Electromagnetic Inverse Source Problems

In this chapter, we give a brief introduction to the electromagnetic inverse source problems in free space. Making use of the spherical harmonic expansions discussed in the previous chapters, the NDFs of the electromagnetic fields at different spherical observation surfaces can be estimated. Effective and stable numerical methods are developed for reconstructing the current sources in domains with regular structures from their radiated fields. In the electromagnetic inverse problem, we use the concept of the effective NDF of a source and the effective NDF of the field of the source. To develop stable reconstruction algorithm, we generally consider that the two NDFs should be matched. When we talk about the effective NDF of a field, we have to associate it with a source region and specify the size and shape of the source region, as well as the distance between the field and the source region. When we talk about the effective NDF of a source, we may have to associate it with the field on an observation surface and specify the distance between them. Basically, we tend to consider the source in a bounded region and its field at the sampling surface as a pair of connected physical quantities.