Generalization of the Ludwig-3 definition for linear copolarization and cross polarization

This article presents a generalization of Ludwig´s (1973) third definition that introduces a θ-dependence that is absent from Ludwig´s original definition. Our generalization is based on the nonconformal mapping between the electric field vector lying in the propagation plane (i.e., the probe aperture plane) and the projection of this vector onto the aperture plane (i.e., the AUT aperture plane). We show the error incurred by the two definitions for both the E-field and the H-field aperture models. Ludwig´s definition incurs the same level of error for both models while our generalized definition incurs slightly more error for the H-field aperture model but no error for the E-field aperture model