April 8/9, 2003 Green Bank GBT PTCS Conceptual Design Review Out of Focus (OOF) Holography for the GBT Claire Chandler

GBT PTCS Conceptual Design Review – April 8/9, 2003 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

GBT PTCS Conceptual Design Review – April 8/9, 2003 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

GBT PTCS Conceptual Design Review – April 8/9, 2003 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 ( obs =850  m) Images of 3C279 with focus  1mm, 0mm, +1mm

GBT PTCS Conceptual Design Review – April 8/9, 2003 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 =  ) Right: amplitude (results from Nikolic, Richer, & Hills 2002)

GBT PTCS Conceptual Design Review – April 8/9, 2003 Early OOF results for the JCMT and GBT (3) One set of OOF maps using 12 GHz CH 3 OH masers have been used to measure the GBT surface: Left: phase; middle: amplitude; right: an example OOF map

GBT PTCS Conceptual Design Review – April 8/9, 2003 Some mathematics (from Richard Hills) Consider the combination of a perfect parabolic antenna with aperture function A 0, and phase errors Q(k). If Q small, A  A 0 (1+ i Q), and the far-field electric field pattern is E = FT [A 0 (1+ i Q)] = E 0 + i [E 0  FT (Q)] = E 0 + i F (defining F = E 0  FT (Q); F contains all the information about Q) Power pattern of the antenna is then P = |E 0 | 2 + |F| 2 + 2[  (E 0 )  (F)  (E 0 )  (F)] Small defocus  last term is negligible, and Q is derived from fitting for |F| 2 Large defocus  end term dominates and different defocus values weight  (F) and  (F) differently to obtain independent information about F

GBT PTCS Conceptual Design Review – April 8/9, 2003 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

GBT PTCS Conceptual Design Review – April 8/9, 2003 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 3  rms limits possible surface accuracy from OOF to 180  m rms) 1/f noise in receiver gain stability: need to have  G/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

GBT PTCS Conceptual Design Review – April 8/9, 2003 Sources of error for OOF on the GBT (2) Aim for S/N ~ 10 3 –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)

GBT PTCS Conceptual Design Review – April 8/9, 2003 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