Dose Course 2018_Flipping book

Calculation techniques:

Convolutions - many dose calculation problems can be approximated as convolutions (invariant kernel -> for homogeneous media):

1D example

Convolution - an averaging operation where at each point a weighted mean of the original function is calculated. The (invariant!!!) weighting function is often called kernel.







 ( )

( ) ( ' f x g x x x − ) ' d '

f g x 

1D

=

−   

 



 ( ) , f g x y 

(

) (

)

', ' f x y g x x y y x y − − ', ' d 'd '

2D cartesian

=

− −

2D polar Google Hankel transforms!

  



 (

)

(

)

(

) ' d ' d 'dz ' z z x y −

, , f g x y z 

', ', ' f x y z g x x y y − − ',

3D cartesian

=

',

  

− − −