Absorption technique (contd...)

The basis of absorptivity measurement is the fact that and are unique functions of the material density. In an experiment, quantities and are measured and yield the absorption coefficient and hence, the transmittivity and absorptivity of the material of thickness L . If the composition of the specimen changes with position, Equation 7.1 shows that a path integral of attenuation of the incident radiation is obtained. A linear form of Equation 7.1 useful in measurements is

	(7.2)

The integral is resolved by working with an average value over the thickness of the material used as sample. Spectral values of absorption coefficient are converted into total values if the dependence on wavelength is weak or the property is averaged over the spectrum of the incident radiation. Hence, a greatly simplified form of Equation 7.2 for an average absorption coefficient is

	(7.3)

If the chemical composition of the medium is known in advance, the absorption properties can be determined from the density of the constituent species and their mass fractions. Thus, differences in the measured values with respect to the estimation will shed light on the microstructural defects in the medium, for example, the presence of voids.

See article 1 and article 2 for an application involving x-ray absorption, tomography, beam hardening, and methods of alleviating inversion errors.

Figure 7.3: Variation of absorptivity of CO₂ in the earth's atmosphere as a function of wavelength.