Grating lobes obey sin θ_g = sin θ_s ± m λ/p, where θ_s is the steered angle of the main lobe, p the pitch and m the lobe order. A solution only corresponds to a real beam if the resulting sine lies between −1 and +1; otherwise that order does not propagate.

Both signs have to be checked. For a strongly steered beam it is normally the −m order that survives: subtracting mλ/p from the steered sine leaves a lobe at a shallower angle on the same side of the array normal, or past it onto the other side. The +m order only propagates when the steering is modest or the pitch coarse, and it then puts a lobe at a steeper angle than the main beam. That is the diagnostic signature: as the probe is moved the ghost travels in the opposite sense to the true indication, and it disappears when the sweep angle is changed while the real reflector stays put.

A grating lobe carries real energy and gives a real echo, so it can be mistaken for a defect and, worse, it is plotted at the main lobe angle – putting the indication at the wrong depth and the wrong stand-off. Where the pitch cannot be changed, keep the sweep inside the grating lobe free range, or confirm suspect indications at a second angle.

Compression or shear

Worked example

Probe frequency	5 MHz
Wave mode	shear
Material velocity	3240 m/s
Element pitch	1 mm
Steered angle of the main lobe	45 deg
Lobe order	1
Wavelength	0.648 mm
Alias term m·λ/p	0.648
sin θ_g for the −m order	0.0591
Grating lobe angle (−m order)	3.39 deg

λ = 3240/5000 = 0.648 mm, so λ/p = 0.648 with a 1.0 mm pitch. sin 45° = 0.70711; the −1 order gives sin θ_g = 0.70711 − 0.648 = 0.05911, i.e. θ_g = 3.39°. The +1 order gives 1.3551, greater than 1, so it does not propagate.

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