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Primary Beam Shape Calibration from Mosaicked , Interferometric ObservationsPowerPoint Presentation

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
- Beam-characterization methods
- Two-point Gaussian fitting
- Chi-squared fitting

- Results
- Simulation applying method to ATA-350 and SKA

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

- 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

PiGSSpointings

Bower et al., 2010

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 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 characterization

- Canonical value of FWHM:

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

- 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 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 solution

- Solution:
- Problems: when S1 ≈ S2and whenθ1 ≈θ2

$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

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

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

- 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

- We see a slightly narrower beam-width
- Due to imperfect understanding of ATA antenna response, inadequacy of Gaussian beam model

Simulation: applying the χ2 minimization method to future telescopes

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

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

- 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

- 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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