# Difference between revisions of "Polarization Calibration"

(→Linear to Circular Conversion) |
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\begin{align} | \begin{align} | ||

R = X + iY \\ | R = X + iY \\ | ||

− | L = X - iY | + | L = X - iY \\ |

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

</math> | </math> | ||

Line 14: | Line 14: | ||

\begin{align} | \begin{align} | ||

RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\ | RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* \\ | ||

− | LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* | + | LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* \\ |

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

</math> | </math> | ||

Line 20: | Line 20: | ||

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> |

− | + | \begin{align} | |

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

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

+ | \end{align} | ||

+ | </math> | ||

For completeness: | For completeness: | ||

Line 28: | Line 31: | ||

:<math> | :<math> | ||

\begin{align} | \begin{align} | ||

− | Stokes \, Q = XX^* - YY^*\\ | + | Stokes \, Q = XX^* - YY^* \\ |

Stokes \, U = XY^* - YX^* \\ | Stokes \, U = XY^* - YX^* \\ | ||

+ | P_{linear} = \sqrt{U^2 + Q^2} \\ | ||

+ | \Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} \\ | ||

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

</math> | </math> | ||

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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. | 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. |

## Revision as of 20:21, 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:

## Polarization Mixing Correction

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