Tunable fractional-order Fourier transformer

A fractional two-dimensional Fourier transformer whose orders are tuned by means of optical quadrupoles is described. It is shown that in the optical scheme considered, the Fourier-transform order $a\in[0,1]$ in one of the mutually orthogonal planes corresponds to the transform order $(2-a)$ in another plane, i.e., to inversion and inverse Fourier transform of the order $a$.