Half-Value Layer

The thickness of any given material where 50% of the incident energy has been attenuated is know as the half-value layer (HVL). The HVL is expressed in units of distance (mm or cm). Like the attenuation coefficient, it is photon energy dependant. Increasing the penetrating energy of a stream of photons will result in an increase in a material's HVL.

The HVL is inversely proportional to the attenuation coefficient. If an incident energy of 1 and a transmitted energy is 0.5 is plugged into the equation introduced on the preceding page, it can be seen that the HVL multiplied by mmust equal 0.693.

If x is the HVL then m times HVL must equal 0.693 (since the number 0.693 is the exponent value that gives a value of 0.5).

Therefore, the HVL and m are related as follows:

The HVL is often used in radiography simply because it is easier to remember values and perform simple calculations. In a shielding calculation, such as illustrated to the right, it can be seen that if the thickness of one HVL is known, it is possible to quickly determine how much material is needed to reduce the intensity to less than 1%.

Approximate HVL for Various Materials when Radiation is from a Gamma Source

Approximate Half-Value Layer for Various Materials when Radiation is from an X-ray Source

Note: The values presented on this page are intended for educational purposes. Other sources of information should be consulted when designing shielding for radiation sources.

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Sources of Attenuation

The attenuation that results due to the interaction between penetrating radiation and matter is not a simple process.  A single interaction event between a primary x-ray photon and a particle of matter does not usually result in the photon changing to some other form of energy and effectively disappearing.  Several interaction events are usually involved and the total attenuation is the sum of the attenuation due to different types of interactions. These interactions include the photoelectric effect, scattering, and pair production. The figure below shows an approximation of the total absorption coefficient, (µ), in red, for iron plotted as a function of radiation energy. The four radiation-matter interactions that contribute to the total absorption are shown in black. The four types of interactions are: photoelectric (PE), Compton scattering (C), pair production (PP), and Thomson or Rayleigh scattering (R). Since most industrial radiography is done in the 0.1 to 1.5 MeV range, it can be seen from the plot that photoelectric and Compton scattering account for the majority of attenuation encountered.

Summary of different mechanisms that cause attenuation of an incident x-ray beam

Photoelectric (PE) absorption of x-rays occurs when the x-ray photon is absorbed, resulting in the ejection of electrons from the outer shell of the atom, and hence the ionization of the atom. Subsequently, the ionized atom returns to the neutral state with the emission of an x-ray characteristic of the atom. This subsequent emission of lower energy photons is generally absorbed and does not contribute to (or hinder) the image making process. Photoelectron absorption is the dominant process for x-ray absorption up to energies of about 500 KeV. Photoelectron absorption is also dominant for atoms of high atomic numbers.

Compton scattering (C) occurs when the incident x-ray photon is deflected from its original path by an interaction with an electron.  The electron gains energy and is ejected from its orbital position.  The x-ray photon loses energy due to the interaction but continues to travel through the material along an altered path.  Since the scattered x-ray photon has less energy, it, therefore, has a longer wavelength than the incident photon. The event is also known as incoherent scattering because the photon energy change resulting from an interaction is not always orderly and consistent.  The energy shift depends on the angle of scattering and not on the nature of the scattering medium

Pair production (PP) can occur when the x-ray photon energy is greater than 1.02 MeV, but really only becomes significant at energies around 10 MeV. Pair production occurs when an electron and positron are created with the annihilation of the x-ray photon. Positrons are very short lived and disappear (positron annihilation) with the formation of two photons of 0.51 MeV energy.  Pair production is of particular importance when high-energy photons pass through materials of a high atomic number.

Below are other interaction phenomenon that can occur. Under special circumstances these may need to be considered, but are generally negligible.

Thomson scattering (R), also known as Rayleigh, coherent, or classical scattering, occurs when the x-ray photon interacts with the whole atom so that the photon is scattered with no change in internal energy to the scattering atom, nor to the x-ray photon. Thomson scattering is never more than a minor contributor to the absorption coefficient. The scattering occurs without the loss of energy. Scattering is mainly in the forward direction.

Photodisintegration (PD) is the process by which the x-ray photon is captured by the nucleus of the atom with the ejection of a particle from the nucleus when all the energy of the x-ray is given to the nucleus. Because of the enormously high energies involved, this process may be neglected for the energies of x-rays used in radiography.

Effect of Photon Energy on Attenuation
Absorption characteristics will increase or decrease as the energy of the x-ray is increased or decreased. Since attenuation characteristics of materials are important in the development of contrast in a radiograph, an understanding of the relationship between material thickness, absorption properties, and photon energy is fundamental to producing a quality radiograph. A radiograph with higher contrast will provide greater probability of detection of a given discontinuity. An understanding of absorption is also necessary when designing x-ray and gamma ray shielding, cabinets, or exposure vaults.

The applet below can be used to investigate the effect that photon energy has on the type of interaction that the photon is likely to have with a particle of the material (shown in gray). Various materials and material thicknesses may be selected and the x-ray energy can be set to produce a range from 1 to 199 KeV. Notice as various experiments are run with the applets that low energy radiation produces predominately photoelectric events and higher energy x-rays produce predominately Compton scattering events. Also notice that if the energy is too low, none of the radiation penetrates the material.

