Passive aperture beam spread

A one dimensional linear array only controls the beam in the active plane. In elevation the aperture is a single fixed strip of width W, so the beam there behaves exactly like an unfocused single crystal probe: it converges to a natural focus at W²/(4λ), then diverges at a half angle given by sin θ = 0.51·λ / W for the −6 dB edge.

That elevation spread governs how much material either side of the scan line is illuminated, and therefore how the volume is covered on an axial weld scan and how much of a corrosion pit is averaged into one C-scan cell. It also explains why indications from outside the nominal scan plane appear at all.

Passive aperture is chosen by the probe, not by the setup. Where elevation resolution matters – small pits, close parallel indications, thin components – the answer is a probe with a shorter passive aperture, a matrix array, or an elevation focusing lens, not a change of focal law.

Compression or shear

Worked example

Passive aperture (elevation)10 mm
Probe frequency5 MHz
Wave modeshear
Material velocity3240 m/s
Range of interest (sound path)100 mm
Wavelength0.648 mm
−6 dB half spread angle1.89 deg
−6 dB full spread angle3.79 deg
Passive direction near field38.58 mm
−6 dB elevation width at the range of interest6.61 mm

λ = 0.648 mm, so 0.51λ/W = 0.51 × 0.648/10 = 0.033048 and θ_half = asin(0.033048) = 1.8939°, full spread 3.79°. The passive near field is 10²/(4 × 0.648) = 38.58 mm, so at a 100 mm path the elevation width is 2 × 100 × tan 1.8939° = 6.61 mm.

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