X-Ray Fundamentals

Basic physics of X-ray imaging

Carl A Carlsson and Gudrun Alm Carlsson

Department of Radiation Physics

Faculty of Health Sciences

Linköping university

Sweden

REPORT

LiH-RAD-R-008

Second edition 1996

TABLE OF CONTENTS

1. Introduction .........3

2. The physics of the X-ray source: the X-ray tube .........3

3. The energy spectrum of X-rays .........7

4. The interactions of X-rays with matter .........12

5. Contrast .........19

6. Energy absorption of X-rays .........22

7. Stochastics in the X-ray image .........27

8. Appendix .........28

9. References .........29

Basic physics of X-ray imaging

1. INTRODUCTION

In X-ray diagnostics, radiation that is partly transmitted through and partly absorbed in

the irradiated object is utilised. An X-ray image shows the variations in transmission

caused by structures in the object of varying thickness, density or atomic composition. In

Figure 1, the necessary attributes for X-ray imaging are shown: X-ray source, object

(patient) and a radiation detector (image receptor).

Figure 1. The necessary attributes for X-ray imaging: X ray source, object (patient) and

radiation detector

After an introductory description of the nature of X-rays, the most important processes in

the X-ray source, the object (patient) and radiation detector for the generation of an X-ray

image will be described.

2. THE PHYSICS OF THE X-RAY SOURCE: THE X-RAY TUBE

a. The nature of X-rays

X-rays are like radio waves and visible light electromagnetic radiation. X-rays, however,

have higher frequency, ν, and shorter wavelength, λ, than light and radio waves. The

radiation can be considered as emitted in quanta, photons, each quantum having a well

defined energy, hν, where h is a physical constant, Plancks constant, and ν is the

frequency. The energy of X-ray photons are considerably higher than those of light.

A number of the phenomena, which are observed with X-rays are most conveniently

described by the wave properties of the radiation while other phenomena can be more

easily understood if the X-rays are considered as being composed of particles (photons)

with well defined energies and momentum. The rest mass of a photon is zero. This means

that photons can never be found at rest. All photons move at the same velocity, c, in a

vacuum, given by c = 2.998 108 m/s.

b. Relationship between wave length and frequencyThe wave length multiplied with the frequency (number of wave lengths per unit time)

equals the velocity of light

λ⋅ν=c (1)

c. The propagation of X-rays

Similarly to visible light, X-rays propagate linearly. The rays from a point source form a

divergent beam. The number of photons passing per unit area perpendicular to the

direction of motion of the photons is called the fluence, Φ. The fluence in a vacuum

decreases following the inverse square law, given by

Φ(r)=Φ(1)⋅1

r2 (2)

where r is the distance from the point source and Φ(1) is the fluence at r=1 (relative

units).The inverse square law is illustrated in Fig 2.

Figure 2. The fluence, Φ, of X-rays decreases with the square of the distance from the

source.

d. Refraction of X-rays

When visible light passes from one medium to another it is refracted due to the different

velocities of the rays in different media and interference of waves. The velocity of

propagation of X-rays varies much less in different materials and the refraction of X-rays

is negligible. For this reason, X-rays cannot be focused

be means of lenses.e. Diffraction of X-rays

Another wave phenomenon is diffraction. This means that the wave can be bent when

passing an edge or a slit. The slit can then be regarded as a new source of waves

propagating in all directions. If there is a periodic system of slits (lattice), interference

effects will occur. That is, waves which are in phase will be amplified and those that are

out of phase will be weakened. In order to demonstrate diffraction with X-rays the lattice

constant (distance between the scattering slits) must be of the order of 0.1 nm. Such

distances exist between the atomic planes in crystals. Crystals are frequently used for X-

ray spectrometry.

f.