# Quality factor

A dimensionless factor defined to reflect the relative biological effectiveness of high-LET radiations compared with low-LET radiations at low exposure levels. $Q$ is usually given by a function $Q(L)$, where $L$ is the unrestricted LET in water. The quality factor at a point in tissue, is given by:

$Q = \frac{1}{D} \int_{L=0}^\infty Q(L)D_LdL$

where $D$ is the absorbed dose at that point, $D_L$ is the distribution of $D$ in unrestricted LET $L$ at the point of interest, and $Q(L)$ is the quality factor as a function of $L$. The integration is to be performed over $D_L$, due to all charged particles, excluding their secondary electrons.

ICRP Publication 116, 2010 and ICRP Publication 123, 2013

The factor characterising the biological effectiveness of a radiation, based on the ionisation density along the tracks of charged particles in tissue. $Q$ is defined as a function of the unrestricted linear energy transfer, $L_\infty$ (often denoted as $L$ or LET), of charged particles in water:
$Q(L) = \begin{cases} 1, & \text{if } L \lt \text{10 keV/μm} \\ 0.32L - 2.2, & \text{if 10} \le L \le \text{100 keV/μm} \\ 300/\sqrt{L}, & \text {if } L \gt \text{100 keV/μm} \end{cases}$
$Q$ has been superseded by the radiation weighting factor in the definition of equivalent dose, but it is still used in calculating the operational dose equivalent quantities used in monitoring.