Primary beam shape calibration from mosaicked interferometric observations
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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 seminar 8 November 2010. Outline. Motivation

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Primary beam shape calibration from mosaicked interferometric observations
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


Outline
Outline

  • Motivation

  • Beam-characterization methods

    • Two-point Gaussian fitting

    • Chi-squared fitting

  • Results

  • Simulation applying method to ATA-350 and SKA


The allen telescope array
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




Motivation
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


Pigss pointings
PiGSSpointings

Bower et al., 2010


Primary beam characterization
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


Primary beam characterization1
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.


Primary beam characterization2
Primary-beam characterization

  • Canonical value of FWHM:


Same source multiple appearances
Same source, multiple appearances

Pointing 1

Pointing 2

Images courtesy of Steve Croft

Can use sources’ multiple appearances to characterize the beam


Method 1 two point gaussian solution
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


Method 1 two point gaussian solution1
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


Method 1 two point gaussian solution2
Method 1: Two-point Gaussian solution

  • Solution:

  • Problems: when S1 ≈ S2and whenθ1 ≈θ2


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


Method 1 calculated fwhm values
Method 1: Calculated FWHM values

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


Method 2 2 minimization
Method 2: χ2minimization

  • Find the FWHM value that minimizes

  • Benefits:

    • Uses all the data

    • Can be extended to fit ellipticity, beam angle, etc.




Method 2 best fit fwhm
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


Method 2 comparison with theory
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


Simulation applying the 2 minimization method to future telescopes
Simulation: applying the χ2 minimization method to future telescopes

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


Simulation applying the 2 minimization method to future telescopes1
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


Simulation results
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%


Conclusions
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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