Memo 118 Focal Plane Array Simulations with MeqTrees III: Observations with an AzEl Mount Telescope A.G. Willis

10/09

www.skatelescope.org/pages/page_memos.htm

Focal Plane Array Simulations with MeqTrees III:Observations

with an AzEl Mount Telescope

A.G. WillisNational Research Council of Canada

Dominion Radio Astrophysical ObservatoryPenticton, BC, Canada V2A 6J9

Tony.Willis@nrc-cnrc.gc.ca

October 9, 2009

1 Introduction

Antennas with phased array feeds have been successfully used by the military as part of radar systems torapidly scan the sky for potential enemy aircraft as well as steer surface-to-air missiles[1]. Electronic steeringallows such systems to track many targets simultaneously. Can such electronic steering systems be combinedwith an aperture synthesis radio telescope to track astronomical targets in a similarly useful manner?

In a previous memo [2] we showed examples of phasing up the beams of a phased-array feed at separatelocations on a grid of positions at given offsets from boresight. If we wish to track a fixed position on thesky away from the boresight with a phased array feed located at the prime focus of a parabolic dish havinga conventional AzEl mount, we must adjust the phased array weights to track the position because the skyrotates with respect to the feed as a function of time. Figure 1 shows a prototype of such a system: thePHAD/CART phased array feed and dish currently being developed at the Dominion Radio AstrophysicalObservatory. What kind of impact can we expect this adjustment of weights to have on the quality of thedata collected by an aperture synthesis telescope equipped with such a configuration? Here I present sometracking simulations that make use of a ‘pure’ AzEl telescope similar to the CART/PHAD design and lookat some initial performance issues. (It is also my understanding that the antenna design selected for the U.S.TDP project will use an AzEl mount, albeit with an offset reflector, so similar simulations may eventuallybe of interest for that design.)

2 Experimental Setup

I used the same experimental setup as that described in [2]. This consisted of a simulated focal plane arrayplaced at the prime focus of a parabolic dish. The configuration consisted of:

• Parabolic dish diameter = 10m; Focal length = 4.5m

• 90 dipole elements in each of X and Y directions.

• Frequency = 1500 MHz; Spacing = lambda / 2

• No coupling between elements; No feed struts in simulation

As we pointed out in [2] this dipole simulation is not something one would want to use for an actualantenna design, but it does allow us to examine how adjustment of the phased array weights can be used tomodify and shape the instrumental response. Here I place such an instrument at the VLA site. Using theMeqTrees simulation software, I track a field centre offset by 2 x FWHM in L, 0 x FWHM in M at transitover the range -4 to +4 hours in hour angle. Separate ’observations’ are simulated at the declinations of28.5 and 57 degrees. If I have an AzEl mounted dish, the dish orientation is rotated with respect to the sky

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Figure 1: Left - the CART (Composite Applications for Radio Telescopes) dish at DRAO with the PHAD(Phased Array Demonstrator) mounted at the prime focus. The dish has an Azimuth-Elevation mount.Right - a closeup of the PHAD system.

Figure 2: Track in the telescope frame of a field centre centred at L=2xFWHM, M = 0 at transit. Theobservation is 8 hours long, centred on transit. The plot show the phase-up positions on the FPA grid atparallactic angles of -1.2, -0.8, -0.4, -0.2, 0, 0.2, 0.4, 0.8, and 1.2 radians for an observation at 28 degreesDeclination. The L and M coordinates are given in degrees.

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by the parallactic angle. This means that in order to track a given position on the sky I must continuallyadjust the FPA weights as the phase-up position will change as a function of time with respect the the FPAarray, which is fixed in AzEl coordinates. Figure 2 shows the locations of this position on the FPA grid atparallactic angles of -1.2, -0.8, -0.4, -0.2, 0, 0.2, 0.4, 0.8, and 1.2 radians for the observation at 28 degreesDeclination.

Figure 3 though Figure 6 show the corresponding phased up beam response at these positions afterrotation back to the plane of the sky. I perform this adjustment of the primary beam by including theP-Jones projection matrix, Pi, which models the projected orientation of the receptors with respect to theelectrical frame on the sky, in the Measurement Equation (see Equations 1 and 2 of [2]). For properly alignedlinearly polarized feeds, as is the case for our dipole simulation, this may be reduced to

P+i =

(cos β − sin βsin β cos β

)(1)

where β is the parallactic angle. This is normally a unit diagonal matrix the case where the receptors arealigned perfectly with the East and North (L and M) axes for equatorially mounted dishes. For azimuth-elevation telescopes at transit this is a unit diagonal matrix, but such is not the case for the off-transitsituation.

What is noticeable from examination of Figures 3 though 6 is that although there is variation ofthe phased up primary beam response as a function of parallactic angle, the GRASP fit weighting schemedescribed in [2] reduces the amount of variation.

Figures 3 though Figure 6 basically give a qualitative overview of what the formed-up beams look likeas a function of parallactic angle. For an observation at 28 deg Declination, I can give a more quantitativeview by plotting the phased-up beam response over an entire 8 hour observation at a position 41 arcminpositive offset in L relative to the phase-up position of L= 2 x FWHM at transit. This position is closeto the expected half-power response of the Stokes I beam. Figures 7 and 8 show the results plotted as afunction of parallactic angle and hour angle respectively. Since 28 deg Declination is quite close to the VLAzenith of 33 degrees, most of the variation in gain occurs within one hour of transit, which then correspondsto a large change in parallactic angle. The plots clearly show that the variations in both total intensity andinstrumental response are dramatically lowered by the Gaussian and GRASP fitting procedures. The resultsalso show that the fitted Gaussian and GRASP beams both have slightly broader response (and thus higherStokes I response) than does the Conjugate weighted beam.

