Polarization Calibration: Difference between revisions

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:<math> L = X - iY </math>
:<math> L = X - iY </math>
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation.  The quantities RR* and LL* are then
In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation.  The quantities RR* and LL* are then
:<math> RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* </math>
:<math> RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* </math>
:<math> LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* </math>
:<math> LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* </math>
One problem is that there is generally a non-zero delay in Y with respect to X.  This creates phase slopes in XY* and YX* from which we can determine the delay very accurately.  As a check,
One problem is that there is generally a non-zero delay in Y with respect to X.  This creates phase slopes in XY* and YX* from which we can determine the delay very accurately.  As a check,
:<math> Stokes I = \frac{RR^* + LL^*}{2} = XX^* + YY^*</math>
:<math> Stokes I = \frac{RR^* + LL^*}{2} = XX^* + YY^*</math>
:<math> Stokes V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)</math>
:<math> Stokes V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)</math>
For completeness:
For completeness:
:<math> Stokes Q = XX^* - YY^* </math>
:<math> Stokes Q = XX^* - YY^* </math>
:<math> Stokes U = XY^* - YX^* </math>
:<math> Stokes U = XY^* - YX^* </math>
:<math> P_{linear} = \sqrt{U^2 + Q^2} </math>
:<math> P_{linear} = \sqrt{U^2 + Q^2} </math>
:<math> \theta = \frac{1}{2}\arctan{\frac{U}{Q}} </math>
:<math> \theta = \frac{1}{2}\arctan{\frac{U}{Q}} </math>


== Polarization Mixing Correction ==
== Polarization Mixing Correction ==
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas
Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas

Revision as of 20:04, 24 September 2016

Linear to Circular Conversion

At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:

In terms of autocorrelation powers, we have the 4 polarization products XX*, YY*, XY* and YX*, where the * denotes complex conjugation. The quantities RR* and LL* are then

One problem is that there is generally a non-zero delay in Y with respect to X. This creates phase slopes in XY* and YX* from which we can determine the delay very accurately. As a check,

For completeness:

Polarization Mixing Correction

Due to relative feed rotation between az-al mounted antennas and equatorial mounted antennas