Now showing items 1-20 of 27

    • Accumulated Gouy phase shift in Gaussian beam propagation through first-order optical systems 

      Erden, M. F.; Özaktaş, Haldun M. (Optical Society of America, 1997-09)
      We define the accumulated Gouy phase shift as the on-axis phase accumulated by a Gaussian beam in passing through an optical system, in excess of the phase accumulated by a plane wave. We give an expression for the accumulated ...
    • 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 ...
    • 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 ...
    • 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 ...
    • Evaluation of the validity of the scalar approximation in optical wave propagation using a systems approach and an accurate digital electromagnetic model 

      Kulce, O.; Onural, L.; Özaktaş, Haldun M. (Taylor and Francis Ltd., 2016)
      The cause and amount of error arising from the use of the scalar approximation in monochromatic optical wave propagation are discussed using a signals and systems formulation. Based on Gauss’s Law, the longitudinal component ...
    • 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) ...
    • Fast and accurate linear canonical transform algorithms 

      Özaktaş, Haldun M.; Koç, A. (IEEE, 2015)
      Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform ...
    • 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 ...
    • The fractional fourier transform 

      Özaktas, Haldun M.; Kutay, M. A. (IEEE, 2001)
      A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phase-space representations (time- or space-frequency representations) and the concept of fractional Fourier domains are ...
    • 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 ...
    • Generalization of time-frequency signal representations to joint fractional Fourier domains 

      Durak, L.; Özdemir, A. K.; Arıkan, Orhan; Song, I. (IEEE, 2005-09)
      The 2-D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose ...
    • 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 ...
    • High-throughput, high-resolution interferometric light microscopy of biological nanoparticles 

      Yurdakul, C.; Avcı, O.; Matlock, A.; Devaux, A. J.; Quintero, M. V.; Özbay, Ekmel; Davey, R. A.; Connor, J. H.; Karl, W. C.; Tian, L.; Ünlü, M. Selim (American Chemical Society, 2020-01)
      Label-free, visible light microscopy is an indispensable tool for studying biological nanoparticles (BNPs). However, conventional imaging techniques have two major challenges: (i) weak contrast due to low-refractive-index ...
    • Optical implementation of the two-dimensional fractional Fourier transform with different orders in the two dimensions 

      Sahin, A.; Özaktaş, Haldun M.; Mendlovic, D. (Elsevier BV * North-Holland, 1995-10-15)
      Previous optical implementations of the two-dimensional fractional Fourier transform have assumed identical transform orders in both dimensions. We let the orders in the two orthogonal dimensions to be different and present ...
    • Optical information processing: A historical overview 

      Kutay, Mehmet Alper; Özaktaş, Haldun Memduh (Academic Press, 2021-12)
      Optical information processing lies at the intersection of optics and signal processing. It involves the processing of optical information as well as the use of optical means to process information, the later being the ...
    • Optical information processing: A historical overview 

      Özaktaş, Haldun Memduh; Kutay, Mehmet Alper (Academic Press, 2021-12)
      Optical information processing lies at the intersection of optics and signal processing. It involves the processing of optical information as well as the use of optical means to process information, the later being the ...
    • Optimal image restoration with the fractional Fourier transform 

      Kutay, M. A.; Özaktaş, Haldun M. (OSA - The Optical Society, 1998-04)
      The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for space-invariant degradation models and space-invariant signal and noise characteristics. For space-varying degradations and ...
    • Optimal representation and processing of optical signals in quadratic-phase systems 

      Arik, S. Ö.; Özaktaş, Haldun M. (Elsevier, 2016)
      Optical fields propagating through quadratic-phase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. ...
    • Optimization of orders in multichannel fractional Fourier-domain filtering circuits and its application to the synthesis of mutual-intensity distributions 

      Yetik, İ. Ş.; Kutay, M. A.; Özaktaş, Haldun M. (Optical Society of America, 2002)
      Owing to the nonlinear nature of the problem, the transform orders in fractional Fourier-domain filtering configurations have usually not been optimized but chosen uniformly. We discuss the optimization of these orders for ...