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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