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

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

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 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,

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

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

For completeness:

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 Stokes \! Q = XX^* - YY^* }

$StokesU=XY^{*}-YX^{*}$

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 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