4. X-Ray Image Formation

Imaging

• As photons interact with matter, they are absorbed, scattered, and/or transmitted
• Transmitted (& some scattered) photons reach the x-ray detector
• Photon interaction depends on the material’s density and atomic number, as well as the photon’s energy

Modes of Interaction

* Orange highlight indicates the mode is more likely to occur in diagnostic imaging

Rayleigh (Coherent) Scattering

• In rayleigh scattering, the photon interacts with an entire atom and is deflected into a new direction
• Little to no change in photon energy with scattering
• More likely in mammography
• Electrons within the matter oscillate in phase when the photon interacts, but none are ejected
• The higher the atomic number, the more likely rayleigh scattering is
• Rayleigh scattering has a pretty low energy range, but this affects quality

]]Compton Scattering]]

• Compton is the most common mode of interaaction within the imaging energy range
• In compton scattering, the photon interacts with a single (probably valence) electron
• Electron is ejected and the photon loses energy, veering off of its path
• Compton scattering depends on material density and its electron density
• Small note, 511 keV is a constant equal to one half of mc^2

]]Photoelectric Effect]]

• The photoelectric effect describes a photon interacting with a single electron, which bumps around energy levels
• All of the photon’s energy is absorbed by the electron in the photoelectric effect
• Energy absorbance in the photoelectric effect produces a photoelectron , an ion, and a low-energy characteristic radiation
• Photoelectric energy produced = incident energy - binding energy
• The photoelectric energy produced increases as atomic number increases, but decreases as the indicent energy increases (aka electrons might pass through without being absorbed)

Pair Production

• Pair Production occurs when the photon interacts with the nucleus
• Energy must be greater than 1.02 MeV (double the static general photon energy, which is 511) to produce a positron-electron pair
• The energy range for pair production is used more in radiation therapy than in diagnostic imaging
• Positron and electron may interact and produce a pair of annihilation photons in the opposite direction, each with 511 keV

Photodisintegration

• Photodisintegration occurs when the photon interacts with the nucleus
• A nuclear particle is produced
• Requires VERY high energy

Energy & Modes of Interactions

Propagation Model - Beer’s Law

• N0 is the number of incident photons, N is the number of photons coming out of a material, and Δx is the distance the photons travel (object’s thickness)
• Beer’s Law: N = N0 * e^-μΔx
• μ is the linear attenuation coefficient
    * cm^-1
    * μ is dependent on material density and atomic number
    * Usually between 0.05 and 0.5 cm^-1
    * Mass attenuation coefficient: μ / density
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