At the focus the beam width between the −6 dB points is W₋₆ = 1.02·λ·F / A. It scales directly with wavelength and focal depth and inversely with aperture, so the three levers available are a higher frequency, a shallower focus, or more elements in the group.

The same expression, read as 2·F·tan(asin(0.51·λ/A)), is the far field divergence of the aperture: focusing simply moves the narrow waist from the end of the near field to the chosen depth. An unfocused aperture is at its narrowest at N, where the width is 1.02·λ·N / A, so the improvement from focusing at depth F is roughly N/F.

Beam width sets lateral resolution and it sets scan increment. Two reflectors closer together than the −6 dB width merge into one indication, and an index step larger than the −6 dB width leaves unswept material between passes. It also sets the amount of gain gained by focusing: a narrower beam concentrates the same energy on a smaller reflector.

Compression or shear

Worked example

Elements in the active group	16
Element pitch	0.6 mm
Passive aperture (elevation)	10 mm
Probe frequency	5 MHz
Wave mode	shear
Material velocity	3240 m/s
Focal distance (sound path)	30 mm
Active aperture	9.6 mm
Wavelength	0.648 mm
−6 dB beam width at the focus	2.07 mm
−6 dB half divergence angle	1.97 deg
Near field length	51 mm
−6 dB width of the unfocused beam at N	3.51 mm

A = 9.60 mm, λ = 0.648 mm. W₋₆ = 1.02 × 0.648 × 30/9.6 = 19.829/9.6 = 2.07 mm. The −6 dB half angle is asin(0.51 × 0.648/9.6) = asin(0.034425) = 1.97°. With N = 51.0 mm the unfocused beam is narrowest at 1.02 × 0.648 × 51.0/9.6 = 3.51 mm, so focusing at 30 mm narrows it by 51.0/30 = 1.70.

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