Physics and Radiobiology of Nuclear Medicine

Modulation Transfer Function

A more complete and quantitative assessment of spatial resolution of
imaging devices is made by using modulation transfer function (MTF)
(Rollo, 1977). The concept of MTF is illustrated in Figure 10.6. Suppose a
source of activity (e.g., a patient) has a sinusoidal distribution with peaks
(maximum activity,Amax) and valleys (minimum activity,Amin), as illustrated
in Figure 10.6. Such a distribution gives a spatial frequency () in cycles per
centimeter or cycles per millimeter. The contrast, or modulation(Ms), in the
source activity is given by

(10.3)

If a perfect imaging device were to image the source faithfully, it would
depict the same distribution of activity in the image with Amaxand Aminas
in the source activity. Because the imaging devices are not absolutely
perfect, it will portray the distribution of activity in the image with Cmaxfor
the peak and Cminfor the valley, which are smaller in magnitude than Amax
and Amin. The modulation in the image (Mi) is then expressed by

(10.4)

The MTF at a spatial frequency is then calculated as the ratio of Mito
Ms:

(10.5)

When Ms=Mi, MTF =1. This is true if the sinusoidal cycles are well sepa-
rated and if the imaging device reproduces the image of each cycle faith-
fully. Thus, the system with MTF =1 gives the best overall spatial resolution.

MTF() =

M

M

i

s

M

CC

CC

i

max min

max min

=

−

+

M

AA

AA

s

max min

max min

=

−

+

Evaluation of Spatial Resolution 125

Fig. 10.6. An illustration of the principles of modulation transfer function (MTF)
of an imaging system. See text for details.