2.3.1 - Photon Beam Spectrum

Fluence and Spectrum

Monoenergetic Beams

A beam of photons is most easily thought of as a containing a single energy of photons. This simplifies calculation of energy within the beam. Numerous descriptors can be used to classify this beam.


The fluence of a beam is the number of photons (N) that enter an imaginary sphere, with a cross-sectional area of A m2. The units of fluence are m-2.

\begin{align} \Phi = \frac{N}{A} \text{m}^{-2} \end{align}

Fluence Rate

The fluence rate describes the fluence per unit time, with units of m-2.s-1.

\begin{align} \phi = \frac{\Phi}{t} \text{m}^{-2}\text{s}^{-1} \end{align}

Energy Fluence

Instead of particles, the energy fluence is the amount of energy (in Joules) that enters the imaginary sphere with cross-sectional area of A m2. It has units of $\frac{J}{m^2}$

\begin{align} \Psi = \frac{E}{A} \frac{\text{J}}{\text{m}^2} \end{align}

Energy fluence can be found by multiplying the particle fluence by the energy (E) of individual photons:

\begin{align} \Psi = \Phi.E = \frac{N \times E}{A} \end{align}

Energy Fluence Rate

This has a similar usage to Fluence Rate, and is the energy fluence per unit time.

\begin{align} \psi = \frac{\Psi}{t} \frac{\text{J}}{\text{m}^2 \text{s}} \end{align}

Polyenergetic Beams

The above values are not suitable descriptions of a polyenergetic beam (which all therapeutic beams are).

Fluence Spectrum

The fluence spectrum describes the number of particles of different energies that enter the imaginary sphere.

Energy Spectrum

The energy fluence spectrum describes the amount of energy that enters the sphere of area A m2, accounting for the different energies of the representative particles.


Describing Photon Beams

It is difficult to describe a photon beam as 'containing a spectrum of energies, from 0 to a maximum of 200 keV, following a particular curve…' etc etc. Therefore there are shorter ways of describing a beam without going into all the specifics.

Half Value Layer

The half value layer is a useful descriptor of (particularly low energy) photon beams. However, it does not always describe the distribution of dose within a volume well.
HVL values are often given for kilovoltage beams, often as a metal type and a thickness. This is the thickness of a particular metal that will attenuate half of the beam. Low kilovoltage beams will typically use a thickness of aluminium (Z = 13); orthovoltage beams typically use HVL of copper.

Peak Voltage (kVp)

The peak voltage is the voltage potential that exists within the x-ray tube. This is typically under 150 keV for superficial beams and under 500 keV for orthovoltage beams.
By combining the peak voltage and the HVL, a clinically useful description of the beam is generated.

Effective Energy

The effective energy is the equivalent energy of a theoretical monoenergetic photon beam that would be attenuated at the same rate as the beam in question. For megavoltage beams, this is usually quoted as a HVL of lead to attenuate half of the theoretical beam. This is not a very useful description as the distance for the first and second HVL of a beam are not equal.

Mean Energy

The mean energy is the average fluence or energy fluence of a beam. It is not commonly used to describe photon beams.


The TPR20,10 is the method recommended by the IAEA to describe a megavoltage photon beam. This is the absorbed dose at a depth of 20 cm divided by the dose at a depth of 10 cm within a water phantom. This ratio gives a number under 1 which provides a useful description of how the photon beam is attenuated in water, the most commonly irradiated material in radiotherapy.