Separating Field Contributions by their Source Volumes: Uniqueness and Limitations

Being able to reconstruct the sources of a radiated electromagnetic field is important for echo suppression of antenna measurements as well as source diagnostics. If two source domains are too close, the sources cannot be assigned uniquely to either of the source domains due to the finite measurement accuracy. This work investigates how the ability of separating the sources of an observed field depends on the separation distance between the source domains. By studying the singular value spectrum of the system matrices an estimate for the critical distance is developed after which source ambiguities no longer appear. If only one of the source domains is considered in the reconstruction, source contributions from the other source domain distort the reconstructed sources. An estimate for the magnitude of the distortion is also reported. Modifications of the formulations avoid explicit singular value decompositions and make it possible to apply the estimates also to electrically large source domains. A numerical example shows that the predictions accurately match the observed error behavior in the reconstructed sources.