Assume that a slab of homogeneous material of thickness Ax is placed in the path of a very narrow incident photon beam, and that the number of incident photons for the time of measurement is N (see Fig. 4.2). Then, since the chance of a single scattering interaction that will remove a photon from the incident beam depends on N (the incident photon fluence) and the properties of the attenuator (its linear attenuation coefficient), the equation for the number of photons removed (N- n) can be written as
AN = ~ AxN,
where AN is the number of transmitted photons scattered and /x is a constant of proportionality. In other words, the number of photons removed (usually expressed as a fraction of the incident fluence AN~N)depends upon the thickness of the absorber and a constant of proportionality, /z, which is determined by the properties of the homogeneous absorber and which will be different for different radiations and different materials. This constant, /z, is known as the linear attenuation coefficient: detector P is positioned to measure only photons that have
not undergone a scattering event. This arrangement of source and detector is known as a "good" geometry measure of attenuation, because all events that have undergone any energy transition will suffer a momentum and energy change and will not be seen at this location on their new scattered path. The other requirement for good geometry is that the beam, N, be very small in physical dimensions. If a broad beam is used, there is the possibility that photons that were not included in the definition of N will be scattered in from other areas of the attenuator. Therefore, good geometry for attenuation measurements is described as measurements made with a small, highly collimated pencil beam of incident photons and a measurement system that "sees" only unscattered photons. "Bad" geometry is sometimes described as broad-beam geometry, since that nonpejorative term describes a condition that will provide unwanted scatter-in photons.
There is no adequate analytical expression for measurement of attenuation in broad-beam conditions. The narrow beam, or good geometry, expression for attenuation from an incident photon beam can be obtained by integration ofwhere N O is the incident fluence, N is the fluence remaining after a thickness, x, of specified absorber, and /z is the linear attenuation coefficient.
MASS, ELECTRONIC, AND ATOMIC ATTENUATION COEFFICIENTS
Further examination of the interaction processes shows that the interactions of radiation with matter may depend on either the density of electrons with which the photons interact or the density of the atoms with which, under certain other circumstances, the photon will interact. The former will be shown to be the most important for tissue equivalent systems, but for the general case, attenuation coefficients are described in terms of the linear dimension, the unit mass dimension, which is simply related to the linear coefficient by the density, the probability of interaction per electron, and the probability of interaction per atom. These various attenuation coefficients are, respectively, the linear, mass, electronic, and atomic attenuation coefficients. shows the relationships among attenuation coefficients.
AN = ~ AxN,
where AN is the number of transmitted photons scattered and /x is a constant of proportionality. In other words, the number of photons removed (usually expressed as a fraction of the incident fluence AN~N)depends upon the thickness of the absorber and a constant of proportionality, /z, which is determined by the properties of the homogeneous absorber and which will be different for different radiations and different materials. This constant, /z, is known as the linear attenuation coefficient: detector P is positioned to measure only photons that have
not undergone a scattering event. This arrangement of source and detector is known as a "good" geometry measure of attenuation, because all events that have undergone any energy transition will suffer a momentum and energy change and will not be seen at this location on their new scattered path. The other requirement for good geometry is that the beam, N, be very small in physical dimensions. If a broad beam is used, there is the possibility that photons that were not included in the definition of N will be scattered in from other areas of the attenuator. Therefore, good geometry for attenuation measurements is described as measurements made with a small, highly collimated pencil beam of incident photons and a measurement system that "sees" only unscattered photons. "Bad" geometry is sometimes described as broad-beam geometry, since that nonpejorative term describes a condition that will provide unwanted scatter-in photons.
There is no adequate analytical expression for measurement of attenuation in broad-beam conditions. The narrow beam, or good geometry, expression for attenuation from an incident photon beam can be obtained by integration ofwhere N O is the incident fluence, N is the fluence remaining after a thickness, x, of specified absorber, and /z is the linear attenuation coefficient.
MASS, ELECTRONIC, AND ATOMIC ATTENUATION COEFFICIENTS
Further examination of the interaction processes shows that the interactions of radiation with matter may depend on either the density of electrons with which the photons interact or the density of the atoms with which, under certain other circumstances, the photon will interact. The former will be shown to be the most important for tissue equivalent systems, but for the general case, attenuation coefficients are described in terms of the linear dimension, the unit mass dimension, which is simply related to the linear coefficient by the density, the probability of interaction per electron, and the probability of interaction per atom. These various attenuation coefficients are, respectively, the linear, mass, electronic, and atomic attenuation coefficients. shows the relationships among attenuation coefficients.
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