Wide-field VLBI Techniques: A Beginner's Guide

Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Wide-field VLBI Techniques: A Beginner’s Guide
John Morgan, ICRAR, Curtin University, Perth
10th EVN Symposium
Manchester
Tuesday 21st September 2010
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
1 Wide-field VLBI
VLBI Sensitivity
Correlation
Imaging
2 UV Shifting
Transforming correlated data
Using the baseline vectors
Using correlator delay model
3 Using Wide-field VLBI
4 Future Work
Future Work
Conclusions
Overview
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Acknowledgements
I would like to acknowledge useful discussions and material help from
many people.
⇒ Adam Deller
⇒ Walter Brisken
Also many others including (in no particular order) Franco Mantovani, Steven
Tingay, Walter Alef, Helge Rottman, Enno Middelberg, Richard Porcas
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
A simple ‘figure of merit’
For an interferometer with dishes of diameter d separated by D the
primary beam Θ and resolution θ are given by
θ ≈ λ λ
,Θ ≈ 1.22·
D d
(1)
So the number of resolution units across the primary beam is
Θ
θ = D ( ) D 2
d ⇒ n pixel ∼ (2)
d
n.b. for imaging purposes the true number of pixels will be ∼ 10× bigger
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Image size of different arrays
Array d D D/d
m km
VLA 25 36 1440
MERLIN 32 217 8680
EVN 100 10180 101800
VLBA 25 8611 344440
n.b. All arrays in longest-baseline/smallest-antenna configuration
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Three Caveats
Widefield VLBI techniques are only useful if:
⇒ There are enough bright sources on the sky that more than one will fall
within the primary beam
⇒ It is possible to correlate with sufficient resolution to cover the large area
⇒ There are appropriate techniques to handle the resulting large datasets
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Caveat 1: Density of Detectable Sources
⇒ This depends on the sensitivity of VLBI
⇒ However even a decade ago it was possible to detect multiple sources
⇒ Sensitivity (and therefore density of detectable sources on the sky) is
increasing all the time
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Caveat 2: Offset source visibility phases in
time/frequency
Phase/Degrees
200
150
100
50
0
-50
-100
⇒ The size of the image that can be
made is determined by how much
averaging is done of the data
→ The number of channels
→ The integration time
-150
-200
Time or Frequency
0 offset
offset
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How to generate the Wide-field Dataset
⇒ Generating high-resolution datasets was a problem for hardware correlators
→ It was this which limited the field of view for Wide-field VLBI until recently
⇒ With software correlators such as DiFX (Deller et al. 2007) the time penalty
is acceptable.
→ Greater CPU resources required for greater number of channels
⇒ The main problem is the output data volume
→ ∼ TB for a typical VLBA observation
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Caveat 3: Wide-field Imaging
Direct wide-field imaging
Very quickly becomes slow
⇒ Will quickly fill computer memory
⇒ Non-coplanar effects to handle
⇒ parallel algorithms are in development
Correlating with different phase centres
⇒ Ties up correlator (and media)
Correlating, transforming and averaging
⇒ Correlate to create one large dataset
⇒ Use this to generate several smaller datasets
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Transforming correlated data
Phase/Degrees
200
150
100
50
0
-50
-100
⇒ Transform one dataset into the
other.
⇒ Then the data can be averaged
⇒ Repeat for every region of interest
-150
-200
Time or Frequency
0 offset
offset
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Geometry
The correlator has already shifted the datastreams so that the two antennas are
on a baseline perpendicular to the original phase centre:
Consider a phase centre offset from this position
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Correlating, Transforming and Averaging
⇒ We start with the correlated data
⇒ Calculate a new delay for
→ each baseline
→ each time integration
⇒ Apply a phase shift to each datum
→ time dependent
→ frequency dependent
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
How to calculate the delay?
This is what the baseline vectors are for!
They can be used to calculate the delay at any point in the image:
∆φ = 2π λ
(lu+mv) (3)
The correlator delay model takes more into account than simple
geometry (Sovers et al. 1998)
DiFX actually calculates the baselines using the full accuracy of the
correlator delay model:
( ∂τ
(u, v, w) = c
∂l , ∂τ )
∂m ,τ , (4)
These differ by up to 1 part in 10 000 from purely geometrical vectors.
(Walter Brisken Priv. Comm.)
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How to calculate the delay?
