TFM amplitude fidelity

Amplitude fidelity is the amount by which the displayed amplitude of a reflector can change purely because of where it happens to fall on the reconstruction grid. A reflector whose true response peaks exactly on a pixel is reported at full height; the same reflector half a pixel away is reported low. ASME Section V Article 4 Mandatory Appendix XI limits that variation to 2 dB.

The loss can be estimated from the shape of the point spread function. Approximating the response near its peak by a Gaussian whose −6 dB width is w, a peak sitting half a pixel from the nearest grid point is under-reported by 20·log10(2)·(Δ/w)² decibels - the 6 dB in that expression being exactly the 6 dB that defines w. Sampling in both image axes adds the two contributions, because the worst case is a peak sitting diagonally between four pixels.

Rearranged for a 2 dB budget split over two axes, the coarsest usable pitch is about 0.41 of the −6 dB spot size. For a full aperture TFM image the spot is roughly half a wavelength, which lands close to the familiar λ/5 grid rule - the rule of thumb and the requirement are consistent, but only the requirement is enforceable.

This is an estimate that assumes a smooth, symmetric point spread function. The demonstration required by the code is a measurement: move a reflector through the zone in small steps and record the largest peak-to-peak variation in reported amplitude.

loss ≈ 20·log10(2) · (Δ / w₋₆)²  per axis
total ≈ loss_x + loss_z
Δ_max = w₋₆ · √(limit / (2 × 20·log10(2)))
w₋₆ ≈ λ/2 for a full aperture TFM image