Browsing by Author "Mendlovic, D."
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About the Wigner distribution of a graded index medium and the fractional fourier transform operation
Özaktaş, Haldun M.; Mendlovic, D.; Lohmann, A. W. (SPIE, 199308)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, 19951110)An additional degree of freedom is introduced to fractionalFouriertransform 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 processinga 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, 19941110)In the Wigner domain of a onedimensional 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 timelens devices. A temporal processor based on chirpz transformers is suggested. This configuration is more compact than a conventional 4f temporal processor. On the basis of ... 
Convolution and filtering in fractional fourier domains
Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D. (SpringerVerlag, 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 * NorthHolland, 19970301)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 fractionalFourierdomain filtering
Özaktaş, Haldun M.; Mendlovic, D. (Optical Society of America, 19960610)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, 199404)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 fractionalFouriertransform 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, 199504)There exists a fractional Fouriertransform 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 fractionalFouriertransform operation. We show that the original bulkoptics ... 
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 spacebandwidth 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 ... 
Gradedindex fibers, Wignerdistribution 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 gradedindex medium, and the other is based on rotating a function's Wigner ...