Now showing items 1-20 of 32

    • About the Wigner distribution of a graded index medium and the fractional fourier transform operation 

      Özaktaş, Haldun M.; Mendlovic, D.; Lohmann, A. W. (SPIE, 1993-08)
      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 ...
    • Anamorphic fractional Fourier transform: optical implementation and applications 

      Mendlovic, D.; Bitran, Y.; Dorsch, R. G.; Ferreira, C.; Garcia, J.; Özaktaş, Haldun M. (Optical Society of America, 1995-11-10)
      An additional degree of freedom is introduced to fractional-Fourier-transform systems by use of anamorphic optics. A different fractional Fourier order along the orthogonal principal directions is performed. A laboratory ...
    • Applications of the fractional Fourier transform in optics and signal processing-a review 

      Özaktaş, Haldun M.; Mendlovic, D. (SPIE, 1996)
      The fractional Fourier transform The fractional Fourier transform is a generalization of the common Fourier transform with an order parameter a. Mathematically, the ath order fractional Fourier transform is the ath power ...
    • Applications of the fractional Fourier transform to optical pattern recognition 

      Mendlovic, D.; Zalevsky, Z.; Özaktaş, Haldun M. (Cambridge University Press, 1998)
    • Chirp filtering in the fractional Fourier domain 

      Dorsch, R. G.; Lohmann, A. W.; Bitran, Y.; Mendlovic, D.; Özaktaş, Haldun M. (Optical Society of America, 1994-11-10)
      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 ...
    • Compact optical temporal processors 

      Mendlovic, D.; Melamed, O.; Özaktaş, Haldun M. (Optical Society of America, 1995)
      Optical signal processing can be done with time-lens devices. A temporal processor based on chirp-z transformers is suggested. This configuration is more compact than a conventional 4-f temporal processor. On the basis of ...
    • Convolution and filtering in fractional fourier domains 

      Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D. (Springer-Verlag, 1994)
      Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that ...
    • Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms 

      Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D.; Onural, L. (, 1994)
      A concise introduction to the concept of fractional Fourier transforms is followed by a discussion of their relation to chirp and wavelet transforms. The notion of fractional Fourier domains is developed in conjunction ...
    • Design of dynamically adjustable anamorphic fractional Fourier transformer 

      Erden, M. F.; Özaktaş, Haldun M.; Sahin, A.; Mendlovic, D. (Elsevier BV * North-Holland, 1997-03-01)
      We form optical systems by using only free space portions and cylindrical lenses, and consider these systems as anamorphic fractional Fourier transformers. We dynamically adjust the transform order, scale factor and field ...
    • Every Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering 

      Özaktaş, Haldun M.; Mendlovic, D. (Optical Society of America, 1996-06-10)
      We consider optical systems composed of an arbitrary number of lenses and filters, separated by arbitrary distances, under the standard approximations of Fourier optics. We show that every such system is equivalent to (i) ...
    • Filtering in fractional Fourier domains and their relation to chirp transforms 

      Özaktaş, Haldun M.; Barshan, Billur; Onural, Levent; Mendlovic, D. (IEEE, 1994-04)
      Fractional Fourier transforms, which are related to chirp and wavelet transforms, lead to the notion of fractional Fourier domains. The concept of filtering of signals in fractional domains is developed, revealing that ...
    • Fourier transforms of fractional order and their optical interpretation 

      Özaktaş, Haldun M.; Mendlovic, D. (Elsevier, 1993)
      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 ...
    • Fractional correlation 

      Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W. (Optical Society of America, 1995)
      Recently, optical interpretations of the fractional-Fourier-transform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent ...
    • Fractional Fourier Optics 

      Özaktaş, Haldun M.; Mendlovic, D. (Optical Society of America, 1995-04)
      There exists a fractional Fourier-transform relation between the amplitude distributions of light on two spherical surfaces of given radii and separation. The propagation of light can be viewed as a process of continual ...
    • The Fractional Fourier transform and its applications in optics and signal processing 

      Mendlovic, D.; Özaktaş, Haldun M. (SPIE International Technical Working Group Newsletter, 1999)
    • Fractional Fourier transform as a tool for analyzing beam propagation and spherical mirror resonators 

      Özaktaş, Haldun M.; Mendlovic, D. (Optical Society of America, 1994)
      The complex amplitude distributions on two spherical reference surfaces of given curvature and spacing are simply related by a fractional Fourier transform. The order of the fractional Fourier transform is proportional to ...
    • Fractional Fourier transform: simulations and experimental results 

      Bitran, Y.; Mendlovic, D.; Dorsch, R. G.; Lohmann, A. W.; Özaktaş, Haldun M. (Optical Society of America, 1995)
      Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractional-Fourier-transform operation. We show that the original bulk-optics ...
    • Fractional Fourier transforms and their optical implementation. II 

      Özaktaş, Haldun M.; Mendlovic, D. (Optical Society of America, 1993)
      The derivation of a linear transform kernel for fractional Fourier transforms is presented. Discussed in direct relation to fractal Fourier transforms are spatial resolution and the space-bandwidth product for propagation ...
    • Fractional Fourier transforms and their optical implementation: I 

      Mendlovic, D.; Özaktaş, Haldun M. (Optical Society of America, 1993)
      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 ...
    • Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform 

      Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W. (Optical Society of America, 1994)
      Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a graded-index medium, and the other is based on rotating a function's Wigner ...