April 8/9, 2003 Green BankGBT PTCS Conceptual Design Review

Out of Focus (OOF) Holography for the GBTClaire 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=850m)

• 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 CH3OH 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 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 FT (Q)] = E0 + iF

(defining F = E0 FT (Q); F contains all the information about Q)

• Power pattern of the antenna is then

P = |E0|2 + |F|2 + 2[(E0)(F) (E0)(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 180m rms)

• 1/f noise in receiver gain stability: need to have

G/G 103

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 ~ 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)

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