Near-field image transfer by magneto-inductive arrays: A modal perspective

Abstract

A simple model of near-field pixel-to-pixel image transfer using magneto-inductive arrays is presented. The response of N-dimensional rectangular arrays is first found as an excitation of eigenmodes. This analytical method involves approximating the effect of sources and detectors, and replaces the problem of solving large numbers of simultaneous equations with that of evaluating a sum. Expressions are given for the modal expansion coefficients, and in the low-loss case it is shown that the coefficient values depend only on the difference in reciprocal frequency space of the operating frequency from the resonant frequency of each mode. Analytic expressions are then derived for quasi-optical quantities such as the spatial frequency response, point-spread function and resolving power, and their implications for imaging fidelity and resolution are examined for arrays of different dimension. The results show clearly that there can be no useful image transfer for in-band excitation. Out-of-band excitation allows image transfer. Provided the array is larger than the expected image by at least the size of the point spread function, the effect of the array boundaries may be ignored and imaging is determined purely by the properties of the medium. However, there is a tradeoff between fidelity and throughput, and good imaging performance using thick slabs depends on careful choice of the operating frequency. The approximate analytic method is verified by comparison of exact numerical solution of the full set of coupled equations, and the conditions for its validity are identified.