Polarization Calibration

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:

[math]\displaystyle{ R = X + iY }[/math]

[math]\displaystyle{ 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

[math]\displaystyle{ RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* }[/math]

[math]\displaystyle{ 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,

[math]\displaystyle{ Stokes I = \frac{RR^* + LL^*}{2} = XX^* + YY^* }[/math]

[math]\displaystyle{ Stokes V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*) }[/math]

For completeness:

[math]\displaystyle{ Stokes Q = XX^* - YY^* }[/math]

[math]\displaystyle{ Stokes U = XY^* - YX^* }[/math]

[math]\displaystyle{ P_{linear} = \sqrt{U^2 + Q^2} }[/math]

[math]\displaystyle{ \theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} }[/math]

Polarization Mixing Correction

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