The backwall signal is the compression wave that travels down from the transmitter, reflects from the far surface and returns to the receiver. Its path is 2*sqrt(S^2 + T^2), so it arrives at 2*sqrt(S^2 + T^2)/c plus the wedge delay, where S is half the probe centre separation and T is the wall thickness. Together with the lateral wave it brackets the whole of the useful ToFD image.

These two signals are the calibration features of every ToFD scan. Their measured separation fixes the depth scale: with the wall thickness and PCS known, the material velocity and the probe delay can be solved directly from the two arrival times, so depth linearity does not need a separate calibration block.

Along a scan, a change in backwall arrival means something physical has changed. A later backwall means the wall is thicker or the probes have lifted; an earlier arrival means thinning or a flaw approaching the far surface. A phase reversal of the backwall, or its local disappearance, is the classic ToFD signature of a root-breaking flaw, and is often more reliable than looking for a separate lower-tip diffraction so close to the backwall.

Note that the backwall is a specular reflection, not a diffraction, so it depends on the far surface being reasonably flat and parallel. On a counterbored or misaligned joint the backwall may be lost even though the material is sound.

Compression wave

Worked example

Probe centre separation	70 mm
Wall thickness	25 mm
Compression velocity	5900 m/s
Total probe delay	2.5 µs
Half separation	35 mm
Total backwall sound path	86.02 mm
Backwall transit time in material	14.58 µs
Backwall arrival on the A-scan	17.08 µs
Lateral wave arrival on the A-scan	14.36 µs
Lateral wave to backwall window	2.72 µs

S = 35 mm. sqrt(35^2 + 25^2) = sqrt(1225 + 625) = sqrt(1850) = 43.0116 mm, so the total path is 86.0233 mm (86.02 to 2 dp). At 5.9 mm/us that is 14.5802 us in material, so 14.58 us; adding the 2.50 us wedge delay gives 17.0802 us, that is 17.08 us. The lateral wave is 70 / 5.9 + 2.5 = 14.3644 us, so 14.36 us, and the window between them is 2.7158 us, that is 2.72 us.

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