I dont really know what co-polarization is but i think axial ratio is the ratio of the Φ and θ components of the field. But you have to choose either EΦ/Eθ ≥1 or Eθ/EΦ≥1. I mean you have to take the ratio that is greater than 1.
axial ratio is a parameter to describe the circular polarization performance of an antenna. For more information, you can refer some classical antenna book, such as Balanis's Antenna Theory: Analysis and Design.
A linear polarization is specified by its spatial orientation(co-polarization) and by its cross-polarization.
+Co-polarizartion is desired signal
+Cross-polarizarion is undesired signal.
Circular polarization is specified by its sense and by its axial ratio.
A peak-peak value is the axial ratio and represents the polarization quality for a circular polarized antenna.