Physics and Engineering of Radiation Detection

7.1. Some Important Terminologies and Quantities 435

Input

Edge Response

Measured ESF

Figure 7.1.11: Edge spread function

can be obtained by placing a rectan-

gular object having sharply defined

edges between the source and the de-

tector. The shades shown in the fig-

ure should not be taken as having

sharp boundaries, as the figure might

suggest.

of the graph is defined by

M =

y 1

y 2

=

(Nmax−Nmin)/ 2

(Nmax+Nmin)/ 2

=

Nmax−Nmin

Nmax+Nmin

, (7.1.14)

wherey 1 andy 2 are as defined in Fig.7.1.12.NmaxandNminrepresent the maximum
and minimum values of the function used to quantify the contrast. The function
could, for example be the transmittance determined by the pixel readout. Modula-
tion, in principle, can have any value between 0 and 1, although a value of 1 is very
difficult, if not impossible, to achieve.

f()x

fmax

fmin

y 2

y 1

y 1

x

Figure 7.1.12: Definition of the

parameters in equation 7.1.15.

f(x) represents any convenient

function for quantifying the

contrast.

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

MT=

Mim

Mob

, (7.1.15)

whereMimandMobjrepresent respectively the modulations in the image and the
object. The modulation transfer ratio defined here is a function of spatial frequency
and therefore can not be used to characterize the response of the system. For that
one must determine the modulation transfer ratio at each spatial frequency. The
dependence on the modulation transfer ratio on the spatial frequency is called the