Wedge attenuation and steering loss

Sensitivity across a sectorial sweep is not uniform, and two mechanisms account for most of the variation. The first is wedge path: steering away from the natural angle raises the incident angle, which lengthens the path from the element to the interface as h / cos θ_i. The wedge plastic attenuates strongly, so a couple of millimetres of extra path costs real decibels, twice over in pulse-echo.

The second is element directivity. Steering is measured from the normal to the array face, so the element pattern cos θ · sin(u)/u applies at the steered angle inside the wedge, again twice in pulse-echo. Near the natural angle it costs nothing; at the extremes of a wide sweep it dominates.

The sum is the angle corrected gain, the extra gain that has to be applied at that angle so that the same reflector gives the same amplitude. Instruments build the curve by measuring a side drilled hole at each angle. This calculation shows what shape to expect and whether an unexpected ACG curve points to a real problem - poor coupling, a worn wedge, or an incident angle running past the total reflection limit.

Transmission loss at the interface also varies with angle and is not included here. Where absolute numbers matter, measure the angle corrected gain on a reference block; use this to sanity check it.

θ_i = asin(c_wedge · sin θ_r / c)
h = H1 + (n_start + (n−1)/2 − 1)·p·sin θ_w  (derived entry)
wedge path L = h / cos θ_i
attenuation term = 2 · α_wedge · (L − L_natural)
directivity D = cos(θ_i − θ_w) · |sin u / u|, u = π·e·sin(θ_i − θ_w)/λ_wedge
total extra gain = attenuation term − 40·log10 D