Browsing by Subject "Wigner distribution function"

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    About the Wigner distribution of a graded index medium and the fractional fourier transform operation
    (SPIE, 1993-08) Özaktaş, Haldun M.; Mendlovic, D.; Lohmann, A. W.
    Upon propagation through quadratic graded index media, the Wigner distribution of the wavefunction of light rotates uniformly. As a consequence, a definition of fractional Fourier transforms based on rotating the functions Wigner distribution, and another based on propagation through graded index media, are equivalent.
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    Chirp filtering in the fractional Fourier domain
    (Optical Society of America, 1994-11-10) Dorsch, R. G.; Lohmann, A. W.; Bitran, Y.; Mendlovic, D.; Özaktaş, Haldun M.
    In the Wigner domain of a one-dimensional function, a certain chirp term represents a rotated line delta function. On the other hand, a fractional Fourier transform (FRT) can be associated with a rotation of the Wigner-distribution function by an angle connected with the FRT order. Thus with the FRT tool a chirp and a delta function can be transformed one into the other. Taking the chirp as additive noise, the FRT is used for filtering the line delta function in the appropriate fractional Fourier domain. Experimental filtering results for a Gaussian input function, which is modulated by an additive chirp noise, are shown. Excellent agreement between experiments and computer simulations is achieved.
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    Optical implementations of two-dimensional fractional Fourier transforms and linear canonical transforms with arbitrary parameters
    (Optical Society of America, 1998-04-10) Sahin, A.; Özaktaş, Haldun M.; Mendlovic, D.
    We provide a general treatment of optical two-dimensional fractional Fourier transforming systems. We not only allow the fractional Fourier transform orders to be specified independently for the two dimensions but also allow the input and output scale parameters and the residual spherical phase factors to be controlled. We further discuss systems that do not allow all these parameters to be controlled at the same time but are simpler and employ a fewer number of lenses. The variety of systems discussed and the design equations provided should be useful in practical applications for which an optical fractional Fourier transforming stage is to be employed.