ESTRO course Dose Modelling and Verification 2017

Convolution

Ԧ =ම Ԧ Ԧ , Ԧ

T Ԧ

Ԧ , Ԧ

This is an integral transform of with as the kernel function

If the kernel is invariant, such that , the transform becomes a convolution, and (following the convolution theorem) Ԧ , Ԧ = Ԧ − Ԧ

−1

Ԧ = Ԧ ∗ Ԧ , Ԧ =

( ) ⋅

( )

In general, however, the kernel varies with position, due to divergence, changes in energy, and the heterogeneity of the medium

03/01/13