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Calibration of Primary Beam Shape for ATA Using Mosaicked Interferometric Observations

This presentation discusses methods for calibrating the primary beam shape of the Allen Telescope Array (ATA) using mosaicked interferometric observations. Focused on beam characterization through two-point Gaussian fitting and chi-squared minimization, the study evaluates the beam's sensitivity relative to the telescope’s pointing center. The results indicate a calculated FWHM consistent with theoretical expectations and provide insights applicable to future radio telescopes. The session was part of the RAL seminar at UC Berkeley on November 8, 2010.

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Calibration of Primary Beam Shape for ATA Using Mosaicked Interferometric Observations

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  1. 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 seminar 8 November 2010

  2. Outline • Motivation • Beam-characterization methods • Two-point Gaussian fitting • Chi-squared fitting • Results • Simulation applying method to ATA-350 and SKA

  3. 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 SETI

  4. Bad mosaic

  5. Good mosaic

  6. 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 FWHM = 833 pixels Image courtesy of James Gao

  7. PiGSSpointings Bower et al., 2010

  8. Primary-beam characterization • Primary-beam pattern is an Airy disk • Central portion of the beam is roughly Gaussian • Good approximation down to the ~10% level

  9. 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.

  10. Primary-beam characterization • Canonical value of FWHM:

  11. Same source, multiple appearances Pointing 1 Pointing 2 Images courtesy of Steve Croft Can use sources’ multiple appearances to characterize the beam

  12. Method 1: Two-point Gaussian solution • We know the flux densities and the distances from the pointing centers • Can calculate the FWHM of a Gaussian connecting this two points

  13. 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

  14. Method 1: Two-point Gaussian solution • Solution: • Problems: when S1 ≈ S2and whenθ1 ≈θ2

  15. BART ticket across the Bay $3.65 Projected Cost of SKA $2,000,000,000.00 Not being able to use the best part of your data Priceless

  16. Method 1: Calculated FWHM values Median primary-beam FWHM values using 2-point method:

  17. Method 2: χ2minimization • Find the FWHM value that minimizes • Benefits: • Uses all the data • Can be extended to fit ellipticity, beam angle, etc.

  18. Observed flux pairs

  19. Corrected flux pairs

  20. Method 2: Best-fit FWHM • High values (~21 for ATATS; ~10 for PiGSS) • Due to systematic underestimation of flux density errors, non-circularity of the beam, mismatched sources

  21. Method 2: comparison with theory • We see a slightly narrower beam-width • Due to imperfect understanding of ATA antenna response, inadequacy of Gaussian beam model

  22. Simulation: applying the χ2 minimization method to future telescopes • As Nant increases, rms noise decreases, and number of detectable sources increases:

  23. 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

  24. Simulation: results • 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%

  25. 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

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