Physics and Engineering of Radiation Detection

434 Chapter 7. Position Sensitive Detection and Imaging

f( )x 0

f( )/2x 0

x 0

f( )x

σ(2ln2)1/2 σ(2ln2)1/2

x 0 −σ x 0 +σ

FWHM

x

σσ

Figure 7.1.9: Definition of

various terms in a the ex-

pression 7.1.10 for Gaussian

distribution. ThePSF of

most imaging systems has

Gaussian shape.

Impulse

Input

Measured LSF

Slit Response Figure 7.1.10: The LSF from a

thin line can be thought to consist

of a large number ofPSFs at closely

spaced points on the line. The shades

shown in the figure should not be

taken as having sharp boundaries, as

the figure might suggest.

A.6 Modulation Transfer Function (MTF)............

The modulation transfer function determines how much contrast of 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.
To understand theMTF, we must first understand what is meant by the modu-
lation function. 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. Fig.7.1.12 shows the graphical representation of such a wave.
Since contrast can be defined in terms of how much light is transmitted, therefore
such a graph will always remain positive valued at all spatial points. The modulation