Browsing by Author "Erden, M. F."

Now showing 1 - 13 of 13

Open Access
Accumulated Gouy phase shift in Gaussian beam propagation through first-order optical systems
(Optical Society of America, 1997-09) Erden, M. F.; Özaktaş, Haldun M.
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 Gouy phase shift in terms of the parameters of the system through which the beam propagates. This quantity complements the beam diameter and the wave-front radius of curvature to constitute three parameters that uniquely characterize the beam with respect to a reference point in the system. Measurement of these parameters allows one to uniquely recover the parameters characterizing the first-order system through which the beam propagates.
Open Access
Comparison of fully three-dimensional optical, normally conducting, and superconducting interconnections
(Optical Society of America, 1999-12-10) Özaktaş, Haldun M.; Erden, M. F.
Several approaches to three-dimensional integration of conventional electronic circuits have been pursued recently. To determine whether the advantages of optical interconnections are negated by these advances, we compare the limitations of fully three-dimensional systems interconnected with optical, normally conducting, repeatered normally conducting, and superconducting interconnections by showing how system-level parameters such as signal delay, bandwidth, and number of computing elements are related. In particular, we show that the duty ratio of pulses transmitted on terminated transmission lines is an important optimization parameter that can be used to trade off signal delay and bandwidth so as to optimize applicable measures of performance or cost, such as minimum message delay in parallel computation.
Open Access
Cost-efficient approximation of linear systems with repeated and multi-channel filtering configurations
(IEEE, 1998-05) Kutay, Mehmet Alper; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Candan, Ç.; Güleryüz, Ö.
It is possible to obtain either exact realizations or useful approximations of linear systems or matrix-vector products arising in many different applications, by synthesizing them in the form of repeated or multi-channel filtering operations in fractional Fourier domains, resulting in much more efficient implementations with acceptable decreases in accuracy. By varying the number and configuration of filter blocks, which may take the form of arbitrary flow graphs, it is possible to trade off between accuracy and efficiency in the desired manner. The proposed scheme constitutes a systematic way of exploiting the information inherent in the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.
Open Access
Design of dynamically adjustable anamorphic fractional Fourier transformer
(Elsevier BV * North-Holland, 1997-03-01) Erden, M. F.; Özaktaş, Haldun M.; Sahin, A.; Mendlovic, D.
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 curvature of both orthogonal dimensions of anamorphic fractional Fourier transformation by just changing the focal lengths of cylindrical lenses used in the proposed setups. Here, we also consider two approaches for implementing cylindrical lenses with dynamically adjustable focal lengths. There may also be some other methods to obtain cylindrical lenses having adjustable focal lengths which can successfully be used in these proposed setups.
Open Access
Extensions to common laplace and fourier transforms
(Institute of Electrical and Electronics Engineers, 1997-11) Onural, L.; Erden, M. F.; Özaktaş, Haldun M.
The extended versions of common Laplace and Fourier transforms are given. This is achieved by defining a new function fe(p), p 2 C related to the function to be transformed f(t), t 2 R. Then fe(p) is transformed by an integral whose path is defined on an inclined line on the complex plane. The slope of the path is the parameter of the extended definitions which reduce to common transforms with zero slope. Inverse transforms of the extended versions are also defined. These proposed definitions, when applied to filtering in complex ordered fractional Fourier stages, significantly reduce the required computation.
Open Access
Propagation of Mutual Intensity Expressed in terms of the Fractional Fourier Transform
(OSA Publising, 1996) Erden, M. F.; Özaktaş, Haldun M.; Mendlovic, D.
The propagation of mutual intensity through quadratic graded-index media or free space can be expressed in terms of two-dimensional fractional Fourier transforms for one-dimensional systems and in terms of fourdimensional fractional Fourier transforms for two-dimensional systems. As light propagates, its mutual intensity distribution is continually fractional Fourier transformed. These results can also be generalized to arbitrary first-order optical systems. Furthermore, the Wigner distribution associated with a partially coherent field rotates in the same manner as the Wigner distribution associated with a deterministic field.
Open Access
Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of first-order optical systems
(Elsevier BV * North-Holland, 1997-11-01) Özaktaş, Haldun M.; Erden, M. F.
