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Primary Beam Shape Calibration from Mosaicked, Interferometric

Observations

Chat Hull

Collaborators: Geoff Bower, Steve Croft, Peter Williams, Casey Law, Dave Whysong, and the rest of the ATA team

UC Berkeley, RAL seminar8 November 2010

8 November 2010

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Outline

• Motivation• Beam-characterization methods– Two-point Gaussian fitting– Chi-squared fitting

• Results• Simulation applying method to ATA-

350 and SKA

8 November 2010

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The Allen Telescope Array

• Centimeter-wave large-number-of-small-dishes (LNSD) interferometer in Hat Creek, CA

• Present: ATA-42, 6.1-meter antennas• Wide-band frequency coverage: 0.5 –

11.2 GHz (3-60 cm)• Excellent survey speed (5 deg2 field of

view)• Commensal observing with SETI8 November 2010

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Bad mosaic

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Good mosaic

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Motivation• We want to make mosaics

• Need to have excellent characterization of the primary beam shape

– Primary beam: sensitivity relative to the telescope’s pointing center

– Start by characterizing the FWHM of the primary beam using data from ATATS & PiGSS

8 November 2010

Image courtesy of James Gao

FWHM = 833 pixels

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PiGSS pointings

8 November 2010

Bower et al., 2010

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Primary-beam characterization

8 November 2010

• Primary-beam pattern is an Airy disk

• Central portion of the beam is roughly Gaussian

• Good approximation down to the ~10% level

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Primary-beam characterization

• In this work we assume our primary beam is a circular Gaussian.

• Our goal: to use ATA data to calculate the actual FWHM of the primary beam at the ATATS and PiGSS frequencies.

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Primary-beam characterization

• Canonical value of FWHM:

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Same source, multiple appearances

8 November 2010

Images courtesy of Steve Croft

Pointing 1 Pointing 2

Can use sources’ multiple appearances to characterize the

beam

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Method 1: Two-point Gaussian solution

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• We know the flux densities and the distances from the pointing centers

• Can calculate the FWHM of a Gaussian connecting this two points

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Method 1: Two-point Gaussian solution

• Analytic solution to the Gaussian between two source appearances:

• θ1 , θ2 distances from respective pointing centers

• S1 , S2 fluxes in respective pointings

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Method 1: Two-point Gaussian solution

• Solution:

• Problems: when S1 ≈ S2 and whenθ1 ≈θ2

8 November 2010

158 November 2010

BART ticket across the Bay

Projected Cost of SKA

Not being able to use the best part of your data

Priceless

$3.65

$2,000,000,000.00

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Method 1: Calculated FWHM values

8 November 2010

Median primary-beam FWHM values using 2-point method:

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Method 2: χ2

minimization

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• Find the FWHM value that minimizes

• Benefits: – Uses all the data– Can be extended to fit ellipticity, beam

angle, etc.

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Observed flux pairs

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Corrected flux pairs

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Method 2: Best-fit FWHM

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• High values (~21 for ATATS; ~10 for PiGSS)• Due to systematic underestimation of flux

density errors, non-circularity of the beam, mismatched sources

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Method 2: comparison with theory

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• We see a slightly narrower beam-width

• Due to imperfect understanding of ATA antenna response, inadequacy of Gaussian beam model

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Simulation: applying the χ2 minimization method to future

telescopes

• As Nant increases, rms noise decreases, and number of detectable sources increases:

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Simulation: applying the χ2 minimization method to future telescopes

• Perform simulation for arrays with NA increasing from 42 to 2688, in powers of 2

• Generate sources across a 12.6 deg2, 7-pointing PiGSS-like field– Use S-2 power-law distribution, down to the rms flux

density of the particular array– Add Gaussian noise to flux densities– Note: pointing error not included

• “Observe” and match simulated sources• Applyχ2 minimization technique to calculate

uncertainty of the FWHM of the primary beam of each array

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Simulation: results

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• 42-dish simulation returns FWHM uncertainty of 0.03º

• In the absence of systematic errors, the FWHM of the SKA-3000 primary beam could be measured to within 0.02%

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Conclusions

• ATA primary beam has the expected FWHM– Our calculated value:

• Chi-squared method is superior to 2-point method• Results are consistent with canonical value (Welch et

al.), radio holography (Harp et al.), and the Hex-7 beam characterization technique

• Arrived at an answer with zero telescope time• Potential application to other radio telescopes needing

simple beam characterization using science data

8 November 2010