Fractional Fourier transforms and their optical implementation: I

Mendlovic, David; Özaktaş, Haldun M.

doi:10.1364/josaa.10.001875

Cited by 791 publications

(320 citation statements)

References 9 publications

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“…We substitute (12) in (11), change sequence of integration and summation and use certain algebraic manipulations to obtain the following expression:…”

Section: Simulationmentioning

confidence: 99%

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Modeling of propagation of optical signals in gradient index media based on fractional Fourier transform

Zubtsov¹,

Kirilenko²

2015

Collection of Selected Papers of the I International Conference on Information Technology and Nanotechnology

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Abstract. This research has simulated the propagation of the light beams through the quadratic index media. Five methods of simulation were considered and the propagating beams corresponding to different input signals such as Airy-Gaussian beams, rectangular function pulses, triangular function pulses, cosine function signals and finite eigenfunctions were demonstrated. Originally, FrFT was used in quantum mechanics; however, recently it has increasingly become a focus of opticists. As a result, extensive research involving its properties, optical realization and potentiality opportunities in optic applications has been performed. Thus, currently FrFT is actively used in optical image processing [3]. Moreover, the fractioning of some transformation provides a new degree of freedom (fraction order) that can be used for a more complete description of the object (signal) or as an additional encoding parameter.FrFT is used in differential equation solving, in quantum mechanics and quantum optics, in optical theory of diffraction, in optical system and optical signal processing

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“…We substitute (12) in (11), change sequence of integration and summation and use certain algebraic manipulations to obtain the following expression:…”

Section: Simulationmentioning

confidence: 99%

“…One of application of FrFT is the description of laser beam propagation in gradient index media [11,12].…”

Section: Introductionmentioning

confidence: 99%

Modeling of propagation of optical signals in gradient index media based on fractional Fourier transform

Zubtsov¹,

Kirilenko²

2015

Collection of Selected Papers of the I International Conference on Information Technology and Nanotechnology

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“…Definition based on propagation in graded index media. The first FRT definition [9][10][11] is based on the field propagating along a quadratic graded index (GRIN) medium having a length proportional to p ( p being the FRT order). The eigenmodes of quadratic GRIN media are the Hermite-Gaussian (HG) functions, which form an orthogonal and complete basis set.…”

Section: Definitionmentioning

confidence: 99%

Fractional Fourier transform-exceeding the classical concepts of signal’s manipulation

2007

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-The fractional Fourier transform is a signal processing tool which is strongly associated with optical data manipulation. It has fast computational algorithms and it suggests solutions to interesting signal processing tasks. In this paper we review its properties as well as present a new set of its applications for blind source separation of images and for RF photonics (a field in which photonic devices are used to process RF signals).

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“…Since the fractional Fourier transform (FRT) was introduced to the optics community in 1993 [9,10] a large number of publications have successfully developed this operation in the area of signal processing and have extended the concept of 'fractionalization' to other mathematical transformations in optics (see [11] for an extensive review of these operations and their applications).…”

Section: Fresnel Patterns Calculation Through the Fractional Fourier mentioning

confidence: 99%

Refractive analysis of the human cornea through propagated fields

Illueca

Mas

Pérez

et al. 2001

Journal of Modern Optics

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Abstract.A new technique for analysing the optical quality of the human cornea is presented. Corneal maps are obtained through keratographies and then converted into phase maps. The propagated elds generated from this surface are plotted and studied. It is shown that any irregularity in the cornea a ects the propagated eld and the energy distribution at the focal plane. Simple applications are also indicated.

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Fractional Fourier transforms and their optical implementation: I

Cited by 791 publications

References 9 publications

Modeling of propagation of optical signals in gradient index media based on fractional Fourier transform

Modeling of propagation of optical signals in gradient index media based on fractional Fourier transform

Fractional Fourier transform-exceeding the classical concepts of signal’s manipulation

Refractive analysis of the human cornea through propagated fields

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