X-rays are a type of electromagnetic radiation with very high frequency and energy which lie between ultraviolet and gamma radiation on the electromagnetic spectrum. In such conditions electromagnetic radiation assumes particle like properties, whereby interactions are collisional by nature. This allows X-ray photons with sufficient energy to interact with and remove electrons bound to an atom (the process of ionization) (Seibert, 2004), hence the reason X-rays are referred to as ionizing radiation. Photon energy is directly proportional to the frequency of the wave as determined by Planck's hypothesis. This states that X-rays and all other electromagnetic energy occur in finite "packets" of energy (photons) and have a quantum of energy equal to the product of Planck's constant (h) and the frequency (v). According to the hypothesis photons wavelengths can vary from 12nm to 0.002nm (Cnudde, 2005):
Where Planck's constant h = 6.626068 x 10-34 Js and the speed of light c = 3 x 108 m/s. Although X-rays can penetrate through most materials, a loss of intensity occurs due to absorption. This absorption is dependent on firstly the composition and density of a material and secondly the energy of the X-rays used. The influence of these aspects on the intensity of the X-rays is expressed as the linear attenuation coefficient Âµ, which is a product of the density and mass-absorption coefficient of the material (this will be elaborated further in subsequent sections).
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Figure 2 Example of some attenuation coefficients for different elements (Adapted from Cnuude, 2005)
The production of X-rays occurs when electrons, accelerated by a cathode filament, are retarded by a metal object (anode target). Electrons traveling from the filament to the target convert a small percentage (1%) of their kinetic energy into X-ray photons by the formation of bremsstrahlung and characteristic radiation.
Bremstrahlung radiation or "braking radiation", the primary source of X-ray photons, can be produced by the sudden stopping, braking or slowing of high-speed electrons due to the forces of the atoms in the target material. The interaction of electrons with the atoms creates photons either through direct nucleus impact (rare) or their path is adjacent to the nucleus. If direct impact occurs the total kinetic energy, K, of the electron is converted to create a single X-ray photon (i.e total absorption has occurred). Due to the potential difference, V, between the target and filament, their kinetic energy will be eV as they hit the target. Thus the resultant photon will be numerically equal to the energy of the electron. In general, electrons pass in varying proximity to the nuclei. During these interactions, a negatively charged high-speed electron is attracted toward the positively charged nucleus and loses some of its velocity. This deceleration incurs a loss of kinetic energy, ï„ï‹ï€¬ in the electron which is released in the form of a photon from the target. The closer the electron approaches the nuclei, the greater the electrostatic charge, thus the greater the energy of the resulting photon. All electrons with a kinetic energy between zero and eV can undergo this Bremsstrahlung process and thus contribute to the creation of a continuous X-ray spectrum. A number of factors influence this spectrum such as target material, voltage fluctuation between target and filament, and target thickness.
Figure 2 Bramstrung process: an electron of kinetic energy E1, passes near the nucleus of a target atom, generates an X-ray photon of energy hv
The production of characteristic X-rays involves interactions between the accelerated electrons and the electrons of the target material. Impacting electrons excite the electrons in the shells of atoms in the target material to move them out of inner orbit to higher energy states (into the outer shells) or even liberating them altogether which leaves the atom in an excited (or ionised) state. To resolve this, electrons in the outer shells of the atom cascade down to fill the void and in the process release a discrete amount of energy equal to the difference in the two orbital binding energies (Figure 2 . Characteristic X-ray production: A KÎ± photon is produced when an L shell electron moves to fill a vacancy in the K shell). The energy of the interactions with the inner K, L and M shells of the atoms is sufficient to produce an X-ray photon. The energy of the emitted photon is related to the atomic number in that as the number increases, the wavelength of the photon decreases. Each interaction varies according to the element which produces a specific (or characteristic) radiation spectrum (Figure 2 . Characteristic radiation from electrons striking a tungsten target).
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Figure 2. Characteristic X-ray production: A KÎ± photon is produced when an L shell electron moves to fill a vacancy in the K shell
Figure 2. Characteristic radiation from electrons striking a tungsten target
Basic Interactions of Photons with Matter
As an X-ray beam passes through a material it undergoes attenuation which results in a gradual decrease in intensity through absorption and scattering. Although photons contain electromagnetic energy, they have no 'charge' and thus are less likely to interact with matter than charged particles such as electrons or protons. The five main methods of interaction are (1) the Rayleigh effect, (2) the Compton effect (incoherent scattering), (3) Photoelectric effect, (4) Pair production, (5) Triplet production and Photodisintegration. The first three interactions listed are considered here as the latter interactions require higher energy than used in current microtomography systems. For example Pair production occurs when a photon interacts with a nucleus, it is transformed into an electron and a positron, with the excess energy transferred to the new particles in the form of kinetic energy. Pair production can only occur at energy levels higher than 2mc2, which is approximately 1 MeV. Existing cone beam micro CT systems only extend to 450keV while fan beam systems can reach 1MeV (Kruth et al., 2011). For a more detailed outline of photon interactions, see Appendix A.