SAMPLING THEORY FOR NEUROMAGNETIC DETECTOR ARRAYS

The sampling theorem for wave-number-limited multivariable functions i s applied to the problem of neuromagnetic field mapping. The wave-numb er spectrum and other relevant properties of these fields are estimate d. A theory is derived for reconstructing neuromagnetic fields from me asurements using sensor arrays which sample either the field component B(z) perpendicular to the planar grid of measurement points, or the t wo components partial derivative B(z)/partial derivative x and partial derivative B(z)/partial derivative y of its gradient in the xy plane. The maximum sensor spacing consistent with a unique reconstruction is determined for both cases. It is shown that, when two orthogonal comp onents of the gradient are measured at every site of the measurement g rid, the density of these sensor-pair units can be reduced, without ri sk of aliasing, to half of what is necessary for single-channel sensor s in an array sampling B. alone. Thus the planar and axial gradiometer arrays are equivalent in the sampling sense provided that the number of independent measurements per unit area is equal.