1. X-Ray Physics Assumptions:
Matter is composed of discrete particles (i.e. electrons, nucleus)
Distance between particles >> particle size
X-ray photons are small particles
Interact with body in binomial process
Pass through body with probability p
Interact with body with probability 1-p (Absorption or scatter)
No scatter photons for now (i.e. receive photons at original energy or not at all.

2. µ = linear attenuation coefficient (units cm-1)
N |∆x|N + ∆N
The number of interactions (removals)  number of x-ray photons and ∆x
∆N = -µN∆x
µ = linear attenuation coefficient (units cm-1)

3. Id (x,y) = ∫ I0 () exp [ -∫ u (x,y,z,) dz] d 
Integrate over  and depth.
If a single energy I0() = I0  ( -  o),
If homogeneous material, then µ (x,y,z,  0) = µ0
Id (x,y) = I0 e -µ0l

4. X-ray Source Accelerate electrons towards anode.
Braking of electrons by nuclei creates x-ray photons
Typically Tungsten Target
High melting point
High atomic number
Andrew Webb, Introduction to Biomedical Imaging, 2003, Wiley-Interscience.

5. Thin Target X-ray Formation
There are different interactions creating X-ray photons between the accelerated electrons and the target. Maximum energy is created when an electron gives all of its energy, 0 , to one photon. Or, the electron can produce n photons, each with energy 0/n. Or it can produce a number of events in between. Interestingly, this process creates a relatively uniform spectrum. Power output is proportional to 0 2
Intensity
= nh 0
Photon energy spectrum

6. Thick Target X-ray Formation
We can model target as a series of thin targets. Electrons
successively loses energy as they moves deeper into the target.
Gun 
X-rays
Each layer produces a flat energy
spectrum with decreasing
peak energy level.
Relative
Intensity 0

7. Thick Target X-ray Formation
In the limit as the thin target planes get thinner, a wedge
shaped energy profile is generated.
Relative
Intensity 0
Again, 0 is the energy of the accelerated electrons.

8. Thick Target X-ray Formation
Andrew Webb, Introduction to Biomedical Imaging, 2003, Wiley-Interscience. (
Lower energy photons are absorbed with
aluminum to block radiation that will be absorbed
by surface of body and won’t contribute to image.
The photoelectric effect(details coming in attenuation section)
will create significant spikes of energy when
accelerated electrons collide with tightly bound electrons, usually in the K shell.

9. How do we describe attenuation of X-rays by body?
µ = f(Z, ) Attenuation a function of atomic number Z and energy 
Solving the differential equation suggested by the second slide of this lecture,
dN = -µNdx
Ninx Nout
Nout x
∫ dN/N = -µ ∫ dx
Nin 0
ln (Nout/Nin) = -µx
Nout = Nin e-µx

10. If material attenuation varies in x, we can write attenuation as u(x)
Nout = Nin e -∫µ(x) dx
Io photons/cm2
(µ (x,y,z))
Id (x,y) = I0 exp [ -∫ µ(x,y,z) dz]
Assume: perfectly collimated beam ( for now),
perfect detector
no loss of resolution
Actually recall that attenuation is also a function of energy ,
µ = µ(x,y,z, ). We will often assume a single energy source, I0 = I0(). After analyzing a single energy, we can add the effects of other energies by superposition.
Detector Plane
Id (x,y)

11. Rotate anode to prevent melting
Diagnostic Range
50 keV < E < 150 keV
 ≈ 0.5%
Rotate anode to prevent melting
What parameters do we have to play with?
Current
Units are in mA
Time
Units · sec
What to be said about mAsec?
3. Energy ( keV)

12. Notation  I0
I = I0 e - l l
Often to simplify discussion in the book or
problems on homework, the intensity transmission, t, will be
given for an object instead of the attenuation coefficient 
t = I/Io = e-µl

13. Mass Attenuation Coefficient
Since mass is providing the attenuation, we will consider the
linear attenuation coefficient, µ, as normalized to the density of the object first. This is termed the mass attenuation coefficient.
µ/p cm2/gm
We simply remultiply by the density to return to the linear
attenuation coefficient. For example:
t = e- (µ/p)pl
Mixture
µ/p = (µ1/p1) w1 + (µ2/p2) w2 + …
w0 = fraction weight of each element

14. Mechanisms of Interaction
1. Coherent scatter or Rayleigh (Small significance)
2. Photoelectric absorption
3. Compton Scattering – Most serious significance

15. Attenuation Coefficient
Physical Basis of
Attenuation Coefficient
Coherent Scattering - Rayleigh • •
Coherent scattering varies
over diagnostic energy range as: • ••
µ/p  1/2 • • •  

16. Photoelectric Effect Photoelectric effect varies
Andrew Webb, Introduction to Biomedical Imaging, 2003, Wiley-Interscience. (
Add figures from page 6 of lecture 9
Photoelectric effect varies
over diagnostic energy range as:
ln /p
  1
p 3
ln 
K-edge

17. Photoelectric Effect Longest electron range 0.03 cm
Fluorescent radiation example:
Calcium 4 keV Too low to be of interest.
Quickly absorbed
Items introduced to the body:
Ba, Iodine have K-lines close to region of diagnostic interest.

18. We can use K-edge to dramatically increase absorption in areas where material is injected, ingested, etc.
Photoelectric linear attenuation varies by Z4/  3
ln /p 
K edge
µ/p  1/  3