PAUT near field length

The near field is the region where interference between contributions from different parts of the aperture makes the pressure amplitude fluctuate wildly. It ends at the last on-axis maximum, at distance N, beyond which the field decays smoothly and the beam diverges at a fixed angle. For a circular source N = D²/(4λ).

A phased array group is rectangular, not circular: an active aperture A = n × p in the steering plane and a fixed passive aperture W in elevation. The rectangular case is handled with a shape factor k applied to the longer of the two dimensions, N = k·A_long² / (4λ). For a square aperture k is about 1.37 and it falls towards 0.99 as the aperture becomes a long strip.

Near field length is the single most important number in a phased array setup, because focusing is only possible inside it. It also fixes where the beam is naturally narrowest and where far field amplitude laws such as DGS and inverse-distance TCG start to apply.

Note that N is a distance along the sound path in the test material. For an angle beam on a wedge, subtract the wedge path expressed as an equivalent steel path before comparing N with a depth or a metal path.

N = k · A_long² / (4λ)
A = n × p
A_long = max(A, W), A_short = min(A, W)
k = f(A_short / A_long) from the rectangular aperture table
N_remaining = N − L_wedge · (c_wedge / c)