What is the formula for dgs / avg equivalent reflector size?

λ = c / f; near field N = D_eff² / (4 λ); normalised distance A = z / N; disc echo relative to back wall at the same range: ΔV = 20 log₁₀( π d² / (2 λ z) ); so d_ERS = √( 2 λ z · 10^(ΔV/20) / π ); ΔV = [20 log₁₀(H/H_ref) − (g_ind − g_bw)] − [−20 log₁₀(z_f/z_bw) − 2α(z_f − z_bw)] + ΔV_transfer; H = screen height %, g = instrument gain in dB — not the A and G of the DGS diagram. Sizes an indication as an equivalent flat disc reflector from a back-wall reference, using the far-field DGS relation together with normalised distance and near-field length.

What should I check before relying on the result?

Far-field relation only — keep the evaluation range beyond about 3 N. Equivalent reflector size is a reporting convention. Real planar flaws are rough and tilted and return less than an ideal disc, so ERS under-states them. Use the probe's own DGS diagram and effective element diameter; a nominal crystal size gives the wrong near field. Transfer correction for surface finish, curvature and attenuation difference between the reference and the component is entered as its own input - a rough or curved component returns less than the reference block, and sizing without the credit under-states the flaw. Verify against the governing edition: Krautkramer, Ultrasonic Testing of Materials (DGS/AVG method); EN ISO 16811 sensitivity setting; EN ISO 11666 acceptance levels.

DGS / AVG equivalent reflector size

DGS — Distance, Gain, Size, called AVG in German — replaces a set of drilled reference blocks with a calculation. Instead of comparing an indication with a machined reflector at a similar range, the response is compared with a plane back wall, and theory supplies the rest: how far the echo from a small disc reflector falls below the back-wall echo at the same distance.

In the far field the on-axis pressure of a circular probe decays as S/(λz). A small disc of area S_r re-radiates like a piston of that area, which makes the disc-to-back-wall ratio 2 S_r/(λ z), or π d²/(2 λ z) for a disc of diameter d. Rearranged, that gives the equivalent reflector size: the diameter of the flat, circular, perfectly-oriented disc that would produce the echo actually observed.

The relation is a far-field one, so the sound path must be beyond about three near-field lengths, N = D²/(4λ). Inside the near field the on-axis pressure oscillates through maxima and minima and no simple amplitude law applies, which is why DGS diagrams are drawn against normalised distance A = z/N and normalised size G = d/D, and why probes are chosen so the region of interest lies past the last maximum.

ERS is a sizing convention, not a flaw size. A real crack is rough, tilted and partly transparent, and almost always returns less than a disc of the same area, so ERS under-states planar flaws and over-states nothing. Codes that accept DGS say so explicitly and require the probe’s own DGS diagram, a back-wall reference on sound material, and a transfer correction for surface and attenuation differences.

Compression or shear

Worked example

Wave mode	compression
Compression velocity	5900 m/s
Shear velocity	3240 m/s
Probe frequency	2 MHz
Effective element diameter	10 mm
Sound path to the reference back wall	100 mm
Gain to set the back wall to reference height	30 dB
Reference screen height	80 %
Sound path to the indication	50 mm
Indication screen height	40 %
Gain at the indication	42 dB
Attenuation coefficient	0 dB/mm
Transfer correction	0 dB
Wavelength	2.95 mm
Near field length	8.47 mm
Normalised distance A = z/N	5.9
Indication below an equal-range back wall	-24.04 dB
Equivalent reflector size (disc diameter)	2.43 mm
Normalised size G = d/D	0.243

2 MHz, 10 mm element in steel: λ = 5900/2000 = 2.95 mm and N = 100/(4 × 2.95) = 8.47 mm, so the indication at 50 mm is at A = 5.9 — comfortably in the far field. The indication sits at 40 % with 12 dB more gain than the back-wall reference, i.e. 20 log₁₀(0.5) − 12 = −18.02 dB relative to reference, while a back wall at 50 mm would be 6.02 dB above it. The disc is therefore 24.04 dB below an equal-range back wall, giving d = √(2 × 2.95 × 50 × 10^(−24.04/20) / π) = 2.43 mm, or G = 0.243.

Use at your own risk — verify before you act

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