We show that an arbitrary paraxial optical system, compounded with its reflection in an appropriately warped mirror, is a pure fractional Fourier transformer between coincident input and output planes. The geometric action of reflection on optical systems is introduced axiomatically and is developed in the paraxial regime. The correction of aberrations by warp of the mirror is briefly addressed.
© 2002 Optical Society of America
(070.2590) Fourier optics and signal processing : ABCD transforms
(080.1010) Geometric optics : Aberrations (global)
(080.2720) Geometric optics : Mathematical methods (general)
(080.2730) Geometric optics : Matrix methods in paraxial optics
Kurt Bernardo Wolf and Guillermo Krötzsch, "Fractional Fourier transformers through reflection," J. Opt. Soc. Am. A 19, 1191-1196 (2002)