Eddy current phase lag with depth

Phase lag is what turns eddy current testing into a depth-measuring method instead of an amplitude-measuring one. The current at depth x lags the surface current by x/delta radians, which is 57.3 degrees for every standard depth of penetration. Amplitude decays over the same distance, but amplitude is also driven by flaw volume, probe wobble and lift-off, whereas the phase angle is dominated by depth alone. That is why depth is sized from the angle of the signal on the impedance plane and not from its height.

On the impedance plane this is the whole basis of mixing and discrimination. With the display rotated so that lift-off lies horizontal, a surface-breaking flaw at the near surface plots almost perpendicular to lift-off, and as the flaw origin moves away from the coil the signal rotates progressively clockwise. Two reflectors that differ in depth by half a standard depth are separated by about 29 degrees - comfortably resolvable. Two that differ by a tenth are separated by 5.7 degrees and will not be separable in practice.

The rotation is also the practical depth limit. At three standard depths the lag is 172 degrees and the remaining field is 5 %; at pi standard depths the lag reaches a full 180 degrees, the signal is back in line with lift-off, and beyond it deeper flaws start plotting like shallower ones. Combined with the amplitude loss, this fixes the useful inspection depth at roughly three standard depths regardless of available gain.

Use this when building or checking a calibration curve, when deciding whether two reflectors will be separable, and when explaining why a known deep flaw plots where it does on the screen.

delta = 1 / sqrt(pi · f · mu0 · mur · sigma)
theta [rad] = x / delta        theta [deg] = 57.3 · x / delta
one standard depth = 57.3 deg      90 deg at x = 1.571 · delta      180 deg at x = 3.142 · delta
field at x = 100 · e^(-x/delta) %