The UV locations for each 8-hour observation were updated every 60 seconds so there are 480 samplepoints and accordingly 480 separate adjustments of the focal plane array weights.There is some jitter in thegains calculated for the Gaussian fits, but notice that this jitter decreases significantly for the case of the fitsto the GRASP-designed central feed. The remaining jitter of approximately 2 percent at the half maximumpoint for a primary beam at 1.5 GHz is roughly equivalent to the gain fluctuations that would be caused bypointing errors of about 30 arcsec. A discerning eye may note that the plots are not quite symmetric withrespect to transit. This was caused by our having to avoid rotating the sky by a parallactic angle of exactly0 degrees in the current version of MeqTrees.

Figures 9 and 10 show similar plots, but here I have selected an even larger distance to the phase-upposition (an increase in the value of the L offset to 1 degree from the phase up point). Here the total intensityresponse has decreased to approximately 20 percent (GRASP or Gaussian fitting). Since this position isquite far from the field centre position, instrumental polarization responses in especially the phase-conjugateweighting case become quite large and vary dramatically as a function of time.

The final two figures 11 and 12 show similar gain plots for an observation centred at 58 degreesDeclination. This location is much further away from the VLA zenith, so the discrepancy between hourangle and parallactic angle is not so large. Consequently, I just show the plots as a function of hour angle.Note how in this case the sign of the instrumental U and V as a function of hour angle is opposite to thatof the 28 deg Declination case.

Note that our plots only show the responses at two particular locations within the phased up beams, atL + 41 arcmin and + 1 degree relative to the phase-up point. Responses in other directions will certainlybe different and hopefully will be investigated in future work.

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3 Conclusions

The simulations reported here suggest that tracking of a point on the sky with an AzEl mounted focal planearray by appropriate adjustment of focal plane array weights can be done successfully. I note that actualimplementations of focal plane arrays using elements such as Vivaldi antennas can have significantly lowerinstrumental polarization [4] than the dipoles used for our simulations; consequently I expect that analysisand use of data from actual focal plane arrays, which I hope to report on in later memos, may give evenbetter results than those reported here.

4 Acknowledgements

I thank Walter Brisken for initial guidance and advice which led eventually to SKA Memo 115 and to thismemo.

References

[1] Tech. Rep. [Online]. Available: http://en.wikipedia.org/wiki/Phased array

[2] A. G. Willis, B. Veidt, and A. Gray, “Focal Plane Array Simulations with Meqtrees1:Beamforming,” International SKA Project Office Memo 115, Tech. Rep., 2009. [Online]. Available:http://www.skatelescope.org/PDF

[3] B. Veidt unpublished, 2009.

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Figure 3: Phased-up beam I and instrumental Q responses as a function of parallactic angle for the caseof phase-conjugate weighting. The beams are shown as they would appear rotated back to the normal skyRA/DEC reference frame. The Parallactic angle increases in the directions left to right, top to bottom andcorresponds to the positions marked in Figure 2. In this and succeeding figures the two contours delineatethe 10% and 50 % response of the Stokes I primary beam.

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Figure 4: Phased up beam instrumental U and V responses as a function of parallactic angle for the case ofphase-conjugate weighting.

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Figure 5: phased-up beam I and instrumental Q responses as a function of parallactic angle for the case ofGRASP-fitted weighting. Parallactic angle increases in in the directions left to right, top to bottom.

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Figure 6: phased-up beam instrumental U and V responses as a function of parallactic angle for the case ofGRASP-fitted weighting.

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Figure 7: Track showing the approximate phased-up half power beam response in the sky reference frame fora field centred at L=2xFWHM, M = 0 at transit at Declination 28 degrees. The observation is 8 hours long,centred at transit.In this and the following figures, the green line shows the response when phase-conjugateweighting is used. The blue line shows the response when Gaussian weighting is used. The red line shows theresponse when the weights derived from a fit to the GRASP-designed feed are used. Here the responses asa function of parallactic angle are shown. In this and succeeding plots I show the Stokes I response directly,and the instrumental Stokes Q, U and V as a fraction of I.

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Figure 8: Track showing the approximate phased-up half power beam response in the sky reference framefor a field centred at L=2xFWHM, M = 0 at transit at Declination 28 degrees. The observation is 8 hourslong, centred at transit. Here the responses as a function of hour angle are shown.

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Figure 9: Track showing the approximate phased-up beam response near the 20% level in the sky referenceframe for a field centred at L=2xFWHM, M = 0 at transit at Declination 28 degrees. The observation is 8hours long, centred at transit. Here the responses as a function of parallactic angle are shown.

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Figure 10: Track showing the approximate phased-up beam response near the 20% level in the sky referenceframe for a field centred at L=2xFWHM, M = 0 at transit at Declination 28 degrees. The observation is 8hours long, centred at transit. Here the responses as a function of hour angle are shown.

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Figure 11: Track showing the approximate phased-up half power beam response in the sky reference framefor a field centred at L=2xFWHM, M = 0 at transit at Declination 58 degrees. The observation is 8 hourslong, centred at transit. The responses are plotted as a function of hour angle.

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Figure 12: Track showing the approximate phased-up beam response near the 20% level in the sky referenceframe for a field centred at L=2xFWHM, M = 0 at transit at Declination 58 degrees. The observation is 8hours long centred at transit. The responses are plotted as a function of hour angle.

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