Near field length, circular probe

A circular transducer behaves like a large number of point sources. Close to the face their contributions interfere, producing a chaotic pattern of maxima and minima along the axis — the near field or Fresnel zone. Its length is N = D²/4λ = D²f/4c. Beyond N the pressure falls smoothly and predictably with distance; this is the far field, where all the amplitude-based sizing methods (DAC, DGS, AVG) are valid.

The last on-axis maximum sits at N, and the beam is at its narrowest there — roughly half the element diameter. That is the natural focus of an unfocused probe and the point of highest sensitivity. Inside the near field an amplitude reading tells you almost nothing about reflector size: a small reflector sitting on a pressure maximum can out-shout a larger one sitting in a null.

Practical consequences: evaluate flaws beyond N wherever possible; for thin sections use a low-frequency or small-diameter probe so the near field is short; when the near field is unavoidably long, use a twin-crystal (TR) probe whose crossed roof angle puts the sensitive zone close to the surface, or a focused probe. When you switch from compression to shear the wavelength almost halves and the near field almost doubles for the same probe — a point that catches people out on angle-beam work.

The rim of the crystal is clamped by its mounting and does not vibrate at full amplitude, so many references and probe data sheets work with an effective diameter of 0.97·D for a circular element, which shortens N by about 6 %. Choose the effective-diameter option below to apply that factor; leave it on nominal if your procedure uses the plain D²/4λ form, or if you are already entering a measured effective diameter.

N = D² / (4λ)   with λ = c / f
N [mm] = D² [mm²] × f [MHz] × 1000 / ( 4 × c [m/s] )
D_eff = 0.97 · D when the effective-diameter option is selected