ToFD off-axis depth error

The ToFD depth equation assumes the diffractor sits on the line midway between the two probes. A tip offset across the weld, or lying ahead of or behind the current probe position along the scan axis, has a longer total path than a tip at the same depth on the centreline, so it always reads deeper than it really is.

With the transmitter and receiver index points at plus and minus S, an offset x across the weld and y along the scan direction, the total path is sqrt((S+x)^2 + y^2 + d^2) + sqrt((S-x)^2 + y^2 + d^2). Feeding half of that into the standard depth relation gives the apparent depth. The error is always positive and grows quickly for shallow flaws and large offsets, for the same reason that shallow depths are sensitive to PCS error: the arrival-time curve is nearly flat near the surface.

The y term is why point-like reflectors draw hyperbolic arcs in a D-scan. As the probes approach and pass the reflector, y falls to zero and rises again, so the apparent depth drops to the true depth at the apex and rises on either side. Always take depth readings at the apex of the arc.

ToFD gives no transverse position information at all. A signal from a diffractor well off the weld centreline is indistinguishable from a deeper one on the centreline. Where transverse position matters, use offset scans, a complementary pulse-echo or phased-array scan, or move the ToFD pair across the weld and watch how the indication depth changes.

S = PCS / 2
L = √((S + x)² + y² + d²) + √((S − x)² + y² + d²)
d_apparent = √( (L / 2)² − S² )
error = d_apparent − d