Characterization of the spatial response functions of ionization chambers for photon
beam dosimetry
H.K. Looe, T.S. Stelljes, D. Harder, B. Poppe
In the plane perpendicular to the beam direction, the volume effect of a detector can be
characterized by its response functions along the coordinates of this plane. The measured
dose profile in a direction perpendicular to the beam, M(x), resulting from the volume effect,
can be mathematically described as resulting from the convolution of the true dose profile
D(x) with the detector’s response function K(x): M(x) = D(x) * K(x). We have shown that both
the lateral and longitudinal response functions can be best described by Gaussian
distributions, characterized by their standard deviations, σlat and σlong respectively.
The examples displayed in Figure 1 and Figure 2 illustrate the performance of the method
used to determine of the detectors' response functions by comparison between the
convolved true signal profiles measured with the Si diode and the signal profiles broadened
by the lateral response functions of two cylindrical ionization chamber (PTW 31013 and IBA
CC13).
Figure 1. Determination of the response
function in the lateral direction of an
ionization chamber. Measurements of a 1
cm wide slit beam profile were carried out
at depths of secondary electron equilibrium
buildup: (a) 6 MV, depth = 1.5 cm; (b) 15
MV, depth = 2.5 cm. Shown are the
measured Si diode signal profiles (thick
lines), the signal profiles measured with the
PTW 31013 Semiflex chamber (open
circles) and the convolved Si diode signal
profiles (thin lines). The noted σlat values
were determined by varying the σ values
until optimal fit of the thin lines with the
measured values was achieved.
Figure 2. Determination of the response
function in the longitudinal direction of the
CC13 ionisation chamber. Beam profiles
were obtained by scanning a 4 cm wide
slit profile at (a) 6 MV and 5 cm depth; (b)
6 MV and 15 cm depth; (c) 15 MV and 5
cm depth and (d) 15 MV and 15 cm
depth. The meaning of the symbols is the
same as in Figure 1. For better
visualization only the penumbral region of
the left hand profile wing is shown.
The astounding fact that the "tails" of the Gaussian response functions definititely reach
across the chambers' geometrical boundaries is an effect of the ranges of the secondary
electrons. This can be best understood by regarding the chamber as a sensor for the photon
fluence distribution, whose range of sensitivity is influenced by the dimensions of the
chamber volume as well as by the ranges of the secondary electrons. Thereby the chamber
"senses" regions of the photon fluence profile which are also responsible for regions of the
true dose profile in the vicinity of the chamber. This explanation is in line with the slight
energy dependence of the σ values as well as with their invariability with depth.