[evlatests] Closure and polarization - Erratum
Barry Clark
bclark at nrao.edu
Tue Mar 18 11:02:05 EDT 2008
I omitted the complex conjugate symbol from the polarization closure
equation. Below a derivation and the corrected equation.
Assumptions:
1. Single point source being observed
2. Bandpass of leakage terms same as bandpass of I, including delay
3. No CP
4. RR and LL have been calibrated and normalized to 1
Terminology: D1L is the leakage of L polarization into R for antenna 1, etc.
* is complex conjugate
Baseline RL LR
1-2 D1L + D2R* D1R + D2L*
1-3 D1L + D3R* D1R + D3l*
2-3 D2L + D3R* D2R + D3L*
Adding first and third lines and subtracting second gives
RL12 - RL13 + RL23 = D2R* + D2L
LR12 - LR13 + LR23 = D2L* + D2R
hence
RL12 - LR12* - RL13 + LR13* + RL23 - RL23* = 0
Notice it makes no difference whether these D's arise from instrumental
leakage, a polarized source, or a combination thereof, the closure relation
should continue to hold.
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