# Difference between revisions of "Polarization Calibration"

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:<math>\begin{align} | :<math>\begin{align} | ||

− | XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} | + | XY^{*'} &= XY^*e^{-i(\phi(v) + \frac{\pi}{2})} \\ |

YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})} | YX^{*'} &= YX^*e^{ i(\phi(v) + \frac{\pi}{2})} | ||

\end{align} | \end{align} | ||

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:<math>\begin{align} | :<math>\begin{align} | ||

− | RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* | + | RR^* &= XX^* - iXY^{*'} + iYX^{*'} + YY^* \\ |

LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^* | LL^* &= XX^* + iXY^{*'} - iYX^{*'} + YY^* | ||

\end{align} | \end{align} |

## Revision as of 20:37, 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:

When I plot the quantities I, V, R and L as measured (Figure 1) for geosynchronous satellite Ciel-2, the results look reasonable, except that there are parts of the band where R and L are mis-assigned, and others where they do not separate well.

The problem is that residual phase slope of Y with respect to X, caused by a difference in delay between the two channels. This can be seen in the upper panel of Figure 2, which shows the uncorrected phases of XY* and YX*. To correct the phases, the RCP phase was fit by a linear least-squares routine, and then the phases were offset by π/2 for both XY* and YX* according to:

where φ(v) is the phase fit by the linear function. The corrected phases are shown in the lower panel of Figure 2.

When the corrected (primed) quantities are used in

## Polarization Mixing Correction

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