Frequency-Domain Integral Equations of Scattering for Complex Scalar Responses

A rigorous frequency-domain forward model of scattering is derived that relates any desired complex-valued scalar response to the vectors of the electromagnetic field. The model is valid in any reciprocal medium. The S-parameter forward model is derived as a special case. The forward model for the open-circuit voltage at the terminals of a receiving antenna is also given. The proposed model is useful in microwave imaging since it eliminates the need to employ inadequate approximations of: 1) Green's dyadic function and 2) the relation between the field in the antenna vicinity and its response. As a validation, the magnitude and phase distributions of fields are mapped using a small scattering probe in reflection-coefficient measurements. The maps contain both the magnitude and the phase distributions. The application of the proposed model in imaging is also demonstrated.