The polarization sphere as a graphical aid in determining the polarization of an antenna by amplitude measurements only

The polarization sphere and its stereographic projections, the polarization charts, are useful graphical aids in computations and measurements involving polarization. They may be advantageously utilized in the study and optimization of a technique for determining the polarization of an antenna by amplitude measurements only. In this technique, the response of the antenna to four waves of known-but-different polarization states is measured. From the measurements, three ratios are formed which are the relative polarization efficiencies of the antenna to the waves. Each ratio is representable as a contour on the polarization chart; the intersection of the three contours determines the antenna polarization. Defects or imperfections in the measurement system are representable as translations or distortions of the contours, yielding a simple relation between defects and resulting errors in determination of the antenna polarization. The contours may be used to minimize errors by, for example, choosing the four wave polarization states so that two of the three contours are nearly orthogonal for all expected values of the antenna polarization.