Extrapolation Of Two Vector Components Of A Biomagnetic Field From Measurements Of The Third Component
Heidi A. Schlitt, Kelly Rehm, William J. Dallas, W Kullmann · Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE · 1989
Techniques exist for reconstructing current density vectors from measurements of the three components of the generated magnetic field. In order to have a practical data collection scheme, the number of measurements must be as small as possible. In addition, some technical difficulties exist in using SQUID detectors to measure all three components of a magnetic field simultaneously. This paper presents a method for extrapolating the missing x- and y-components of a biomagnetic vector field from the measured z-component, under certain readily met boundary conditions. Specifically, we address the solution of such a problem when the measured data consists of the z-component in a single plane. The boundary conditions that must be met in order to perform the extrapolation require that the z-component values fall off to zero on the edges of the measurement plane, and that the extrapolation be performed in a region free of current sources.