Focal spot size
A focused probe — a curved element, an acoustic lens, or a phased-array focal law — concentrates the beam at a chosen distance. The −6 dB diameter of the spot it makes is BD = 1.02 · λ · F / D, where F is the focal length in the material and D is the aperture. Smaller wavelength or bigger aperture gives a tighter spot; a longer focal length gives a wider one.
The hard limit is the near field. A probe cannot be focused beyond its own near-field length. The normalised focal length S_F = F/N must be less than 1; at S_F = 1 the ‘focus’ is just the natural last maximum of the unfocused beam and no gain is available. Practical focusing is normally limited to about S_F = 0.6 or less, which is why increasing the aperture (or the frequency) is the only way to focus deeper.
Focusing buys sensitivity and lateral resolution in a narrow band of depth and pays for it everywhere else. A tight spot raises the echo from a small reflector at the focus by many dB, so focused probes are used for small-defect detection, near-surface resolution, corrosion mapping and flaw sizing — but the beam diverges rapidly past the focal zone and the technique must be qualified at the depth of interest.
Use the focal zone length calculation alongside this one: the spot diameter tells you how fine the beam is at the focus, the focal zone tells you over what depth range that focusing is actually useful.
Compression or shear
Worked example
| Wave mode | compression |
| Material velocity (override) | 0 m/s |
| Probe frequency | 5 MHz |
| Aperture diameter | 10 mm |
| Focal length in the material | 15 mm |
| Velocity used | 5900 m/s |
| Wavelength λ | 1.18 mm |
| Near field length N | 21.19 mm |
| Normalised focal length S_F | 0.708 |
| Focal spot diameter (−6 dB) | 1.81 mm |
| Spot diameter in wavelengths | 1.53 |
10 mm, 5 MHz compression probe focused at 15 mm in steel. λ = 1.18 mm; N = 21.19 mm so S_F = 15/21.19 = 0.708, inside the near field and therefore focusable. BD = 1.02 × 1.18 × 15 / 10 = 1.8054 mm ≈ 1.81 mm, about 1.5 wavelengths.
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