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.

Compression wave

Worked example

Wall thickness	90 mm
Number of zones	2
Zone number	2
Refracted beam angle for this zone	45 deg
Compression velocity	5900 m/s
Crossing point within the zone	twothirds
Recommended number of zones	2
Zone depth range	45 mm
Zone upper boundary	45 mm
Zone lower boundary	90 mm
Beam crossing depth	75 mm
Half separation	75 mm
PCS for this zone	150 mm
Arrival time at zone top	29.65 µs
Arrival time at zone bottom	39.71 µs

A 90 mm wall falls in the band needing two setups. Each zone is 90/2 = 45 mm deep, so zone 2 runs from 45 mm to 90 mm. The crossing point is two-thirds through the zone, 45 + 30 = 75 mm. tan(45 deg) = 1, so S = 75 mm and PCS = 150 mm. With c = 5.9 mm/us, the zone top gives 2 x sqrt(75^2 + 45^2)/5.9 = 2 x sqrt(7650)/5.9 = 2 x 87.4643/5.9 = 29.6489 us, that is 29.65 us; the zone bottom gives 2 x sqrt(75^2 + 90^2)/5.9 = 2 x sqrt(13725)/5.9 = 2 x 117.1537/5.9 = 39.7131 us, that is 39.71 us.

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