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Physics-Based Splines Interpolating Electric=Field Measurements


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Mitigating Electro-Magnetic Interference (EMI) is a long-term engineering problem for shipboard RF systems [15], [14]. Measuring the electric field is basic to EMI mitigation. This report analyses electric-field measurements taken on the flight deck of a carrier. These electric field is sparsely sampled at selected locations on the flight deck. Interpolation schemes fill in the electric field between sample points. The quality of these interpolated electric fields is the object of discussion of this report. Standard splines do not encode the physics of the problem that the electric field in free space has zero divergence. This report develops a class of splines with zero divergence. Comparisons between these divergence-free splines and standard splines demonstrates enforcing zero divergence improves the quality of the spline fewer sample points are required to recover the electric field with greater accuracy than the standard splines. Applying a divergence-free spline to these flight-deck measurements requires a hybrid approach because only the electric field magnitude was measured. The hybrid approach exploits knowledge of the physical measurement to constrain the divergence-free splines to interpolate the amplitude at each sample point while leaving the phases as free variables at each sample point. The phases are optimized to approximate the splined electric-field magnitude. Consequently, the hybrid approach produces a divergence-free spline that matches the measured amplitude at each sample point and is a best approximation to the standard spline



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