Beam Fields, Resolution and Coverage Modelling

Learning outcomes

By the end of this chapter, the learner should be able to distinguish near-field interference, far-field divergence and focal behaviour; explain axial, lateral and elevational resolution; select modelling assumptions appropriate to the component; convert an inspection objective into demonstrable coverage; and identify masking, dead zones and geometric uncertainty.

5.1 The beam is a field, not a centreline

An ultrasonic beam has a spatial distribution of pressure and sensitivity. The centreline is useful for geometry calculations, but detection depends on the full field, reflector orientation, phase and receiver response. Beam boundaries drawn in training diagrams are normally amplitude contours, not hard walls.

For an ideal unfocused circular aperture, an approximate near-field length is:

N = D^2 / (4 lambda)

where D is element diameter. The expression assumes a uniform circular piston and should be corrected for the effective aperture, wedge and material where necessary. Within the near field, constructive and destructive interference produces amplitude maxima and minima. A monotonic distance-amplitude assumption is unreliable there.

In the far field, divergence depends on wavelength and aperture. Published beam-spread formulas use different amplitude boundaries, so a procedure must state the convention. A -6 dB contour and a -20 dB contour are not the same beam edge.

5.2 Resolution dimensions

Axial resolution is the ability to separate reflectors along the sound path. It is strongly influenced by pulse duration and bandwidth. Lateral resolution is separation across the beam width. Elevational resolution is separation through the beam height or slice thickness. Focusing may improve lateral or elevational resolution near the focus while reducing depth of field.

Sensitivity is not resolution. Increasing gain may reveal a small reflector, but it does not shorten the pulse or narrow the beam. Two responses merged by poor resolution do not become separate because the trace is taller.

5.3 Coverage model

A defensible coverage plan identifies:

• inspection volume and coordinate system;
• expected discontinuity locations and orientations;
• entry surfaces and inaccessible regions;
• wave modes, angles and sound paths;
• beam dimensions or validated sensitivity region;
• scan index, overlap and positional tolerance;
• first-leg, second-leg and skip limitations;
• dead zones, geometry echoes and areas masked by attenuation;
• verification using representative reflectors or modelling.

The coverage claim should be expressed as a bounded statement. For example: "The demonstrated technique covers the weld body and specified heat-affected-zone volume from the nominated surface, except the listed root-shadow region." It should not say "100 percent coverage" unless every relevant dimension and limitation has been defined and demonstrated.

5.4 Curvature and surface effects

Curved entry surfaces alter contact, beam direction and sound-field shape. Concave and convex interfaces can focus or defocus the beam. Small-diameter pipe introduces skip-position, footprint and coupling constraints. Rough surfaces scatter energy and vary coupling. Wedge contouring, immersion, smaller apertures or alternative access may be required.

5.5 Coverage decision case

A 70-degree nominal shear probe is proposed for a thick weld. The calculated centreline reaches the upper fusion face, but a representative side-drilled hole near the root cannot be detected at the required signal-to-noise ratio. The coverage claim must follow demonstrated capability, not the centreline drawing. Options include a lower angle, different frequency or aperture, another surface, supplementary technique, or a formally recorded limitation.

Failure modes and decision control

Weak practice commonly includes drawing one ray and calling it coverage; ignoring near-field amplitude variation; confusing sensitivity with resolution; using an undefined beam-spread formula; overlooking curvature and wedge rocking; and claiming inaccessible or masked regions without demonstration.