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:

$R=X+iY$

$L=X-iY$

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

$RR^{*}=(X+iY)(X+iY)^{*}=XX^{*}-iXY^{*}+iYX^{*}+YY^{*}$

$LL^{*}=(X-iY)(X-iY)^{*}=XX^{*}+iXY^{*}-iYX^{*}+YY^{*}$

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,

$Stokes\,I={\frac {RR^{*}+LL^{*}}{2}}=XX^{*}+YY^{*}$

$Stokes\,V={\frac {RR^{*}-LL^{*}}{2}}=i(XX^{*}-YY^{*})$

For completeness:

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Stokes\,Q=XX^{*}-YY^{*}}

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle Stokes\,U=XY^{*}-YX^{*}}

Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle P_{linear}={\sqrt {U^{2}+Q^{2}}}}

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} }

Polarization Mixing Correction

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