# Truncation Artefact

Most manufacturers use asymmetric data sampling, with 128 to 256 phase encoding steps and 256 to 512 acquired in the less-time dependent frequency axis. This means that fewer data points are in the phase encoding direction, and because of the cause of the artefact (truncation of the ideally infinite Fourier series), it will be more pronounced in this direction. It can theoretically occur in the frequency encoding direction, but is not normally seen. The characteristic ringing is due to under-sampling of high spatial frequencies (edges and fine detail), and is specifically related to pixel size.

An excellent Fourier approximation tool may be found online (select a Rectangular pulse, click Calculate, and then play with the number of Fourier terms used).

Truncation of the Fourier series causes a Gibb's overshoot and ringing close to the step-change. A truncated Fourier series cannot accurately represent the true shape.

Further reading on this topic:

Books: MRI From Picture to Proton p97-99, MRI The Basics p181-184, Q&A in MRI p130-132

Online: Basics of MRI, MRItutor, St Paul's, Chickscope, e-MRI