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Automatic Omniscope Calibration Using Redundant Baselines

This paper presents an innovative method for the automatic calibration of omniscopes using redundant baselines. Unlike traditional interferometers, omniscopes present unique challenges due to identical baselines yielding different results. The proposed method demands that redundant baselines produce consistent outcomes, facilitating a mathematically fit over-determined system that accounts for true sky signals and instrumental noise. By leveraging these redundant baselines, we can navigate issues inherent in classic calibration techniques, enabling improved measurement accuracy with simulated data.

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Automatic Omniscope Calibration Using Redundant Baselines

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  1. Automatic Omniscope Calibration UsingRedundant Baselines SwFRT, Fermilab, 2009 Adrian Liu (with Max Tegmark, Andy Lutomirski, Scott Morrison, Matias Zaldarriaga)

  2. Unlike Traditional Interferometers, Omniscopes Have Many Redundant Baselines

  3. In Reality, Identical Baselines Will Give Different Results

  4. Main Idea: Demand that redundant baselines give the same results and fit for everything

  5. Mathematically, an over-determined system

  6. True sky signal Instrumental noise Measured signal Complex gain: where si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  7. si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  8. Real Part: Gains Have this (data) Know this Want this si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  9. Real Part: Gains d A b si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  10. A Problem With Degeneracies • Real part (gains): • No knowledge of absolute gain. • Imaginary part (phases): • No knowledge of absolute phase. • No knowledge of x-tilt. • No knowledge of y-tilt. si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  11. si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  12. si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  13. si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  14. A Weighty Issue

  15. Weighted Fit

  16. si = signal measured by antenna i ; gi = gain of antenna i y = true corr; cij = measured corr

  17. Some Bias

  18. Differences Between This and Traditional Calibration

  19. Summary • Redundant baselines provided by omniscopes can be exploited for calibration • Proposed automatic calibration scheme works on simulated data • Using redundant baselines allows one to sidestep certain problems with traditional techniques (like the necessity of having isolated point sources).

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