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.

Compression or shear

Worked example

Probe frequency	5 MHz
Wave mode	shear
Material velocity	3240 m/s
Element width	0.5 mm
Requested steering angle	30 deg
Wavelength	0.648 mm
−6 dB steering limit	40.39 deg
One-way steering loss at the requested angle	3.49 dB
Pulse-echo steering loss at the requested angle	6.98 dB

λ = 0.648 mm. 0.5λ/e = 0.5 × 0.648/0.5 = 0.648, so θ_st = asin(0.648) = 40.39°. At 30° steering u = π × 0.5 × sin30°/0.648 = 1.2120, sin u/u = 0.77253, times cos 30° = 0.86603 gives D = 0.66904, i.e. 3.49 dB one way and 6.98 dB pulse-echo.