Scaled fractional Fourier transform and optical systems

Scaled fractional Fourier transform (SFRT) (a perfect FRT with a scaling factor in input and output) is presented based on the rotation of the Wigner distribution function (WDF). It differs from the imperfect FRT and not only has several useful properties similar to the perfect FRT, but can also be used more widely than the perfect FRT. The application of SFRT to optical systems is emphasized, The order of SFRT and the magnitude of the scaling factor vary when translating the output plane in a single lens geometry. This helped us to interpret wave propagation in optical systems. By deriving the cascading rules of the composite SFRT, the SFRT in composite optical systems is analyzed and can be used to design desired optical systems. (C) 1998 Published by Elsevier Science B.V.