Modulation transfer function (MTF)

The modulation transfer function (MTF) determines how much contrast in the original object is maintained by the detector.

In other words, it characterizes how faithfully the spatial frequency content of the object gets transferred to the image.

Earlier we introduced the concept of spatial frequency and saw that the spatial variation of contrast in an image can be represented by waves having different frequencies.

Figure 7.1.12 shows the graphical representation of such a wave. Since contrast can be defined in terms of how much light is transmitted, such a graph will always remain positive valued at all spatial points. The modulation of the graph is defined by

where y1 and y2 are as defined in Figure 7.1.12. N_max and N_min
represent the maximum and minimum values of the function used to quantify the contrast. This function may, for example, be the transmittance determined by the pixel readout. Modulation, in principle, can have any value between 0 and 1, though a value of 1 is generally difficult to achieve.

Now, the modulation is present not only in the object but also in the image. The ratio of their respective modulations is called the modulation transfer ratio; that is,

where
M_i and M_o represent the modulations in the image and the object, respectively (image/object).

The modulation transfer ratio defined here is a function of spatial frequency and therefore cannot be used to characterize the response of the system.

For that one must determine the modulation transfer ratio at each spatial frequency.

The dependence of the modulation transfer ratio on the spatial frequency is called the MTF. Figure 7.1.13 shows the shape of a typical MTF.