The fractional Fourier transform is a new topic in optics. To make use of the fractional Fourier transform as an experimental tool, I design a fractional Fourier transformer of variable order: I introduce a lens system that is able to perform equidistant fractional Fourier transforms that cover the whole range of orders and that consist of a minimum number of modules. By module, I mean an elementary fractional Fourier transform of certain order that consists of a lens between two free-space lengths. Because of the commutative additivity of the transform, various fractional orders can be achieved by means of different constellations of the modules. It is possible to perform a large variety of fractional Fourier transforms with a small number of modules.
© 1995 Optical Society of America
Original Manuscript: September 14, 1994
Revised Manuscript: April 24, 1995
Published: September 10, 1995
Rainer G. Dorsch, "Fractional Fourier transformer of variable order based on a modular lens system," Appl. Opt. 34, 6016-6020 (1995)