By using the ABCD matrix formalism, we present and analyze some optical con
figurations for implementing both the perfect and imperfect fractional Four
ier transforms, and then extend them to achieve the Radon-Winger display fo
r one-dimensional signals. In all these proposed configurations, the free-s
pace propagation distance is designed to be fixed or it varies linearly wit
h the coordinate, which is convenient for practical applications. (C) 1999
Elsevier Science B.V. All rights reserved.