determining conductivity using eddy current testing
Hi, I have a question about measuring conductivity using an eddy current device. I obtained results from several unknown samples using an eddy current tester which simply displays an impedance diagram. I've also applied the eddy current tester to some samples of known conductivity, so I have some calibration points on my impedance display. All my measurements were done at the knee of the impedance plot, where mostly the imaginary component varies. Now I would like to find the conductivity of the unknown samples, by measuring their location on the impedance plot and comparing that result to the location of the calibration samples. However in order to get the conductivity of the unknown samples, I need a function relating the position of a sample on the locus to its conductivity. This function should partially be based on the experimental calibration data, however the form of this function should be based on some underlying physical theory, whether it's an equivalent circuit model or the EM equations underlying the eddy current test.
That is I need to know if the graph of location on the locus vs. conductivity for the calibration points should follow a polynomial of a certain order, or 1/(r^2-1) or what. If I had enough calibration point is could just fit some polynomial to them, but I don't, so I need to base it on the underlying theory. Any suggestions on how to do this, whether using physical theory or equivalent circuit?