Browsing by Author "Lohmann, A. W."
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Item Open Access 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.Item Open Access 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.Item Open Access Fractional correlation(Optical Society of America, 1995) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.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 with the definition of conventional correlation. Fractional correlation is not always a shift-invariant operation. This property leads to some new applications for fractional correlation as shift-variant image detection. A bulk-optics implementation of fractional correlation is suggested and demonstrated with computer simulations.Item Open Access Fractional Fourier transform: simulations and experimental results(Optical Society of America, 1995) Bitran, Y.; Mendlovic, D.; Dorsch, R. G.; Lohmann, A. W.; Özaktaş, Haldun M.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 configuration for performing the fractional-Fourier-transform operation 3J. Opt. Soc. Am. A 10, 2181 1199324 provides a scaled output using a fixed lens. For obtaining a non-scaled output, an asymmetrical setup is suggested and tested. For comparison, computer simulations were performed. A good agreement between computer simulations and experimental results was obtained.Item Open Access Graded-index fibers, Wigner-distribution functions, and the fractional Fourier transform(Optical Society of America, 1994) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.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 distribution. It is shown that both definitions are equivalent. An important result of this equivalency is that the Wigner distribution of a wave field rotates as the wave field propagates through a quadratic graded-index medium. The relation with ray-optics phase space is discussed.Item Open Access Interpretation of the space-bandwidth product as the entropy of distinct connection patterns in multifacet optical interconnection architectures(Optical Society of America, 1993) Özaktaş, Haldun M.; Brenner, K. -H.; Lohmann, A. W.We show that the entropy of the distinct connection patterns that are possible with multifacet optical interconnection architectures is approximately equal to the space-bandwidth product of the optical system.Item Open Access A New Signal Representation based on the Fractional Fourier Transform: Definitions(OSA Publishing, 1995) Mendlovic, D.; Zalevsky, Z.; Dorsch, R.; Bitran, Y.; Lohmann, A. W.The fractional Fourier transform is a mathematical operation that generalizes the well-known Fourier transform. This operation has been shown to have physical and optical fundamental meanings, and it has been experimentally implemented by relatively simple optical setups. Based on the fractional Fourier-transform operation, a new space-frequency chart definition is introduced. By the application of various geometric operations on this new chart, such as radial and angular shearing and rotation, optical systems may be designed or analyzed. The field distribution, as well as full information about the spectrum and the space-bandwidth product, can be easily obtained in all the stages of the optical system. (C) 1995 Optical Society of AmericaItem Open Access Scaling of diffractive and refractive lenses for optical computing and interconnections(Optical Society of America, 1994-06-10) Özaktaş, Haldun M.; Urey, H.; Lohmann, A. W.We discuss both numerically and analytically how the space-bandwidth product and the information density of lenses scale as functions of their diameter and f-number over many orders of magnitude. This information may be useful for the design of optical computing and interconnection systems. For diffractive lenses, cost is defined as the number of resolution elements the lithographic production system must have; the relationship of this quantity to the space-bandwidth product and information density is also given.Item Open Access Self Fourier functions and fractional Fourier transforms(Elsevier, 1994) Mendlovic, D.; Özaktaş, Haldun M.; Lohmann, A. W.Self Fourier functions and fractional Fourier transforms are two concepts that have been discussed recently. Investigated is the combination of these two concepts: self fractional Fourier functions and the fractional Fourier transform of a self Fourier function. © 1994.