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Fast Fourier Transform (FFT) convolution

FFT is a way to compute the same result more quickly: operations proportional to

N

ln(

N

) per dimension instead of

N

2

decrease calc burden from

N

4

to 2

N

2

ln(

N

),

a factor proportional to 2ln(

N

)/

N

2

shorter time, with

N

x

N

fluence pixels.

Scaling example

N

factor

10 1

100 0.02

200 0.006

R Mohan and CS Chui (1987)

Med Phys 14

, 70-7

1. Perform a 2D FFT on the pencil kernel (can be

pre-stored!)

2. Perform a 2D FFT on the lateral energy fluence

distribution

3. Mulitply the two transformed distributions

4. Perform an inverse 2D FFT (FFT

-1

) on the

resulting product

5. Done – for all points in a plane at a certain depth

(not a 3D matrix, yet)!

Calculation recipe for the lateral

dose distribution at a given depth

through FFT convolution.

calculation techniques:

Used at some stage in most TPS that use pencil kernels