What is the formula for tfm grid sizing?

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. Maximum TFM pixel pitch from the wavelength, the resulting grid dimensions for a zone, and the delay-and-sum load per frame.

What should I check before relying on the result?

Use the wavelength of the mode actually imaged in the zone - a shear mode image needs a finer grid than a compression image at the same frequency. The grid rule is a means to an end: the requirement that has to be demonstrated is amplitude fidelity. Verify against the governing edition: ASME BPVC Section V, Article 4, Mandatory Appendix XI (FMC/TFM) - amplitude fidelity requirement. The λ/5 grid rule is normal industry practice adopted to satisfy it; confirm by measurement..

TFM grid sizing — PAUT Calculator

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.

Compression or shear

Worked example

Probe frequency	5 MHz
Wave mode	compression
Material velocity	5900 m/s
Grid fineness rule	standard
Pixel pitch to be used	0.2 mm
Zone width	40 mm
Zone height (depth extent)	30 mm
Elements used in transmit and receive	64
Wave mode sets imaged	1
Wavelength	1.18 mm
Maximum pixel pitch	0.236 mm
Pixels across the zone	201
Pixels down the zone	151
Pixels in the zone	30351
Delay-and-sum operations per frame (millions)	124.32

At 5 MHz compression in steel λ = 5900/5000 = 1.180 mm, so the λ/5 rule gives a maximum pixel pitch of 0.236 mm. A 0.2 mm grid over a 40 by 30 mm zone is 201 by 151 = 30 351 pixels, and with 64 by 64 transmit-receive pairs that is 30 351 × 4096 = 124.32 million delay-and-sum operations per frame.

Use at your own risk — verify before you act

These calculators support, and never replace, the judgement of qualified NDT and engineering personnel. Results are provided as is, without warranty of any kind, express or implied, and must be independently verified against the governing code edition named in your contract before being used in any inspection, acceptance, rejection, radiation-safety or fitness-for-service decision. By using them you accept full responsibility for how the results are applied; NDT Inspect, its owners and contributors accept no liability for any loss, damage, injury or death arising from their use or from reliance on them. If a result matters to safety, check it by hand and have it reviewed by a competent person.