DAC curve level and indication assessment

The echo from an identical reflector gets weaker the further away it is, for two independent reasons: the beam spreads, and the material absorbs and scatters. A DAC curve records that decay from a row of identical reference reflectors at different sound paths so that any indication can be judged against a like-for-like reference rather than against a fixed screen height.

Beam spread alone gives a fixed law in the far field, set by how the reflector gathers sound. A plane back wall returns amplitude proportional to 1/z — 6 dB per doubling of sound path. A side-drilled hole behaves as a cylinder and falls as 1/z^1.5, 9 dB per doubling. A flat-bottomed hole or any small disc behaves as a point-like area reflector and falls as 1/z², 12 dB per doubling. Attenuation adds a further loss proportional to the distance travelled, 2αz for the round trip, and unlike beam spread it depends on the material, the frequency and the wave mode — shear waves in the same steel typically attenuate two to three times faster than compression waves.

Comparing an indication with the curve is bookkeeping in decibels. Take the indication's screen height relative to the reference height, remove any gain added since the curve was drawn, and subtract the curve's own drop at that sound path. What remains is the indication's level relative to DAC — the number acceptance criteria are written in, whether that is 100 % DAC, the 50 % (−6 dB) evaluation line or the 20 % (−14 dB) recording line.

A drawn DAC is only valid over the range where reference points were actually recorded, on the same surface condition, with the same probe, cable and instrument settings. Extrapolating a curve past the last reference reflector, or transferring it to a rougher component without a transfer correction, is the usual way a real flaw ends up under-called.

DAC drop at z:  ΔdB(z) = −20 k log₁₀(z / z_ref) − 2 α (z − z_ref)
k = 1.0 plane back wall (−6 dB/doubling)
k = 1.5 side-drilled hole (−9 dB/doubling)
k = 2.0 flat-bottomed hole (−12 dB/doubling)
DAC height at z = ref% × 10^(ΔdB/20)
indication vs DAC = 20 log₁₀(A / ref%) − ΔdB(z) − (G_ind − G_ref) + ΔV_transfer