1.
(a) What determines the highest energy of x-ray photons emitted from an x-ray tube?
Tube voltage
(b) In x-ray imaging for medical applications, why are low-energy photons undesired? What
measures can be taken to reduce the number of low-energy photons entering the human body?
Low energy photons are absorbed by tissue and thus potentially harmful while not at all useful
for imaging applications.
We can limit the number of low energy photons by using filters (e.g. such as thin aluminum
plates) that screen the low energy photons while allowing higher energy photons to be
transmitted.
(c ) why are photons undergoing scattering undesired? What measures can be taken to prevent
these photons form entering the detectors?
Scattered photons, created normally by Compton scattering, appear as noise in an x-ray image
since their direction is random. We can prevent (or at least reduce them) by using grids in front
of the detectors.
(a) No contrast agent.
I t  e 0.43.50.20.5  0.2231
I b  e 0.44.0  0.2019
Contrast 
I t  I b 0.2231  0.2019

 0.1052
Ib
0.2019
(a) With contrast agent.
I t  e 0.43.520*0.5  0.0000112
I b  e 0.44.0  0.2019
Contrast 
I t  I b 0.0000112  0.2019

 0.9999
Ib
0.2019
I ( y )  I o cos 3 ( )  e
 1L1

D
I ( y)  I o 
 D2  y2

cos( )
3

 e


e
 2 L2
 1L1
cos( )
D
D2  y 2
 2 L2
e
D
D2  y 2
(a) g(l,90)
g(l,0)
g(l,45)
g(l,135)
(c ) for g(l,90)
g (l ,90)  rect (l )  rect (l / 3)




F (u )   g (l ,90)e  j 2ul dl  
1.5
0.5
1.5
0.5
rect (l )  rect (l / 3)e  j 2ul dl
F (u )   e  j 2ul dl   e  j 2ul dl



 1  j 2u1.5
1
e
 e j 2u1.5 
e  j 2u 0.5  e j 2u 0.5
j 2u
j 2u
sin(2u 1.5) sin(2u  0.5)
3

2u 1.5
2u  0.5

