Physics and Engineering of Radiation Detection

7.1. Some Important Terminologies and Quantities 433

1.0

0.5

0

FWHM

Radial Distance

Relative Intensity

(b)

(a) Figure 7.1.7: (a) Image of a point made by

a pixel detector. (b) Point spread function of

image in (a). FWHMis the width of this

function at exactly half of the full amplitude.

ArealPSFis not necessarily Gaussian-like

as shown in this figure. The shades shown in

the figure should not be taken as having sharp

boundaries, as the figure might suggest.

0

0.5

1.0

Relative Intensity FWHM

FWHM of PSF

Radial Distance

Figure 7.1.8: PSFs of images of

two points close together taken by a

pixel detector. Since the points are

FWHMdistance apart, they are

distinguishable. HencePSFcan be

used to quantify the spatial resolu-

tion of an imaging detector.

A.5 Edge Spread Function (ESF).................

TheLSFdoes not offer a very practical means of determining the system resolution
due to the engineering problem of manufacturing an ideal line object.ESFin this
sense is more convenient since it considers the image of an ideal step function, which
can easily be obtained from a rectangular object as shown in Fig.7.1.11.
The edge spread function can be defined as the integral of one dimensional point
spread functions. That is

ESF(x)=

∫

LSF(x)dx (7.1.12)

or LSF(x)=

d

dx

[ESF(x)]. (7.1.13)