ToFD depth zone division

A single ToFD setup covers a limited depth range. Diffracted amplitude falls away from the beam crossing point, and the near-surface and backwall dead zones consume both ends of the wall. Above roughly 50 mm of thickness one setup can no longer be shown to cover everything, so the examination is split into depth zones, each with its own probe pair, angle, frequency and probe centre separation, and the resulting images are stacked to cover the full wall.

Within each zone the same two-thirds rule is applied: the beam axes are made to cross two-thirds of the way through the zone, measured from the top of that zone. The PCS then follows from the zone boundaries and the beam angle. For a single zone spanning the whole wall this reduces exactly to the familiar PCS = (4/3)*T*tan(theta). Some procedures instead place the crossing point at the centre of each zone; the fraction is selectable here and the governing procedure decides which applies. Deeper zones use lower frequency, larger elements and shallower angles to keep the sound path and the attenuation under control.

The arrival-time window of a zone is bounded by the times from its upper and lower boundary depths, computed with that zone PCS. For the first zone the upper boundary is the scanning surface, so the window starts at the lateral wave. Those two times are what the gate is set from for that setup.

Adjacent zones must overlap, and the coverage of every zone has to be demonstrated on a reference block with targets at the zone boundaries. The calculation fixes geometry only; it does not prove sensitivity, and the boundary regions are exactly where sensitivity is weakest.

zone thickness = T / n
d_top = (k − 1) × T / n,  d_bottom = k × T / n
d_cross = d_top + (2/3) × zone thickness   (½ where the procedure crosses at the zone centre)
PCS = 2 × d_cross × tan(θ)
t = 2 × √(S² + d²) / c  at each zone boundary