Browsing by Subject "Fractional Fourier Transforms"

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    Fractional Fourier transforms and their optical implementation: I
    (Optical Society of America, 1993) Mendlovic, D.; Özaktaş, Haldun M.
    Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a = 1. An optical interpretation is provided in terms of quadratic graded index media and discussed from both wave and ray viewpoints. Several mathematical properties are derived.
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    Propagation of Mutual Intensity Expressed in terms of the Fractional Fourier Transform
    (OSA Publising, 1996) Erden, M. F.; Özaktaş, Haldun M.; Mendlovic, D.
    The propagation of mutual intensity through quadratic graded-index media or free space can be expressed in terms of two-dimensional fractional Fourier transforms for one-dimensional systems and in terms of fourdimensional fractional Fourier transforms for two-dimensional systems. As light propagates, its mutual intensity distribution is continually fractional Fourier transformed. These results can also be generalized to arbitrary first-order optical systems. Furthermore, the Wigner distribution associated with a partially coherent field rotates in the same manner as the Wigner distribution associated with a deterministic field.