Optical structures to implement the discrete Fourier transform (DFT) and fast Fourier transform (FFT) algorithms for discretely sampled data sets are considered. In particular, the decomposition of the FFT algorithm into the basic Butterfly operations is described, as this allows the algorithm to be fully implemented by the successive coherent addition and subtraction of two wavefronts (the subtraction being performed after one has been appropriately phase shifted), so facilitating a simple and robust hardware implementation based on waveguided hybrid devices as employed in coherent optical detection modules. Further, a comparison is made to the optical structures proposed for the optical implementation of the quantum Fourier transform and they are shown to be very similar.

Date Published: 29 April 2013
PDF: 11 pages
Proc. SPIE 8748, Optical Pattern Recognition XXIV, 874806 (29 April 2013); doi: 10.1117/12.2014042

Published in SPIE Proceedings Vol. 8748:
Optical Pattern Recognition XXIV
David Casasent; Tien-Hsin Chao, Editor(s)