Difference between revisions of "Polarization Calibration"

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(Linear to Circular Conversion)
(Linear to Circular Conversion)
Line 5: Line 5:
 
\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>
+
:<math>
 
+
\begin{align}
:<math> Stokes \, V = \frac{RR^* - LL^*}{2} = i(XX^* - YY^*)</math>
+
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>
 
:<math> P_{linear} = \sqrt{U^2 + Q^2} </math>
 
 
:<math> \Theta = \frac{1}{2}\tan^{-1}{\frac{U}{Q}} </math>
 
  
 
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