# Modulation Transfer Function on Type 18UL with references

From AutoPIA

Modulation Transfer Function (MTF) values are calculated according to **Droege RT, Morin RL.** "*A practical method to measure the MTF of CT scanners*"
(Med Phys. 1982 Sep-Oct;9(5):758-60). Authors demonstrate how MTF is
related to the standard distribution of pixel values inside a region
taken from a bar pattern, with the following relations:

MTF(f)=⎧⎩⎨⎪⎪⎪⎪π2√4⋅M(f)M0,π2√4M0⋅M2(f)−M2(3f)9−M2(5f)25−M2(7f)49−−−−−−−−−−−−−−−−−−−−−−−−−−−√,if f≥fc/3if f≥fc/11

where:

M(f)=σ2D−N2−−−−−−−√ M0=|μbar−μbkg|nbar⋅nbkg(nbar+nbkg)−−−−−−−−−−−√ N=(σ2bar+σ2bkg)2

and:

: standard deviation of pixel values inside the bar pattern (detail) regionσD : mean pixel value of the bars reference regionμbar : mean pixel value of the background reference regionμbkg : number of pixels of the bars reference regionnbar : number of pixels of the background reference regionnbkg : standard deviation of pixel values inside the bars reference regionσbar : standard deviation of pixel values inside the background reference regionσbkg

For frequencies outside the range given by the formulas, a linear interpolation is performed.