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Measurement of projection data
Attenuation of X-rays
Assume no loss of intensity of the beam due to divergence, however the beam does attenuate due to photons either being absorbed or scattered by the object.
Photoelectric Absorption.
This consists of an x-ray photon imparting all of its energy to an inner electron of an atom. The electron uses this energy to overcome the binding energy within its shell, and the rest appearing as kinetic energy in this freed electron.
Compton Scattering
This consists of the interaction of the photon with either the free electron or a loosely bound outer shell electron. As a result the x-ray is deflected from its original direction.
Consider N photons cross the lower boundary of this layer in some measured time interval, and N+ΔN emerge from the top side. (ΔN will be negative). ΔN follows the relationship,
µ=photon loss rate (per unit distance) of the Compton and photoelectric effects. In the limit Δx goes to zero so we get
Solving this across the thickness of the slab
Where N0 is the number of photons that enter the object. The number of photons as a function of the position within the slab is given by,
or
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