Half-value layer

Half-value layer is a physical quantity expressing the thickness of the given material that is needed for shielding intensity of the given linear radiation to half the original value. It is usually d1/2 (or simplified d) its unit is a meter. The size of the half-value layer is determined by the material used and the wavelength of the passing radiation. In general, the higher the energy (shorter wavelength) of the radiation, the better the radiation passes through the material (i.e. larger half-value layer is needed).

Formula for monofrequency radiation: $$E = \frac{1}{2^x} E_0$$ , where x is a proportion of the length that the ray traveled through the substance and at the same time a proportion of the half-value layer of this substance.

Homogeneity factor
The homogeneity factor (HF) describes the polychromatic nature of the beam and can be calculated using the half-thickness ratio:

$$HF=\frac{d_1}{d_2}$$

d1 is the first half-thickness; d2 is the second half-thickness (the half-thickness for the beam that has passed through the first half-thickness). The HF of monofrequency radiation is always 1, for polychromatic radiation it takes values less than 1, which explains the so-called. beam hardening effect.

Beam hardening effect
Polychromatic beam (e.g. a beam of X-rays) is composed of photons of various high energies. As the beam passes through matter, lower energy photons are absorbed faster, while higher energy photons pass through better. Thus, if a beam passes through two identical objects, its energy is not half compared to a beam that would pass through only one of the objects, but it is somewhat higher than one would expect. This can result in dark streaks' or smudges between two daytime objects on a CT image.

Pictures

 * An example of an artifact caused by the beam hardening effect

Source

 * https://en.wikipedia.org/wiki/Half-value_layer
 * https://www.nde-ed.org/EducationResources/CommunityCollege/Radiography/Physics/HalfValueLayer.htm
 * https://radiopaedia.org/articles/beam-hardening-phenomenon