Statistical characterization of the point spread function (PSF) of a turbulence degraded imaging system

Ankara : Department of Electrical and Electronics Engineering and Institute of Engineering and Sciences, Bilkent Univ., 1993.Thesis (Master's) -- Bilkent University, 1993.Includes bibliographical references leaves 48-49In tills tlicsis, the circct of atmospheric turbulence on an incoherent imaging systcMii is analyzed. 'I’lie combination of the atmosphere and the imaging system is modelled as a linear system with a stochastic point spread function (PSF). ddie mean and the covariance of the PSF are evaluated and plotted for a variety of system parameters and atmospheric conditions. The results predicted by this work are shown to be in very good agreement with experimental results published in the literature.Erden, M FatihM.S

Repeated filtering in consecutive fractional Fourier domains

Ankara : Department of Electrical and Electronics Engineering and the Institute of Engineering and Science of Bilkent University, 1997.Thesis (Ph. D.) -- Bilkent University, 1997.Includes bibliographical references leaves 96-105.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.Erden, M FatihPh.D

Synthesis of general linear systems with repeated filtering in consecutive fractional Fourier domains

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

Accumulated Gouy phase shift in Gaussian beam propagation through first-order optical systems

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. © 1997 Optical Society of America [S0740-3232(97)01408-7] 1

Propagation of mutual intensity expressed in terms of the fractional Fourier transform

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 four-dimensional 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. © 1996 Optical Society of America

Propagation of mutual intensity expressed in terms of the fractional Fourier transform

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

Extensions to common laplace and fourier transforms

The extended versions of common Laplace and Fourier transforms are given. This is achieved by defining a new function f. (p), p ∈ C' related to the function to be transformed f(t), t ∈ R. Then f, (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