Linear absorbance coefficient

AH three interactions occur when x-rays are absorbed by the human body. The first two dominate, however, owing to the lower energy of the x-rays. If A/q x-ray photons incident on a tissue and N are transmitted, the absorbance, M, is proportional to the thickness, and linear attentuation coefficient ]1, of the absorbing tissue. 

A) The use of a calibration graph. This overcomes any problems created due to non-linear absorbance/concentration features and means that any unknown concentration run under the same conditions as the series of standards can be determined directly from the graph. The procedure requires that all standards and samples are measured in the same fixed-path-length cell, although the dimensions of the cell and the molar absorption coefficient for the chosen absorption band are not needed as these are constant throughout all the measurements. 

Absorption Coefficient—Fractional absorption of the energy of an unscattered beam of x- or gamma-radiation per unit thickness (linear absorption coefficient), per unit mass (mass absorption coefficient), or per atom (atomic absorption coefficient) of absorber, due to transfer of energy to the absorber. The total absorption coefficient is the sum of individual energy absorption processes (see Compton Effect, Photoelectric Effect, and Pair Production). 

Absorption Coefficient, Linear—A factor expressing the fraction of a beam of x- or gamma radiation absorbed in a unit thickness of material. In the expression I=I0e+l x, I0 is the initial intensity, I the intensity of the beam after passage through a thickness of the material x, and p is the linear absorption coefficient. 

Absorption Coefficient, Mass—The linear absorption coefficient per cm divided by the density of the absorber in grams per cubic centimeter. It is frequently expressed as p/p, where p is the linear absorption coefficient and p the absorber density. 

Recall from Eq. (6.71) that the fractional change in light intensity, dl/I, over a distance x within the absorbing medinm is directly proportional to the linear absorption coefficient,... 

Briefly, the total linear absorption coefficient n (cm-1) varies as a function of the wavelength and the nature of the absorber as the photon energy is varied across and beyond the absorption edge. The logical setup for an absorption experiment in transmission mode therefore consists of three primary components (Fig. 2a) (i) an X-ray source, (ii) a monochromator (and collimator), and (iii) a detector. In this case Beer s law,... 

To obtain monochromatic Ka, a filter system is necessary to filter out the continuous X-rays and other characteristic X-rays, which are not generated with Ka from the X-ray tube. X-ray filters can be made from material that strongly absorbs X-rays other than Ka. Generally, materials exhibit various abilities to absorb X-rays. X-ray absorption by materials is a function of the linear absorption coefficient (fi) and mass density (p). The X-ray intensity (/) passing through an absorption layer with thickness x is expressed by the following equation. 

Eq. (94) can be corrected for absorbing samples if the linear absorption coefficient is known. In any case, the value of the linear refractive index must be known. For liquid samples an Abe refractometer can be used. For solid samples index matching liquids can be used, although for thin films the most convenient method is the m-line technique [68]. 

Attenuation of 7 Radiations. When 7 radiations pass through the absorber medium, they undergo one or a combination of the above three processes (photoelectric, Compton, and pair production) depending on their energy, or they are transmitted out of the absorber without any interaction. The combined effect of the three processes is called the attenuation of the 7 radiations (Fig. 1.9). For a 7 radiation passing through an absorber, the linear attenuation coefficient (fie) of the 7 radiation is given by... 

Another quantity called the mass attenuation coefficient (pg) is given by the linear attenuation coefficient (pe) divided by the density ip) of the absorber and is given in units of cm2/g or cm2/mg. 

The detection efficiency of a detector is another important property in PET technology. Since it is desirable to have shorter scan times and low tracer activity for administration, the detector must detect as many of the emitted photons as possible. The 511-keV photons interact with detector material by either photoelectric absorption or Compton scattering, as discussed in Chap. 1. Thus, the photons are attenuated (absorbed and scattered) by these two processes in the detector, and the fraction of incident 7 rays that are attenuated is determined by the linear attenuation coefficient (/x) given in Chap. 1 and gives the detection efficiency. At 511 keV, /x = 0.92 cm-1 for bismuth germanate (BGO), 0.87 cur1 for lutetium oxyorthosilicate (LSO), and 0.34 cm-1 for Nal(Tl) (Melcher, 2000). Consequently, to have similar detection efficiency, Nal(Tl) detectors must be more than twice as thick as BGO and LSO detectors. 

Linear attenuation coefficient (p). The fraction of radiation energy absorbed and scattered per unit thickness of absorber. 

When a beam of X-rays passes through a material the result is an exponential attenuation of the primary beam. The different possible interaction processes, as fluorescence, are characterized by a probability of occurrence per unit path length in the absorber. The flux of transmitted primary photons I after having passed through an attenuator with a thickness x (cm) and a linear attenuation coefficient called yu,(cm ) for the wavelength considered, can be calculated with respect to its initial value f and for an angle of penetration of 90 ° as follows ... 

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