Beam diameter at range

Once the beam is in the far field it spreads as a cone of half-angle θ, where sin θ = k·λ/D. The width of the beam at a sound path z is then BD = 2 · z · tan θ. Choosing k = 0.51 gives the −6 dB width, which is the number to use for coverage; k = 0.87 gives the −20 dB width, the conservative detection envelope.

This is the figure that sets scan index. If successive passes are indexed by more than the −6 dB beam width at the depth of interest, there is a strip between them where sensitivity has dropped below the level the technique was qualified at, and a defect there may be under-called or missed. Procedures normally require an index of one beam width or less at the critical depth, often with a stated overlap.

The beam width also sets the lateral resolution: two reflectors at the same depth cannot be separated if they are closer together than the beam is wide. It is why a wide, low-frequency beam smears a cluster of pores into a single indication, and why measured indication length always exceeds true defect length by roughly one beam width unless a length-correction is applied.

The cone model is only sensible beyond the near field. Inside the near field the beam is roughly the element diameter, has no clean edge, and its width varies erratically; the calculator reports the ratio z/N so you can see whether you are in valid territory. For an angle probe, z is the sound path along the refracted beam, not the vertical depth.

sin θ = k · λ / D
Beam diameter at range:  BD = 2 · z · tan θ
Valid for z beyond the near field N = D²/4λ