PAUT steering limit

Delay laws can point a beam anywhere, but they cannot create energy where a single element does not radiate any. Each element behaves as a strip source of width e, with a directivity that follows sin(u)/u where u = π·e·sin θ / λ, multiplied by an obliquity factor cos θ. The array beam is the element pattern multiplied by the array factor, so the element pattern is a hard envelope on achievable sensitivity.

The accepted working limit is the angle at which that envelope has fallen 6 dB, which gives sin θ_st = 0.5 λ / e. Narrow elements steer well: at 5 MHz shear in steel, a 0.5 mm element steers to about 40 degrees, while a 1 mm element manages only about 19 degrees.

Steering loss is real loss, and it is incurred twice in pulse-echo. At the edges of a wide sectorial sweep the same reflector will give a much smaller signal than at the natural angle, which is why angle-corrected gain or an angle-dependent TCG is needed before amplitude-based acceptance can be applied across the sweep.

For a probe on a wedge, steering happens in the wedge, so use the wedge wavelength and measure the steering angle from the normal to the array face - not from the vertical in the part.

sin θ_st = 0.5·λ / e
u = π·e·sin θ / λ
D(θ) = cos θ · |sin u / u|
loss (pulse-echo) = −40·log10 D(θ)