Post on 03-Jan-2016
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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
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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
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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
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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