Nonadaptive correction of image plane effects

1
Non-adaptive correction of image plane effects

• Tim Cornwell
• Enno Middelberg
• ATNF

http//www.atnf.csiro.au/people/tim.cornwell/wfi20
05nonadapt.ppt
2
Mosaicing at 20cm

• ATCA deep mosaic, lightly cleaned
• Quality of image depends on location of confusing
  sources
• For large enough field, some sources will be
  where the primary beam is poorly known
• Only a problem at 20uJy/beam or below

3
A closer look

• Field 13
• Bright 3.8Jy source seen at 2 level of the
  primary beam
• Sidelobes contribute to on-source noise level
• Peeling works
• But we actually have a number of sources with
  this effect
• After lots of investigation, we found that this
  is caused by the feed legs

4
Can we model this effect?

• Antennas are quite well understood at low end of
  frequency range
• e.g. ATCA antennas work at 3mm so they must be
  pretty good at 20cm!
• How far can we push non-adaptive modeling of
  confusing sources?
• i.e. No free variable in imaging allocated to
  off-axis gain
• Goal ATCA primary beam model accurate over few
  degree field
• Motivation
• Mosaic out to third or fourth sidelobe with known
  voltage pattern model
• Better to minimize number of degrees of freedom
  so that imaging is stable, efficient, and
  computationally feasible
• No need to peel or partition?
• Fallback
• Limit degrees of freedom to those really needed
  physically

5
What is the far-field voltage pattern?

• Ideally would do physical optics calculation
• From feed horn to far field pattern
• Expect to see diffraction from secondary and from
  feed legs
• To test the concept
• Make illumination pattern according to what we
  know
• Fourier transform to get far-field voltage pattern

6
What do we know about the CA antennas?

• 22m diameter
• Holographically adjusted at 12GHz
• Fully symmetrical design
• Feeds are on axis, rotated in as needed
• 3.8m central blockage
• 4 quadrupod legs aligned North-South, East-West
• Illumination tapered slightly
• G. James formula
• Some defocus?

7
Our modeled voltage pattern

• Model calculation
• Wish we could measure it so well!
• Field legs lead to 100 modulation of a source
  near the null

8
Applying the voltage pattern

• AIPS imager
• Applies voltage pattern, rotating from AzEl to
  RaDec
• Can use image of Jones matrix - easy to make
  using whatever tools you have at hand
• Forward model image to visibility
• Images binned in parallactic angle slow
• Components done for each sample quick and
  accurate
• Backwards visibility to residual image
• Images binned in parallactic angle slow
• Forward prediction via components is preferred

9
Bandwidth and time smearing

• Sources in primary beam sidelobes will have
  excessive bandwidth and time smearing
• Our data has Hanning smoothing
• 8MHz channels formed from 4MHz channels
• Hanning This channel average of next
  neighbours
• Hanning smearing easy to apply
• Transforming model to visibilities
• Apply smearing as last step in prediction of
  visibilities
• Transforming visibilities to residual image
• Apply smearing during gridding of residual
  visibilities

10
Summary of approach

• Choose parameters for illumination pattern
• e.g. James parameters, feed legs, defocus (if
  any)
• Calculate voltage pattern by inverse FT of the
  illumination
• Calculate model visibility including primary beam
  and bandwidth smearing
• Subtract from visibility
• Determined best model by fitting feed legs,
  defocus on one source
• There are no free parameters
• But we could selfcalibrate antenna gains on slow
  (day) timescale

11
Field 13 comparison
Original
Minus model
Minus selfcaled model
Peeled
Fit to get width of quadrupod legs 28cm No
evidence for defocus
Minus model
12
Field 13 final result
Outside shows image with cleaning only Inset
shows result after subtraction of predicted
visibility About an order of magnitude
improvement
13
But....
Errors remain but at lower level More modeling
required! Full physical optics calculation of
voltage pattern Pointing errors?
14
Field 15 comparison
Same story as field 13 Absolute value of primary
beam model is surprisingly good at this 1.5 point
15
Field 11 comparison
Much weaker source Correction good to about 20
only Self-calibration doesnt help Peeling
fails completely
16
What about peeling?

• Should have iterated by subtracting out model for
  main source beforehand
• But my point was to find an easy, non-adaptive
  approach
• Peeling will introduce instability
• So that for complex fields, it can be hard to
  control
• Peeling requires somewhat more computational
  resources
• Not necessary for this situation where we have a
  good model for the image plane effects

17
Limits to performance

• Dont know yet
• We need to do the physical modeling of the
  antenna
• My guess is that its hard to get the model
  accurate to better than 10
• Improves dynamic range by at most 10
• Still worth having
• Non-adaptive approach
• No worries about sucking up degrees of freedom
  (such as weak sources in the sidelobes)
• But we could introduce free parameters if needed
• Optimization could be tricky
• Atmospheric non-isoplanatism still a problem
• But still good to separate out non-random effects

18
Next steps

• Improved measurements of the primary beam
• Calculate primary beam model using physical
  optics
• This proof of concept is very encouraging
• Improve mechanics of applying primary beam
• Quite a few optimizations possible
• Extend to multiple feeds
• As in xNTD
• Explore the limits of this approach with better
  modeling of the far-field voltage pattern

19
Implications

• Physical modeling of antenna should become part
  of the calibration and imaging methodology
• Need accountability of optics throughout the data
  path
• For example, where is the focus set?
• Need to pay attention to details of correlation
• e.g. Hanning smoothing
• Computing burden of wide field imaging is
  lessened by non-adaptive methods

20
Crazy Ideas

• Our antennas need to be worse in a controlled way
• Would like this model to work out to some angle
  and then have random sidelobes
• Build random or pseudo-random surfaces
• Spatial equivalent of orthogonal switching
  waveforms
• Take a mallet to an ATA antenna!

21
Summary

• A priori, non-adaptive modeling of the primary
  beam works surprisingly well
• Get significant improvement in ATCA mosaic with
  little computational effort
• Suspect that the voltage pattern model is good
  out to many degrees
• Could probably be improved further by physical
  optics calculations
• We build over-engineered antennas!
• Shouldnt make this mistake with SKA