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### QUESTIONS» Equipment/QA

These questions are concerned MRI hardware and quality control of images.

# Modulation Transfer Function

## What is the modulation transfer function?

The modulation transfer function (MTF) originated in optics. Modulation speaks of variation of some property. In optics, the MTF described the ability of a lens to accurately transfer visual stimuli (through the lens). Degradation occurs as light passes through a lens, and the MTF characterised the extent of the degradation. Although in MRI we aren't using lenses, we still need to describe the extent of the degradation of the representation of an imaged object, compared to the original object. That's what the MTF does. The initial "modulation" of an object ranges from fine to coarse detail. Obviously fine detail (or modulation) is lost first, as degradation increases. The MTF is simply the modulation of the image (Mi) divided by the modulation of the original object (Mo).

MTF (ν) = Mi / Mo

The ν symbol is spatial frequency. What's that about? Well, the ability of a lens (or MRI machine) to transfer say thick lines, as opposed to thin, close lines will be different. The thinner and closer the lines the less contrast there may be between them, as perceived by the imaging device. The MTF gives us a measurement of how much contrast remains between white and black lines after they have been "transferred" by the imager. The thick lines represent a low spatial frequency, and the thin, close lines represent a high spatial frequency. How much contrast is there between the lines in the image, compared to the original? This is what the MTF tells us. If the MTF is 0.85, then 85% of the original contrast between the lines is retained in the image. You see that to quote an MTF you have to say what spatial frequency you're talking about (coarse to fine detail). That's why we represent MTF on a graph of MTF vs ν.

It is clear that very for low spatial frequencies (coarse detail), any imager is likely to have an MTF of 100%. Keep going up in spatial frequency (finer and finer detail), and the MTF reduces to 0%.