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Out of Focus (OOF) Holography for the GBT

Out of Focus (OOF) Holography for the GBT. Claire Chandler. Why OOF when you can do with-phase holography?. There are many advantages to traditional holography, but also some disadvantages: Needs extra instrumentation

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Out of Focus (OOF) Holography for the GBT

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  1. Out of Focus (OOF) Holography for the GBT Claire Chandler

  2. 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

  3. 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

  4. 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 (lobs=850mm) • Images of 3C279 with focus -1mm, 0mm, +1mm

  5. 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)

  6. 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

  7. 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 + i[E0 ÄFT (Q)] = E0 + iF (defining F = E0 ÄFT (Q); F contains all the information about Q) • Power pattern of the antenna is then P = |E0|2 + |F|2 + 2[Á(E0)Â(F) - Â(E0)Á(F)] • Small defocus Þ last term is negligible, and Q is derived from fitting for |F|2 • Large defocus Þ end term dominates and different defocus values weight Â(F) and Á(F) differently to obtain independent information about F

  8. 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

  9. 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 < 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

  10. Sources of error for OOF on the GBT (2) • 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 • To limit elevation range, make maps at 3 focus positions in less than an hour From Norrod (2003)

  11. 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

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