Modulation Transfer Function on Type 18UL without references
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
M(f)=σ2D−N2−−−−−−−√ M0=|μbar−μbkg|nbar⋅nbkg(nbar+nbkg)−−−−−−−−−−−√ N=(σ2bar+σ2bkg)2
σD: standard deviation of pixel values inside the bar pattern (detail) region μbar: mean pixel value of the bars reference region μbkg: mean pixel value of the background reference region nbar: number of pixels of the bars reference region nbkg: number of pixels of the background reference region σbar: standard deviation of pixel values inside the bars reference region σbkg: standard deviation of pixel values inside the background reference region
For frequencies outside the range given by the formulas, a linear interpolation is performed.