Beam width at the focus

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.

W₋₆ (at focus) = 1.02 · λ · F / A
θ_div = asin(0.51 · λ / A)
W₋₆ (unfocused, at N) = 1.02 · λ · N / A