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.

Shear wave

Worked example

Wedge (roof) angle	36 deg
Wedge velocity	2730 m/s
Refracted shear velocity in the part	3240 m/s
Refracted angle of interest	60 deg
Height of the group centre in the wedge	12.65 mm
Element width	0.5 mm
Probe frequency	5 MHz
Wedge attenuation (dB/mm, one way)	0.15
Height source	direct
First element height (H1)	10 mm
Element pitch	0.6 mm
First element of the active group	1
Elements in the active group	16
Wavelength in the wedge	0.546 mm
Incident angle in the wedge	46.86 deg
Wedge path at this angle	18.501 mm
Wedge path at the natural angle	15.636 mm
Extra wedge attenuation (pulse-echo)	0.86 dB
Steering angle inside the wedge	10.86 deg
Directivity loss (pulse-echo)	1.17 dB
Extra gain needed relative to the natural angle	2.03 dB
Group centre height used	12.65 mm

To refract at 60° the incident angle must be asin(2730 × sin 60°/3240) = asin(0.72971) = 46.86°, i.e. 10.86° of steering above the 36° natural angle. The wedge path grows from 12.65/cos 36° = 15.636 mm to 12.65/cos 46.86° = 18.501 mm, and 2 × 0.15 × 2.864 = 0.86 dB is lost to the extra plastic. The element directivity at 10.86° in a 0.546 mm wedge wavelength is 0.9347, costing 1.17 dB in pulse-echo, so 2.03 dB of extra gain is needed at 60°.

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