TFM grid sizing

The total focusing method reconstructs an image by summing, for every pixel, the contribution of every transmit-receive pair in the full matrix capture. The image is only as good as the grid it is drawn on: if the pixels are coarser than the point spread function, the peak of a reflector response can fall between pixels and be under-reported.

The working rule is a pixel pitch no coarser than a fifth of the wavelength in the zone material, with a tenth used where amplitude accuracy matters most and a third being about the coarsest defensible. That rule exists to satisfy the amplitude fidelity requirement rather than the other way round - ASME Section V Article 4 Mandatory Appendix XI sets a 2 dB amplitude fidelity limit, and the grid has to be fine enough to meet it for the beam actually produced.

Cost rises steeply. Pixel count goes as the inverse square of the pitch, and the delay-and-sum load goes as pixels multiplied by the number of transmit-receive pairs and by the number of wave mode sets being imaged. Halving the pitch quadruples both the pixel count and the processing load, and the frame rate falls in proportion.

Use the wavelength of the mode actually imaged in the zone. Compression on plate at 5900 m/s gives a longer wavelength and a coarser permissible grid than a shear mode weld image at 3240 m/s, so a grid sized for one is not automatically valid for the other.

λ = c / f
pixel pitch ≤ λ / divisor (divisor 5 typical, 10 conservative)
pixels across = zone width / pitch + 1
delay-and-sum operations per frame = pixels × N_tx × N_rx × modes