[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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