Although wave optics is the standard method of analyzing systems composed of a sequence of lenses separated by arbitrary distances, it is often easier and more intuitive to ascertain the function and properties of such systems by tracing a few rays through them. Determining the location, magnification or scale factor, and field curvature associated with images and Fourier transforms by tracing only two rays is a common skill. In this paper we show how the transform order, scale factor, and field curvature can be determined in a similar manner for the fractional Fourier transform, Our purpose is to develop the understanding and skill necessary to recognize fractional Fourier transforms and their parameters by visually examining ray traces. We also determine the differential equations governing the propagation of the order, scale, and curvature, and show how these parameters are related to the parameters of a Gaussian beam.
Open Access
Repeated filtering in consecutive fractional fourier domains and its application to signal restoration
(1999-05) Erden, M. F.; Kutay, M. A.; Özaktaş, Haldun M.
Filtering in a single time domain or in a single frequency domain has recently been generalized to filtering in a single fractional Fourier domain. In this paper, we further generalize this to repeated filtering in consecutive fractinal Fourier domains. We then discuss the applications of the repeated filtering method to signal restoration through several examples. In all of the examples, we see that when our repeated filtering method is compared with single domain filtering methods, significant improvements in performance are obtained with only modest increases in processing time. We also compare our method with the optimum general linear estimation method and see that the use of our method may result in significant computational savings while still yielding acceptable performance.
Open Access
Signal processing with repeated filtering in fractional Fourier domains
(Board of Optronics Lasers, Tian-Jin City, China, 1998) Ozaktas, Haldun M.; Erden, M. F.; Kutay, M. A.
Open Access
Solution and cost analysis of general multi-channel and multi-stage filtering circuits
(IEEE, 1998-10) Kutay, M. Alper; Arıkan, Orhan; Özaktaş, Haldun M.; Erden, M. F.; Özaktaş, Hakan
The fractional Fourier domain multi-channel and multi-stage filtering configurations that have been recently proposed enable us to obtain either exact realizations or useful approximations of linear systems or matrix-vector products in many different applications. We discuss the solution and cost analysis for these configurations. It is shown that the problem can be reduced to a least squares problem which can be solved with fast iterative techniques.
Open Access
Space-bandwidth-efficient realizations of linear systems
(Optical Society of America, 1998-07-15) Kutay, M. A.; Erden, M. F.; Özaktaş, Haldun M.; Arıkan, Orhan; Güleryüz, Ö.; Candan, Ç.
One can obtain either exact realizations or useful approximations of linear systems or matrix-vector products that arise in many different applications by implementing them in the form of multistage or multichannel fractional Fourier-domain filters, resulting in space-bandwidth-efficient systems with acceptable decreases in accuracy. Varying the number and the configuration of filters enables one to trade off between accuracy and efficiency in a flexible manner. The proposed scheme constitutes a systematic way of exploiting the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.
Open Access
Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains
(Optical Society of America, 1998) Erden, M. F.; Özaktaş, Haldun M.
The optical and digital implementations of general linear systems are costly. Through several examples we show that either exact realizations or useful approximations of these systems may be implemented in the form of repeated-filtering operations in consecutive fractional Fourier domains. These implementations are much cheaper than direct implementations of general linear systems. Thus we may significantly decrease the implementation costs of general linear systems with little or no decrease in performance by synthesizing them with the proposed repeated-filtering method. (C) 1998 Optical Society of America.
Open Access
Synthesis of mutual intensity distributions using the fractional Fourier transform
(Elsevier BV * North-Holland, 1996-04-15) Erden, M. F.; Özaktaş, Haldun M.; Mendlovic, D.
Our aim in this paper is to obtain the best synthesis of a desired mutual intensity distribution, by filtering in fractional Fourier domains. More specifically, we find the optimal fractional-domain filter that transforms a given (source) mutual intensity distribution into the desired one as closely as possible (in the minimum mean-square error sense). It is observed that, in some cases, closer approximations to the desired profile can be obtained by filtering in fractional Fourier domains, in comparison to filtering in the ordinary space or frequency domains.