Browsing by Subject "Optical information processing"

Now showing 1 - 8 of 8

Open Access
Convolution and filtering in fractional fourier domains
(Springer-Verlag, 1994) Özaktaş, Haldun M.; Barshan, B.; Mendlovic, D.
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 under certain conditions one can improve upon the special cases of these operations in the conventional space and frequency domains. Because of the ease of performing the fractional Fourier transform optically, these operations are relevant for optical information processing.
Open Access
Every Fourier optical system is equivalent to consecutive fractional-Fourier-domain filtering
(Optical Society of America, 1996-06-10) Özaktaş, Haldun M.; Mendlovic, D.
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) consecutive filtering operations in several fractional Fourier domains and (ii) consecutive filtering operations alternately in the space and the frequency domains.
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.
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.
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.
Open Access
Optical information processing: A historical overview
(Academic Press, 2021-12) Özaktaş, Haldun Memduh; Kutay, Mehmet Alper
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 main emphasis of this work. A historical review of various forms of optical signal processing and holography, optoelectronic and digital optical computing, and optical interconnections is given.
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
(1997) Erden, M. Fatih
In the first part of this thesis, relationships between the fractional Fourier transformation and Fourier optical systems are analyzed to further elucidate the importance of this transformation in optics. Then in the second part, the concept of repeated filtering is considered. In this part, the repeated filtering method is interpreted in two different ways. In the first interpretation the linear transformation between input and output is constrained to be of the form of repeated filtering in consecutive domains. The applications of this constrained linear transformation to signal synthesis (beam shaping) and signal restoration are discussed. In the second interpretation, general linear systems are synthesized with repeated filtering in consecutive domains, and the synthesis of some important linear systems in signal processing and the .synthesis of optical interconnection architectures are considered for illustrative purposes. In all of the examples, when our repeated filtering method is compared with single domain filtering methods, significant improvements in performance are obtained with only modest increases in optical or digital implementation costs. Similarly, when the proposed method is compared with general linear systems, it is seen that acceptable performance may be possible with significant computational savings in implementation costs.