ESTRO course Dose Modelling and Verification 2017

1D example

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

 

  



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

 



 















' d '

2D cartesian

', '

' d 'd '

2D polar Google Hankel transforms!

3D cartesian

, ,

', ', '

f g x

f x g x x x

g x y

f x y g x x y y x y

f g x y z

f x y z g x x y y





 

 











 





 



 





' d 'd 'dz '

z z x y

  

  



 



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.

Calculation techniques:

Convolutions - many dose calculation problems can be approximated as convolutions

(invariant kernel -> for homogeneous media):