is about 20 psec,

Hence, Group Delay is as ‘good’ as phase for SNR >50. Not

limited by SNR, but by intrinsic delay scatter.

Phase needed for Imaging:

Residual closure phases provide an image by Fourier Transform

Non-closing Group delays cannot easily obtain source image

Relative astrometry using phases
Relative Astrometry using Phases

By fast switching between close-by sources:

(VERA observed two sources simultaneously)

--Temporal model delay errors are removed to first order.

--Effect of angular dependent model errors are decreased by source

separation in radians (2o separation = 1/25 decrease).

--Tropospheric unmodeled delay scatter between close sources

becomes < 1 psec, no ambiguity in the differential phase delay.

--Main contribution of residual phase-delay difference are position

offsets. Achieved accuracies are 0.05 mas for VLBA, EVN, VERA.

Fast switching among many close sources:

--The angular model delay errors from nearly all effects produce a

phase-gradient in the source region (including some software bugs).

(We do not care about distinguishing among the various effects.)

--Potential accuracy is <0.02 mas for VLBA even for 50 mJy sources.

The Solar Deflection Experiment of October 2005

Example of Multi-source Phase Referencing

Kopeikin (Missouri), Lanyi (JPL), Fomalont (NRAO)

. 3C273

--J1246, J1248 and J1304 (~0.2 Jy) are used as calibrators for 3C279.

--Observe at 15, 23, 43 GHz to remove coronal bending.

Cannot observe at these frequencies simultaneously!

--Observations on Oct 1, 18 (far from sun)

--Observations on Oct 5-6-7-9-10-11 to measure gravitational bending

Cycle between frequencies every

15 minutes.

Derive position for 3C279 from group

Remove frequency dependent

coronal position change.

Determine g, gravitational bending

Observation switching within

each group.

3C279 ~ 10 Jy. Good SNR

Other cals, ~0.2 Jy okay for

phase, but not group delay


Observed phase

Residual phase after fit


1050 km


4600 km


3900 km


700 km

60 psec

+3C279;+J1304;+J1256; + J1258

Use a ‘mini-solve to determine better

source positions and linear phase

gradient in sky. Phase gradient is

caused by the sum of many

effects but dominated by the error

in the zenith path delay.

Result of best fit to source positions

And phase gradient. What remains

is the residual temporal clock

error. Relative position error

About 0.03 msec. (Structure effect

has been removedl)

OCTOBER 1, 2005

15 GHz phase for 13-min period 43 GHz phases for 20-min period

 13 minutes 

60 psec

20 psec

+3C279;+J1304;+J1256; + J1258

Rms scatter for 3C279 at 4000 km is about 3 psec = 0.03 mas

3C279 at 15 GHz on Oct 10 (1.2o from sun)

Derived position of 3C279

(GR bending of ~150 mas removed)

Disagreement of phase positions (using

an image), with the group delay

position is 0.5 mas. Origin in yet

unknown. Phase cal?, source



  • Weak calibrators (0.05 Jy) can be used.

  • Only need 5-sigma detection in a coherence time

  • Target positional accuracy about 0.05 mas with 2o separation.

  • VLBA, EVN and VERA general results.

  • Multi-calibration sources can produce <0.02 mas accuracy.

  • Weak, undetectable ‘group delay’ targets can be imaged.

  • Useful for bright GAIA quasars that are faint radio sources.

  • Use phase referencing to tie a 0.5 mJy radio star

  • to ICRF grid to 0.1 mas.

  • Techniques not useful for ‘normal’ astrometry/geodetic work


  • Becomes a serious source of error for position

  • accuracy < 0.1 mas, regardless of the method.

Source Evolution with Time (G127, Geldzahler and Fomalont)

Motivation: G127 is a compact 0.5 Jy radio source near the center of a

40’ SNR. Is it the relic of the original star?

Experiment goal: Determine the parallax and proper motion. SNR

distance is ~ 10 kpc, so should be detectable.

Observations: Five 10-hour VLBA observations at 8.4 GHz at

a six month-intervals with maximum east/west parallax signal.

Technique: Phase reference of G127 with a nearby 60 mJy

calibrator only 0.8o away. By the way, weaker calibrations may be

more stable calibrators with less structure than stronger calibrators.

Results: Image and Position of Peak of G127 wrt calibrator.

Source is variable (30%) and

minor structure changes occur,

although dominated by a core

with 50% of the flux density.

Is the peak of the bright

component the stationary

point of G127?


Make image of the source for each epoch.

Little obvious change between epochs

10% weak and very slightly smaller

in size in second epoch. Steeper gradient on

east edge.

Determine inner structure of bright radio

component using a physically realistic mode.

Unresolved radio core plus extended

inner jet in direction of more extended structure

Best fit of two components shown. Algorithm

in difmap to fit observed u-v data directly to

model. Approximate positional accuracy is

1.0 mas / SNR; diameter limit is

1.0 mas / SQRT(SNR)

Now have position of ‘true’ radio core wrt

peak intensity of main component.

Does this improve the experiment accuracy?

Resultant Motion of G127 with Time

Position of G127 with respect

to the reference quasar is

more stable when the position

of the unresolved fitted core is

taken as the stationary point,

compared with the peak of the

bright radio component.

Also, a 0.068 mas shift in position.

Incidently, no significant proper

motion and a parallax < 0.04 mas


Distance > 25 kpc.


3C279 Frequency Dependence

Oct 1, 2005




(0,0) is location

of fringe fit phase


15 GHz 23 GHz 43 GHz

Oct 18, 2005







x=+76, y=+127 x= -5, y=+6 x= -18, y=+32 Core Location(mas)

3.5 of 15 Jy 5.5 of 14 Jy 6.0 of 12 Jy


General Conclusion:

For observations with reasonably high signal-to-noise and a radio structure

which conforms to the general physical model of quasars,

Position of the true radio core may be obtained to 0.1 mas with

respect to the entire source radio extent.


  • Use phase delays instead of group delays:

  • Must decrease residual model errors – troposphere and instrumental.

  • Better troposphere models, WVR corrections, ‘Petrachenko’ array

  • Small scale phase referencing to global astrometry

  • Multi-source (30) phase referencing at 8 GHz in 15o radius

  • including about ~8 ICRF sources. Will obtain <0.05 mas relative

  • positions and images (and maybe core positions.

  • Then, connect each region using normal astrometric procedures.

  • Any gain in this?

  • Monitoring of source images (phase) and position changes (group delay).

  • To reach 0.05 mas level, need reasonable evolution of all sources.

  • How to organized this effectively.

Astrometry Using ALMA

ALMA on its own is a good astrometric/geodetic array!


Size=15 km, Freq=300 GHz  15 mas fringe = 3 psec

4 dual-pol IF’s of 2 GHz each; maximum spanned BW = 25 GHz

58 12-m telescopes and 7 7-m telescopes

Troposphere at 5000 m at Atacama is extremely good.

Must do astrometry/geodesy to Calibrate:

Antenna location needed to 0.06 mm accuracy!

20 deg phase at 300 GHz  0.02 psec accuracy


WVR (Oxygen line at 360 GHz) to measure wv

Accurate tropospheric parameter measurements

Probably use group delays from observations.

Typical calibrator targets:

Quasars. Very variable, but probably very compact

Position nearly coincides with optical object

Many stars available.

Many planets, asteroids easily detectable.


Main difficulty is phasing up array. Need not do entire array