What is the axial ratio of a circularly polarized antenna and how do I measure it?

The axial ratio (AR) of a circularly polarized antenna is the ratio of the major axis to the minor axis of the polarization ellipse traced by the tip of the electric field vector as the wave propagates. For perfect circular polarization, the axial ratio is 1.0 (0 dB), meaning the electric field traces a circle. For elliptical polarization (imperfect CP), the axial ratio is greater than 1 (> 0 dB). For linear polarization, the axial ratio is infinite. The axial ratio in dB is: AR_dB = 20 x log(E_major / E_minor), where E_major and E_minor are the magnitudes of the major and minor axes of the polarization ellipse. To measure the axial ratio: the standard method uses a linearly polarized reference antenna (a standard gain horn or dipole) that is rotated about the line of sight while recording the received signal level. As the linearly polarized antenna rotates through 360 degrees, a circularly polarized signal produces: a perfectly CP signal produces no variation (constant received power), while a non-ideal CP signal produces a sinusoidal variation where: AR_dB = P_max - P_min (the difference between the maximum and minimum received power levels). This spinning-linear method can be performed on a far-field antenna range or in a near-field scanning system. Modern vector network analyzer-based antenna ranges measure both orthogonal linear components (vertical and horizontal) simultaneously, from which the axial ratio is calculated: AR = (|E_R|^2 + |E_L|^2 + 2|E_R||E_L|) / (|E_R|^2 + |E_L|^2 - 2|E_R||E_L|) where E_R and E_L are the right-hand and left-hand circular components.