Reference reflector equivalence: FBH, SDH and notch

Codes and procedures do not agree on a reference reflector. ASME leans on side-drilled holes, DGS and much of the aerospace world on flat-bottomed holes, and surface-breaking acceptance work on machined notches. Sensitivity set on one of them is not the same sensitivity on another, and the gap can be more than 10 dB.

All three can be placed on one scale by asking what each returns relative to a plane back wall at the same range, in the far field. A small disc such as a flat-bottomed hole re-radiates as a piston of its own area, giving π d²/(2 λ z). A side-drilled hole is a convex cylinder: it reflects specularly with a √(a/2z) amplitude factor and spreads cylindrically, which works out as √(D/z) relative to the back wall — the familiar 9 dB per doubling instead of 12. A machined notch presented squarely to the beam behaves as a flat strip of area h × ℓ, with a corner-trap coefficient that depends on how nearly the beam bisects the corner.

Two consequences are worth remembering. The side-drilled hole response contains no wavelength term, so an SDH-referenced sensitivity does not scale with probe frequency the way an FBH-referenced one does — the same hole is a different number of decibels below a disc at 2 MHz and at 5 MHz. And because the SDH decays more slowly with range, an SDH-based DAC and an FBH-based curve diverge steadily with sound path.

These are far-field geometric-acoustic models: they assume the reflector is fully inside the beam, squarely presented, much larger than a wavelength for the cylinder and notch, and small compared with the beam for the disc. They are for understanding and cross-checking sensitivity, not for substituting one reflector type for another in a code that names one — that substitution has to be qualified by measurement on a real block.

λ = c / f
flat-bottomed hole:  V/V_bw = π d² / (2 λ z)
side-drilled hole:   V/V_bw = √( D / z )        (no wavelength term)
notch as flat strip: V/V_bw = 2 R_c h ℓ / (λ z)
equivalent disc diameter:  d = √( 2 λ z · (V/V_bw) / π )
so SDH → FBH:  d² = (2 λ / π) √(D z)