ToFD backwall dead zone

Resolution near the far surface is limited in the same way as near the scanning surface, but by the backwall reflection instead of the lateral wave. A tip close to the backwall diffracts a signal that arrives only slightly before the backwall echo, and if that gap is shorter than the pulse duration the two cannot be separated.

Setting the time difference equal to the pulse duration gives the deepest resolvable tip: d_max = sqrt((sqrt(S^2 + T^2) - c*tau/2)^2 - S^2). The dead zone is what remains of the wall, T - d_max. It is normally much thinner than the near-surface dead zone because the arrival-time curve is steep at that depth, but it is real, and mode-converted signals that follow the backwall make it worse in practice than the geometry alone suggests.

Root defects therefore need a complementary technique. In practice the backwall itself carries most of the useful information: a root-breaking flaw locally removes, delays or phase-reverses the backwall, and that behaviour is usually more reliable than searching for a separate tip signal a fraction of a microsecond ahead of it.

In practice the probe angle is chosen first and the PCS follows from it: with the beams crossed at two-thirds of the wall, PCS = (4/3)·T·tan θ. A 70° setup therefore carries a much wider PCS than a 45° one on the same wall, and since the dead zone grows with the probe separation, the chosen angle directly changes the dead zone. This calculator accepts either the angle (and derives the PCS) or a PCS you have already fixed.

PCS (derived) = (4/3) × T × tan θ   — beams crossed at ⅔ wall
S = PCS / 2
τ = n_cycles / f
R = √(S² + T²)
d_max = √( (R − c × τ / 2)² − S² )
dead zone = T − d_max