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Would be nice to be able to apply/correct rotation measure as one does for dispersion. From an e-mail by Dongzi (recipe slightly edited):
Here is the algorithm to correct the cable delay and RM for linear voltage data. It is straight-forward to test, just form the stokes with the corrected X and Y, and see if all the effects are removed. With the same parameter, if you are able to calibrate the stokes, you are able to calibrate the X and Y. If you want to do it more rigidly, there should be algorithm to calculate the Jones matrix given two calibration sources, it would also be straight-forward to apply (probably ask Luke for this).
correct cable delay: X=X*exp(-i tau f), where tau is the cable delay and f is the frequency
create circular pols L,R=0.5*(X±iY) (definition of L and R might be opposite);
correct RM: L=L*exp(- i RM lambda^2), R=R *exp(i RM lambda^2)
reconstruct linear: X=L+R, Y=(L-R)i
so the combined Jones matrix for the above steps will be
J=[[exp(i tau f) cos (RM lambda^2), -sin (RM lambda^2)],
[exp(-i tau f) sin(RM lambda^2), -cos(RM lambda^2)]]
and J dot [X,Y] would give you the corrected X and Y.
But I highly recommend to break the steps and form stokes parameters for each steps and see the effect for the first burst. I might be missing some constant phase, or the convention for RM/cable delay may be off by a sign, etc. But I think you are very smart, so this will be easy for you to find out.
Would be nice to be able to apply/correct rotation measure as one does for dispersion. From an e-mail by Dongzi (recipe slightly edited):
Here is the algorithm to correct the cable delay and RM for linear voltage data. It is straight-forward to test, just form the stokes with the corrected X and Y, and see if all the effects are removed. With the same parameter, if you are able to calibrate the stokes, you are able to calibrate the X and Y. If you want to do it more rigidly, there should be algorithm to calculate the Jones matrix given two calibration sources, it would also be straight-forward to apply (probably ask Luke for this).
X=X*exp(-i tau f)
, wheretau
is the cable delay andf
is the frequencyL,R=0.5*(X±iY)
(definition of L and R might be opposite);L=L*exp(- i RM lambda^2)
,R=R *exp(i RM lambda^2)
X=L+R, Y=(L-R)i
so the combined Jones matrix for the above steps will be
and
J dot [X,Y]
would give you the correctedX
andY
.But I highly recommend to break the steps and form stokes parameters for each steps and see the effect for the first burst. I might be missing some constant phase, or the convention for RM/cable delay may be off by a sign, etc. But I think you are very smart, so this will be easy for you to find out.
cc @theXYZT
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