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Fast Fourier Transform (FFT) convolution
FFT is a way to compute the same result more quickly: operations proportional to
2 N ln(N) instead
⇒
increase in speed of the order of N/ln(N)
e.g. For a 256 x 256 matrix, complexity in computation of 2 x 617
⇒
increase in
speed by
a factor of 106.
Calculation recipe for the lateral dose
distribution at a given depth through
FFT convolution.
1. Perform a 2D FFT on the pencil kernel
(preferably pre-stored!).
Kernels that are laterally invariant enable FFF convolution
R Mohan and CS Chui (1987)
Med Phys 14
, 70-7
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. Convolution (i.e. dose calculation) completed.