Spatial Prediction of Electromagnetic Fields Using Few Measurements

In this paper, we propose an efficient method to estimate the electromagnetic field distribution as a function of space over the region of interest from the knowledge of field at a few points. For this purpose, we use the Huygens' principle, where the field at any point in the region of interest is expressed in terms of the tangential field on the surface of the scattering object. The tangential fields are expressed as a Fourier series expansions on the scatterer boundaries; these Fourier coefficients are estimated by taking measurements at random spatial points around and outside the scatterer. Once the Fourier coefficients across the boundary of the scatterer are known, we evaluate the field at arbitrary points using the Huygens' principle. Truth data is generated at all locations using either the BI method or a Finite Difference Frequency Domain method. The error is computed between the predicted field (based on noisy measurements) and truth data on a grid of square points around the scattering object. We study this error as a function of noise level, the number of basis functions, and the number of measurements after performing suitable Monte Carlo averages over several realizations of measurement points.