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This is a question about hard-field back-projection as used in x-ray tomography, applied magnetic induction tomography. Al-Zeibak and Saunders have shown that x-ray filtered backprojection can be applied to an exciter and receiver coil, with a straight line of magnetic flux between them along the central axes of the 2 coils, taking the place of a straight line beam of an x-rays, to scan/image and an object (plastic container of saline solution).

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In place of the summation of the x-ray attenuation coefficients $\mu(x,y)$,

$$p_\theta(r) = ln \lgroup \frac{I}{I_0} \rgroup = - \int \mu(x,y) ds$$

https://en.wikipedia.org/wiki/Tomographic_reconstruction

they appear to detect the summation of voltages at receiver coil:

$$p_\theta(r) = \int V(x,y) ds$$

Where $V(x,y)$ is the voltage in the object at $(x,y)$

Would it be possible to convert this (Al-Zeibak and Saunders method) to a square Helmholtz-coil assembly, providing a uniform AC magnetic field (i.e. straight lines of flux) and a square array of air-cored inductors as the receiving/sensor coils. So that a metallic object being scanned would generate a summation of voltages for each approximate straight line of flux of the Helmholtz coils?

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