Phase Closure Relations -- from Eric Weisstein's World of Physics

Phase Closure Relations

Let the measured phase be , the actual phase , the phase error introduced by the atmosphere and other effects , and noise . Given any three antennas,

(1)

(2)

(3)

The sum is uncorrupted by phase errors (although random errors are still present), and is known as the "phase closure."

(4)

This relationship is the basis for both self calibration and hybrid mapping.

References

Cornwell, T. J. "The Application of Closure Phase to Astronomical Imaging." Science 245, 263-269, 1989.

Jennison, R. C. Mon. Not. Royal Astron. Soc. 118, 276-284, 1958.

Pearson, T. J. and Readhead, A. C. S. "Image Formation by Self-Calibration in Radio Astronomy." Ann. Rev. Astron. Astrophys 22, 97-130, 1984.

Readhead, A. C. S. and Wilkinson, P. N. Astrophys. J. 223, 25-36, 1978.