Out of Focus OOF Holography for the GBT

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Out of Focus (OOF) Holography for the GBT

• Claire Chandler

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Why OOF when you can do with-phase holography?

• There are many advantages to traditional
  holography, but also some disadvantages
• Needs extra instrumentation
• Reference antenna needs to be close by so that
  atmospheric phase fluctuations are not a problem
• S/N ratio required limits sources to
  geostationary satellites, which are at limited
  elevation ranges for the GBT (35-45)
• Disadvantages of phase-retrieval holography?
• Traditional methods require very high S/N

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A new technique for OOF

• Hills, Richer, Nikolic (Cavendish Astrophysics,
  Cambridge) have proposed a new technique for
  phase-retrieval holography. It differs from
  traditional phase-retrieval holography in three
  ways
• It describes the antenna surface in terms of
  Zernike polynomials and solves for their
  coefficients, thus reducing the number of free
  parameters
• It uses modern minimization algorithms to fit for
  the coefficients
• It recognizes that the amount of defocusing is
  crucial to lowering the S/N requirements for the
  beam maps

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Early OOF results for the JCMT and GBT (1)

• The technique involves making both in-focus beam
  maps and maps with the secondary mirror defocused
  by known amounts. For the JCMT this has been
  carried out with focus offsets of 1mm
  (lobs850mm)
• Images of 3C279 with focus -1mm, 0mm, 1mm

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Early OOF results for the JCMT and GBT (2)

• Aperture function of the JCMT inferred from OOF
  3C279 maps
• Left, middle phase from two different
  observations on the same night (black to white
  p)
• Right amplitude (results from Nikolic, Richer,
  Hills 2002)

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Early OOF results for the JCMT and GBT (3)

• One set of OOF maps using 12 GHz CH3OH masers
  have been used to measure the GBT surface
• Left phase middle amplitude right an example
  OOF map

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Some mathematics (from Richard Hills)

• Consider the combination of a perfect parabolic
  antenna with aperture function A0, and phase
  errors Q(k).
• If Q small, A A0(1 iQ), and the far-field
  electric field pattern is
• E FT A0(1 iQ)
• E0 iE0 Ä FT
  (Q) E0 iF
• (defining F E0 Ä FT (Q) F contains
  all the information about Q)
• Power pattern of the antenna is then
• P E02 F2 2Á(E0)Â(F) -
  Â(E0)Á(F)
• Small defocus Þ last term is negligible, and Q is
  derived from fitting for F2
• Large defocus Þ end term dominates and different
  defocus values weight Â(F) and Á(F) differently
  to obtain independent information about F

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S/N requirements for OOF holography

• The S/N required for OOF maps depends on the
  highest order of the Zernike polynomial to be
  fitted
• Some more work probably needs to be done to
  determine how S/N affects the accuracy of the
  fitted polynomial coefficients, but the JCMT
  results derived so far for terms up to radial
  order 7 (36 terms) used OOF maps with S/N 200

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Sources of error for OOF on the GBT (1)

• Thermal (system) noise (including a contribution
  from the astronomical source in some cases)
• Pointing errors (current 3² rms limits possible
  surface accuracy from OOF to 180mm rms)
• 1/f noise in receiver gain stability need to
  have
• DG/G lt 10-3
• over time it takes to make a map
• Subreflector errors estimates of these can come
  from fitting the OOF maps, but there are some
  correlations between pointing and subreflector
  offsets
• Changes in surface shape over the time it takes
  to make a map

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Sources of error for OOF on the GBT (2)

• To limit elevation range, make maps at 3 focus
  positions in less than an hour

• Aim for S/N 103
• Thermal noise will not dominate as long as the
  target source is stronger than 1Jy (continuum)
• Receiver stability may be an issue

From Norrod (2003)
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Project plan

• Week ending Apr 13 install OOF software, check
  data formats, have a means of applying derived
  corrections to the GBT surface obtain test
  images using both continuum and spectral line
  sources
• Week ending Apr 20 Bojan Nikolic to assist in
  obtaining data and refining GBT model in OOF
  package analyze receiver stabilities
• Week ending Apr 27 Test software technique by
  applying a known deformation to the GBT surface
  and see if OOF holography can reproduce it
  reliably