Difference between revisions of "Polarization Calibration"

From EOVSA Wiki
Jump to: navigation, search
(Linear to Circular Conversion)
(Linear to Circular Conversion)
Line 1: Line 1:
 
== Linear to Circular Conversion ==
 
== 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:
 
At EOVSA’s linear feeds, in the electric field the linear polarization, X and Y, relates to RCP and LCP (R and L) as:
:<math> R = X + iY </math>
 
:<math> L = X - iY </math>
 
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
 
  
:<math> RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^* </math>
+
:<math>
 +
\begin{align}
 +
R = X + iY
 +
L = X - iY
 +
\end{align}
 +
</math>
 +
 
 +
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
  
:<math> LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^* </math>
+
:<math>
 +
\begin{align}
 +
RR^* = (X + iY)(X + iY)^* = XX^* - iXY^* + iYX^* + YY^*
 +
LL^* = (X - iY)(X - iY)^* = XX^* + iXY^* - iYX^* + YY^*
 +
\end{align}
 +
</math>
  
 
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,

Revision as of 20:19, 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