Frequency is the variable the operator controls directly, and it sets the standard depth of penetration through delta = 1 / sqrt(pi f mu sigma). Rearranged for frequency this becomes f = rho / (pi mu0 mur delta^2). The relationship is inverse-square: quadrupling the frequency halves the depth, so frequency selection is coarse and a factor of two either way is a real change in what the test can see.

Rather than asking for a depth directly, working practice asks how many standard depths deep the target lies. At n standard depths the eddy current field has fallen to e^-n of its surface value and lags the surface current by 57.3 x n degrees. Setting n = 1 puts the target at 37 % field and 57 degrees of lag, which is the usual compromise between penetration and signal. Setting n near 2 or 3 buys depth at the cost of amplitude (13 % and 5 %) and pushes the phase lag towards 115 and 172 degrees.

Beyond roughly three standard depths the response is unusable rather than merely weak: the phase has rotated so far that a deep flaw plots close to the lift-off direction and can be mistaken for probe wobble. If the wall is thicker than about three standard depths at the frequency you need for sensitivity, the answer is a different method or a dual-frequency approach, not more gain.

What comes out of this calculation is a starting frequency. Confirm it on the calibration standard: the frequency that gives the required signal-to-noise and the required phase separation between the shallowest and deepest calibration reflectors is the frequency the procedure gets.

Worked example

Electrical resistivity	72 uohm.cm
Relative permeability	1
Target depth	1.5 mm
Standard depths at the target	1
Required standard depth	1.5 mm
Test frequency	81.06 kHz
Phase lag at target depth	57.3 deg
Field strength at target depth	36.8 %

304 stainless (rho = 72 uohm.cm, mur = 1), 1.5 mm wall, one standard depth at the far surface. Required delta = 1.5/1 = 1.5 mm. In SI: rho = 7.2e-7 ohm.m, delta = 1.5e-3 m, delta^2 = 2.25e-6 m^2, pi.mu0 = 3.947842e-6. f = 7.2e-7 / (3.947842e-6 x 2.25e-6) = 7.2e-7 / 8.882644e-12 = 81057 Hz = 81.06 kHz. Cross-check with the engineering form 2533 x 72 / 2.25 = 81057 Hz. Phase lag at one standard depth = 1 radian = 57.3 degrees; field = 100 x e^-1 = 36.8 %.