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Sources of Attenuation

The attenuation that results due to the interaction between penetrating radiation and matter is not a simple process.  A single interaction event between a primary x-ray photon and a particle of matter does not usually result in the photon changing to some other form of energy and effectively disappearing.  Several interaction events are usually involved and the total attenuation is the sum of the attenuation due to different types of interactions. These interactions include the photoelectric effect, scattering, and pair production. The figure below shows an approximation of the total absorption coefficient, (µ), in red, for iron plotted as a function of radiation energy. The four radiation-matter interactions that contribute to the total absorption are shown in black. The four types of interactions are: photoelectric (PE), Compton scattering (C), pair production (PP), and Thomson or Rayleigh scattering (R). Since most industrial radiography is done in the 0.1 to 1.5 MeV range, it can be seen from the plot that photoelectric and Compton scattering account for the majority of attenuation encountered.

Summary of different mechanisms that cause attenuation of an incident x-ray beam

Photoelectric (PE) absorption of x-rays occurs when the x-ray photon is absorbed, resulting in the ejection of electrons from the outer shell of the atom, and hence the ionization of the atom. Subsequently, the ionized atom returns to the neutral state with the emission of an x-ray characteristic of the atom. This subsequent emission of lower energy photons is generally absorbed and does not contribute to (or hinder) the image making process. Photoelectron absorption is the dominant process for x-ray absorption up to energies of about 500 KeV. Photoelectron absorption is also dominant for atoms of high atomic numbers.

Compton scattering (C) occurs when the incident x-ray photon is deflected from its original path by an interaction with an electron.  The electron gains energy and is ejected from its orbital position.  The x-ray photon loses energy due to the interaction but continues to travel through the material along an altered path.  Since the scattered x-ray photon has less energy, it, therefore, has a longer wavelength than the incident photon. The event is also known as incoherent scattering because the photon energy change resulting from an interaction is not always orderly and consistent.  The energy shift depends on the angle of scattering and not on the nature of the scattering medium

Pair production (PP) can occur when the x-ray photon energy is greater than 1.02 MeV, but really only becomes significant at energies around 10 MeV. Pair production occurs when an electron and positron are created with the annihilation of the x-ray photon. Positrons are very short lived and disappear (positron annihilation) with the formation of two photons of 0.51 MeV energy.  Pair production is of particular importance when high-energy photons pass through materials of a high atomic number.

Below are other interaction phenomenon that can occur. Under special circumstances these may need to be considered, but are generally negligible.

Thomson scattering (R), also known as Rayleigh, coherent, or classical scattering, occurs when the x-ray photon interacts with the whole atom so that the photon is scattered with no change in internal energy to the scattering atom, nor to the x-ray photon. Thomson scattering is never more than a minor contributor to the absorption coefficient. The scattering occurs without the loss of energy. Scattering is mainly in the forward direction.

Photodisintegration (PD) is the process by which the x-ray photon is captured by the nucleus of the atom with the ejection of a particle from the nucleus when all the energy of the x-ray is given to the nucleus. Because of the enormously high energies involved, this process may be neglected for the energies of x-rays used in radiography.

Effect of Photon Energy on Attenuation
Absorption characteristics will increase or decrease as the energy of the x-ray is increased or decreased. Since attenuation characteristics of materials are important in the development of contrast in a radiograph, an understanding of the relationship between material thickness, absorption properties, and photon energy is fundamental to producing a quality radiograph. A radiograph with higher contrast will provide greater probability of detection of a given discontinuity. An understanding of absorption is also necessary when designing x-ray and gamma ray shielding, cabinets, or exposure vaults.

The applet below can be used to investigate the effect that photon energy has on the type of interaction that the photon is likely to have with a particle of the material (shown in gray). Various materials and material thicknesses may be selected and the x-ray energy can be set to produce a range from 1 to 199 KeV. Notice as various experiments are run with the applets that low energy radiation produces predominately photoelectric events and higher energy x-rays produce predominately Compton scattering events. Also notice that if the energy is too low, none of the radiation penetrates the material.

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Compton Scattering

As mentioned on the previous page, Compton scattering occurs when the incident x-ray photon is deflected from its original path by an interaction with an electron.  The electron is ejected from its orbital position and the x-ray photon loses energy because of the interaction but continues to travel through the material along an altered path.  Energy and momentum are conserved in this process.  The energy shift depends on the angle of scattering and not on the nature of the scattering medium.  Since the scattered x-ray photon has less energy, it has a longer wavelength and less penetrating than the incident photon.

Compton effect was first observed by Arthur Compton in 1923 and this discovery led to his award of the 1927 Nobel Prize in Physics.  The discovery is important because it demonstrates that light cannot be explained purely as a wave phenomenon. Compton's work convinced the scientific community that light can behave as a stream of particles (photons) whose energy is proportional to the frequency.

The change in wavelength of the scattered photon is given by:

The applet below demonstrates Compton scattering as calculated with the Klein-Nishina formula, which provides an accurate prediction of the angular distribution of x-rays and gamma-rays that are incident upon a single electron.  Before this formula was derived, the electron cross section had been classically derived by the British physicist and discoverer of the electron, J.J. Thomson. However, scattering experiments showed significant deviations from the results predicted by Thomson's model.  The Klein-Nishina formula incorporates the Breit-Dirac recoil factor, R, also known as radiation pressure. The formula also corrects for relativistic quantum mechanics and takes into account the interaction of the spin and magnetic moment of the electron with electromagnetic radiation. Quantum mechanics is 
a system of mechanics based on quantum theory to provide a consistent explanation of both electromagnetic wave and atomic structure. 

The applet shows that when a photon of a given energy hits an atom, it is sometimes reflected in a different direction. At the same time, it loses energy to an electron that is ejected from the atom. Theta is the angle between the scattered photon direction and the path of the incident photon. Phi is the angle between the scattered electron direction and the path of the incident photon.

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