These 3 quantities play a central role in clinical radiation dosimetry. A detailed discussion and history is given in the article in this issue by Cormack and Carrier[1] and various international reports discuss the definitions in great detail[2]. I wish to give a brief outline here for completeness.
The quantity exposure is defined as the total charge of one sign produced in dry air when all electrons liberated by photons in a unit mass of air are completely stopped in air. The energetic knock-on electrons produce about 30 electrons for every keV of energy they lose, thus a single 100 keV knock-on electron produces 3000 free electrons. The SI unit for exposure is C/kg as
suggested by the definition, but the old unit, the roentgen
(1R=2.58 10
C/kg) is still often used.
The definition refers to all electrons set in motion by photons
in the volume of air with mass m, and the charge is collected
from throughout the electron's
path as it slows down (fig 1). This quantity has the
advantage of being directly measurable, at least for low-energy photons
(<300 keV or so) where the electrons don't move too far as they
slow down.
The primary measurement standard is a free air chamber
which has two parallel plates with a potential across them for
collecting the charge liberated by a well defined photon beam passing
between them. This works very well for low-energy photons, and
allows a direct measurement with an accuracy of about 0.5%.
The measurement technique breaks down for photons with energies typical
of 
beams (up to 1.33 MeV). In this case very different
techniques using ion chambers and Bragg-Gray cavity theory are needed to
measure exposure (discussed below).
However, exposure suffers from two fundamental flaws. The first is that it is
only defined for photons interacting in air; the second is that the
quantity becomes ill-defined as photon energies become higher as in
accelerator beams because the range of the electrons slowing down becomes
so large.
These problems are both overcome by introducing the quantity kerma, which is
the Kinetic Energy Released per unit MAss (unit J/kg or gray). For
photon beams the kinetic energy released is the kinetic energy transferred to
electrons in the material. The quantity must always be defined with respect to
the specific material in which the interactions are taking place (e.g. air
kerma, water kerma etc). This quantity is well defined at all energies and
for all materials and in fig 1 it is just the sum of all the
energy transfers to charged particles, E
, in the volume divided by
the mass m. For kerma, it does not matter whether the charged particles slow
down inside the volume or not. As we shall see below, air kerma and exposure
are closely related, and although the measurement standards are embodied in the
same equipment, air kerma is not directly measurable in the same sense as
exposure. Nonetheless kerma plays an important role in radiation dosimetry
because it is the energy released per unit mass of material, and not
surprisingly this is closely related to the energy absorbed per unit mass
of material.
The absorbed dose to a material, 
is:
where 
is the energy absorbed (J) in a mass m (kg) of the
material
. In
fig 1 the absorbed dose sums the energy deposition on
all the tracks from P to P
. For volumes which are
large compared to the tracklength, the kerma and absorbed dose are
virtually identical, especially since absorbed dose also includes energy
deposition within the volume by electrons set in motion outside the
volume. This tends to balance the energy deposited outside the volume by
those electrons starting inside the volume.
Absorbed dose is
currently taken as the best physical indicator of biological response. Because
of this, absorbed dose to water (which closely resembles human tissue but is
well defined) is the quantity which is used to specify the amount of radiation
to be used in clinical practice. Absorbed dose has the further advantage that
it is directly measurable in a variety of ways. The most straightforward is
by calorimetry which determines the energy
deposited per unit mass of material by measuring the temperature rise.
The temperature rise in water for a typical radiotherapy
dose of 200 cGy (2 J/kg), delivered in 1 or 2 minutes,
is 500 
K (specific heat capacity of water is 4181 J/(kg K)).
