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

This letter presents a generalization of Ludwig's third definition that int roduces a theta -dependence that is absent from Ludwig's original definitio n. Our generalization is based on the nonconformal mapping bt tween the ele ctric 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,, th e AUT aperture plane). We show the error incurred by the two definitions fo r both the E-field and the H-field aperture models. Ludwig's definition inc urs the same level of error for both models while our generalized definitio n incurs slightly more error for the H-field aperture model but no error fo r the E-field aperture model.