There is still a problem
⇒ There is only one value of u and v for each visibility
We are treating the delay across the wide field as a linear function
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
CALC 9 generated delays across the wide field
1000
100
10
delay
1
0.1
0.01
MaMc
MaWz
McWz
0.001
0.01 0.1 1 10 100
offset/arcminutes
The delay function varies smoothly throughout the sky
No reason to think this isn’t typical
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Fractional error of a linear fit
0.1
0.01
0.001
0.0001
1e-05
1e-06
0.01 0.1 1 10 100
offset/arcminutes
Fit forced through 0 at the origin and 0.3 arcminute point
Similar to the derivation done by DiFX
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Error of using a linear fit
⇒ This is the reason for the UV shifting errors noted by others
(Lenc et al. 2008; Middelberg et al. 2008)
⇒ it cannot be calibrated out
⇒ It is made whenever using UV data to look at flux away from the phase
centre
(though the error may be negligable for shorter shifts)
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Accurate UV shifting
By generating a second correlator model for the desired phase centre it
should be possible to UV shift accurately.
No need to recorrelate:
⇒ We start with the correlated data
⇒ Replace the phase centre coordinates
⇒ Replace the baseline vectors (UVW)
⇒ Apply the phase shift to each visibility
→ difference in delay between the two models (multiplied by the frequency)
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Take into account delay rate
There is still an error of one part in
10 6
⇒ The delay is changing with time
⇒ Need to take into account the
change in delay over the shift
Another error which is always
present but only measurable for the
most extreme wide-field VLBI
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Error after a phase shift of 1000000 turns
180
CALC dataset
Reference dataset
90
Phase/Degrees
0
-90
Phase/Degrees
-180
5
4
3
2
1
0
-1
-2
Residuals and Chi 2 linear fit: y = 0.313256x + -2632.42 (r 2 =0.458702)
8408 8409 8410 8411
Frequency/MHz
(Morgan et al. 2010)
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Error after a phase shift of 1000000 turns
180
CALC dataset
Reference dataset
90
Phase/Degrees
0
-90
Phase/Degrees
-180
Residuals and Chi 2 linear fit: y = 0.0505706x + 0.588864 (r 2 =0.408585)
8
6
4
2
0
-2
-4
-6
0 10 20 30 40 50
Time/s
(Morgan et al. 2010)
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Implementations
This is implemented with full accuracy in:
⇒ difx2fits (not in the standard release)
The latest release of DiFX (2.0) also implements the shifting algorithm
with full accuracy
⇒ The extremely high resolution dataset never leaves the computer’s memory
⇒ The PI receives one standard visibility datset for each requested phase
centre
⇒ The computational efficiency is breathtaking!
(Deller et al. 2010)
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Amplitude Correction and Calibration
Correction for smearing:
⇒ Amplitude correction can be calculated fairly accurately from the shift delay
⇒ Larger than simple smearing for DiFX due to triangular weight function
(Morgan et al. 2010)
Primary Beam:
⇒ Assume that within a single image the correction is the same
⇒ Adjust the visibilities for the primary beam response of the baseline
→ time & frequency dependent
(See my poster for more details)
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Amplitude Correction and Calibration
Correction for smearing:
⇒ Amplitude correction can be calculated fairly accurately from the shift delay
⇒ Larger than simple smearing for DiFX due to triangular weight function
(Morgan et al. 2010)
Primary Beam:
⇒ Assume that within a single image the correction is the same
⇒ Adjust the visibilities for the primary beam response of the baseline
→ time & frequency dependent
(See my poster for more details)
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Future Work
We can generate a model for any point on the primary beam
What would be better would be to characterise the delay across the entire
primary beam
⇒ not just u, v and w but also higher terms
This would allow the calculation of the delay at any point with full
accuracy.
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Radio Astronomers do it in four dimensions
⇒ Accurate UV shifting at any point during correlation, calibration or imaging
⇒ This four-dimensional (antenna, l, m, t) could then be refined during
calibration
→ Phase calibration from multiple source within and outside the primary beam
→ Synergies with low-frequency interferometry?
→ Synergies with new and future widefield interferometers?
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Wide-field VLBI UV Shifting Using Wide-field VLBI Future Work References
Conclusion
⇒ VLBI across the primary beam is now possible
⇒ The density of sources on the sky means that many sources are detectable
in an 8-hour observation at L-Band
⇒ I am interested in collaborating on Wide-field VLBI projects
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References
Deller, A., Brisken, W., Phillips, C. J., et al. 2010, submitted PASP
Deller, A. T., Tingay, S. J., Bailes, M., & West, C. 2007, PASP, 119, 318
Lenc, E., Garrett, M. A., Wucknitz, O., Anderson, J. M., & Tingay, S. J. 2008, ApJ, 673, 78
Middelberg, E., Rottmann, H., Alef, W., et al. 2008, in The role of VLBI in the Golden
Age for Radio Astronomy
Morgan, J., Mantovani, F., Deller, A., et al. 2010, Submitted A&A
Sovers, O. J., Fanselow, J. L., & Jacobs, C. S. 1998, Reviews of Modern Physics, 70, 1393
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