Dose 2016

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.

1. Perform a 2D FFT on the pencil kernel (preferably 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. Convolution (i.e. dose calculation) completed.

Calculation recipe for the lateral dose distribution at a given depth through FFT convolution.

R Mohan and CS Chui (1987) Med Phys 14 , 70-7

Kernels that are laterally invariant enable FFF convolution