  In this paper we show that the discrete Fourier transform can be performed by
scattering a coherent particle or laser beam off a two-dimensional potential
that has the shape of rings or peaks. After encoding the initial vector into
the two-dimensional potential, the Fourier-transformed vector can be read out
by detectors surrounding the potential. The wavelength of the laser beam
determines the necessary accuracy of the 2D potential, which makes our method
very fault-tolerant.
