Near-Field Electromagnetic Holography in Conductive Media

A new approach to the inversion of ill-posed boundary value (BV) problems is presented for an infinite conductive, homogeneous media. Our interest is to investigate the possibility of imaging underwater electromagnetic sources from remote electromagnetic sensor data when that data is measured coherently over a spatial sheet, commonly referred to as a hologram. Specifically, given independent holograms of two polarizations of the electric and/or magnetic fields on a cylindrical surface exterior to the electric and magnetic sources, we develop a frequency domain, back-projection (inverse) technique that reconstructs the complete electric and magnetic vector fields in the region between the BV (hologram) surface and the sources. Of particular interest is the Poynting vector that is constructed from the back-projected fields, providing the power per unit area radiated from the sources. We believe it may be of immense practical use in diagnosis of electromagnetic sources, such as underwater ship propulsors. Tikhonov regularization, developed here for the two component measured field, is used to stabilize the inversion. To investigate the accuracy and limitations of this new approach, we carry out a numerical experiment in which an array of either magnetic or electric dipole sources are excited in a frequency range of 1 to 1000 Hz in seawater. They are arranged 8 m apart in a line and generate coherent holograms of the axial components of the electric and magnetic fields on an imaginary cylindrical sheet of radius 30 m. Spatially random noise is added to these two holograms to simulate a relatively poor signal to noise ratio of 20 dB. Results show that we can successfully reconstruct the electric, magnetic and Poynting field vectors on the cylindrical sheet of 20 m radius (10 m closer to sources) with an accuracy of less than 30% for both magnetic dipole sources and electric dipole sources from 1 to 1000 Hz. The computations needed for this approach are easily carried out on a laptop computer and reconstructions of the complete field vectors are extremely fast, with a processing time in seconds.