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Derivation of formalism to convert ionisation in plastic to dose to water
Scaling photon energy fluence
In water at a reference depth
In solid plastic at an equivalent depth
ref
z
Phantoms irradiated with
the same MV photon
beam
w
Ψ
eq
z
s
Ψ
The energy fluences at corresponding depths in the two media can be related using O’Connor’s density
scaling theorem
According to this theorem energy fluences can be related through the inverse square law, once all
distances in irradiation geometry (
SSD, field size and depth
) are scaled with the inverse ratio of relative
electron densities of the two media
O'Connor, J. E, PMB 1, 352-369, 1957
(
)
(
)
2
ref
ref
eq
eq
eq eq
ref
ref
,
,
+
+
=
Ψ
Ψ
z
SSD
z
SSD
r z
r z
s
w
size
field r
:
(ref
:
in water)