Документ взят из кэша поисковой машины. Адрес оригинального документа : http://www.mrao.cam.ac.uk/~bn204/phd_era/publications/ursi-oof-a0poster.pdf Дата изменения: Sat Aug 3 21:40:03 2002 Дата индексирования: Tue Oct 2 15:44:34 2012 Кодировка: Поисковые слова: n02

Phase Retrieval Measurements of Antenna Surfaces Using Astronomical Sources
Bojan Nikolic, John Richer, Richard Hills Mullard Radio Astronomy Observatory, Cavendish Laboratory, Cambridge, U.K.

Abstract
We present a novel technique for accurate measurement of the largescale errors in an antenna surface using astronomical sources and detectors. Out-of-focus images of compact astronomical sources contain a wealth of information about the telescope optics. By characterising the surface as a sum of Zernike polynomials, it is possible to infer in a stable manner the surface of the telescope using an inverse-problem numerical technique. We report preliminary results using data from the 15-m James Clerk Maxwell Telescope and the 100-m Green Bank Telescope, and discuss the merits of this technique for measuring the large scale deformation of telescope antennas.
RMS error in radians weighted by amplitude

Zernike coefficients = 20 0.3 S/N=1000, Additive Noise= In-focus peak/1000 S/N=200, Additive Noise= In-focus peak/200 S/N=100, Additive Noise= In-focus peak/100 S/N=40, Additive Noise= In-focus peak/40 0.25

· We have been kindly provided with one set of three beam maps at 2.5 cm wavelength from the GBT, which used the methanol maser in W3 as a source. · The off-axis geometry makes defocus calculation complicated, so we used a raytracing package. Secondary movement was ±75 mm.

· Target surface accuracy is 240 µ m rms deviation.

0.2

0.15

0.1

0.05

· This was a spectral line observation, so there was no need for chopping. The strength of the source meant the noise characteristics were very different to the SCUBA observations, with proportional noise dominating over additive noise over much of the map.
0 0.0005 0.001 0.0015 0.002 Defocus in meters 0.0025 0.003 0.0035

0

1 Introduction
· Surface deformations of telescope antennas reduce the aperture effi 4 2 ciency ( ex p - ) and increase power in the error beam. · Measuring the deformations using microwaves (often called holography) allows corrections of the antenna and provides an input into theoretical models of the telescope mechanics. · Phase-retrieval holography numerically retrieves the shape of the antenna surface from power-only measurements the beam pattern, at two or more focus settings.

Figure 3: Results from our simulations demonstrating that optimal defocus for the JCMT at around 300 GHz is 1 mm

3 Results
3.1 The James Clerk Maxwell Telescope (JCMT)
· The JCMT is a 15-m submillimetre telescope with conventional Cassegrain optics. It covers the atmospheric windows from 150 GHz to 1.5 THz (2 mm to 200 µ m wavelength). · Target surface accuracy is around 22 µ m root-mean-square (rms) deviation. · We used SCUBA to make typically three out-of-focus maps per measurement, at 0 mm and ±1.0 mm defocus. · Atmosphere subtraction was done by fast chopping of the secondary and slower nodding of the primary. · Our targets included quasars (3C279) and planets (Mars and Venus). Each map took approx. 3 minutes with these sources.

Figure 6: Top row: three GBT maps of W3 used in the analysis, from left to right: in focus, focus + 75 mm and focus -75mm. Bottom row: Simulated beam maps corresponding to the best fit surface.

Figure 1: The primary reflectors of the JCMT (left) and the GBT (right)

2 Description of technique
· Each of our data sets consists of 3 nomical target of known shape (not maps are all taken at different focus our simulations (figure 3 ; normally is about ). to 5 beam maps using an astronecessarily a point source). The settings, which are decided from the phase change at edge of dish Figure 7: Calculated aperture function for the GBT; Left: phase, Right: amplitude

4
Figure 4: Top row: three SCUBA/JCMT maps of 3C279 used in the analysis, from left to right: focus -1.0 mm, in focus and focus +1.0mm. The white patch is due to a noisy bolometer which has been flagged as bad. Bottom row: Simulated beam maps corresponding to the best fit surface.

Closing Remarks
This technique for measurement of large-scale surface errors has several benefits: · It allows measurement of the surface at many different elevation angles, so allowing the measurement of gravitationallyinduced deformations, which should be mainly large scale. · It is also low cost, both in terms of money and time: it uses existing instrumentation, and the maps can usually be made in short periods, usually less than half an hour of observing time. · It uses astronomical receivers, and as these are upgraded and made more sensitive, the technique benefits from automatic increases in speed and accuracy. The technique is most likely to be useful when used as an extra diagnostic of antenna behaviors in conjunction with a conventional transmitter-based holography system which measures accurately the small scale errors.

· The primary reflector of the telescope is characterised by an aperture function, A(x, y). The modulus of the aperture function, |A(x, y)|, corresponds to "illumination", while the phase A(x, y) corresponds to deviations of surface from ideal shape. · We parametrise the phase of A(x, y) in terms of coefficients of Zernike polynomials[1] up to a certain radial order (normally 6 or 7, corresponding to around 25 parameters). Zernike polynomials are convenient because they are orthonormal on unit circle and low order polynomials have only low spatial frequencies which are well constrained with our technique. · We parametrise the modulus of A(x, y) by a two dimensional Gaussian whose centre, orientation, widths and amplitude are free parameters (giving 6 parameters in total). · We can then recover the A(x, y) from our measured dataset by numerical processing using the algorithm sketched in figure 2. We use the Levenberg-Marquardt minimisation algorithm from [2] which we independently check with our own implementation of the Downhill Simplex algorithm.
Calculate A(x, y) from parameters

5

Acknowledgments

Defocus/tilt/add coma to A(x, y) Find power pattern from P( , ) = A(x, y) 2 Repeat for other focus positions Compare P( , ) to observed maps: Find residuals and 2 Feed residuals into minimisation routine

Adjust parameters

We would like to thank Messrs Wouterloot and Friberg at the JCMT, and Maddalena, Balser, Ghigo, and Langston at the GBT, for kindly making observing time available and taking the data presented in this paper. BN would like to acknowledge the support of the U.K. Particle Physics and Astronomy Research Council (PPARC). Figure 5: The inferred aperture function from SCUBA/JCMT maps taken on 01/01/2002; top and bottom rows represent observations taken at different elevations. Left: Phase map (black to white represents a path difference) ; Right: a map of the amplitude of aperture function ("illumination")

Iterate

Figure 2: An outline of the algorithm used to infer the surface deformations

Ў



References
[1] Born and Wolf. Principles of Optics, chapter 9. Pergamon, 1970. [2] STARLINK, http://www.starlink.rl.ac.uk/star/docs/sun194. Public domain algorithms library.

3.2

The Green Bank Telescope

· The GBT is a 100-m off-axis paraboloid telescope, designed for frequencies up to around 100 GHz.

Further information on our holography work, details of other measurements and more detailed plots are available at: http://www.mrao.cam.ac.uk/bn204/oof.html.