Grating lobe angle

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.

sin θ_g = sin θ_s ± m·λ/p
λ = c / f
a real lobe exists only where |sin θ_g| ≤ 1