Browsing by Keywords "Fourier optics"
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Accumulated Gouy phase shift in Gaussian beam propagation through firstorder optical systems
(Optical Society of America, 199709)We define the accumulated Gouy phase shift as the onaxis 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 ... 
Chirp filtering in the fractional Fourier domain
(Optical Society of America, 19941110)In the Wigner domain of a onedimensional 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 ... 
Convolution and filtering in fractional fourier domains
(SpringerVerlag, 1994)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 ... 
Design of dynamically adjustable anamorphic fractional Fourier transformer
(Elsevier BV * NorthHolland, 19970301)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 ... 
Evaluation of the validity of the scalar approximation in optical wave propagation using a systems approach and an accurate digital electromagnetic model
(Taylor and Francis Ltd., 2016)The cause and amount of error arising from the use of the scalar approximation in monochromatic optical wave propagation are discussed using a signals and systems formulation. Based on Gauss’s Law, the longitudinal component ... 
Every Fourier optical system is equivalent to consecutive fractionalFourierdomain filtering
(Optical Society of America, 19960610)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) ... 
Fast and accurate linear canonical transform algorithms
(IEEE, 2015)Linear canonical transforms are encountered in many areas of science and engineering. Important transformations such as the fractional Fourier transform and the ordinary Fourier transform are special cases of this transform ... 
Fourier transforms of fractional order and their optical interpretation
(Elsevier, 1993)Fourier transforms of fractional order a are defined in a manner such that the common Fourier transform is a special case with order a=1. An optical interpretation is provided in terms of quadratic graded index media and ... 
Fractional correlation
(Optical Society of America, 1995)Recently, optical interpretations of the fractionalFouriertransform operator have been introduced. On the basis of this operator the fractional correlation operator is defined in two different ways that are both consistent ... 
The fractional fourier transform
(IEEE, 2001)A brief introduction to the fractional Fourier transform and its properties is given. Its relation to phasespace representations (time or spacefrequency representations) and the concept of fractional Fourier domains are ... 
Fractional Fourier transform: simulations and experimental results
(Optical Society of America, 1995)Recently two optical interpretations of the fractional Fourier transform operator were introduced. We address implementation issues of the fractionalFouriertransform operation. We show that the original bulkoptics ... 
Generalization of timefrequency signal representations to joint fractional Fourier domains
(IEEE, 200509)The 2D signal representations of variables rather than time and frequency have been proposed based on either Hermitian or unitary operators. As an alternative to the theoretical derivations based on operators, we propose ... 
Gradedindex fibers, Wignerdistribution functions, and the fractional Fourier transform
(Optical Society of America, 1994)Two definitions of a fractional Fourier transform have been proposed previously. One is based on the propagation of a wave field through a gradedindex medium, and the other is based on rotating a function's Wigner ... 
Introduction to the fractional Fourier transform and its applications
(Academic Press, 1999)The concept of fractional Fourier transform and its applications is discussed. The fractional Fourier transforms has several applications in the area, analog optical information processing, or Fourier optics. Fourier optical ... 
Optical implementation of the twodimensional fractional Fourier transform with different orders in the two dimensions
(Elsevier BV * NorthHolland, 19951015)Previous optical implementations of the twodimensional fractional Fourier transform have assumed identical transform orders in both dimensions. We let the orders in the two orthogonal dimensions to be different and present ... 
Optimal image restoration with the fractional Fourier transform
(OSA  The Optical Society, 199804)The classical Wiener filter, which can be implemented in O(N log N) time, is suited best for spaceinvariant degradation models and spaceinvariant signal and noise characteristics. For spacevarying degradations and ... 
Optimal representation and processing of optical signals in quadraticphase systems
(Elsevier, 2016)Optical fields propagating through quadraticphase systems (QPSs) can be modeled as magnified fractional Fourier transforms (FRTs) of the input field, provided we observe them on suitably defined spherical reference surfaces. ... 
Optimization of orders in multichannel fractional Fourierdomain filtering circuits and its application to the synthesis of mutualintensity distributions
(Optical Society of America, 2002)Owing to the nonlinear nature of the problem, the transform orders in fractional Fourierdomain filtering configurations have usually not been optimized but chosen uniformly. We discuss the optimization of these orders for ... 
Preface
(Springer, New York, 2016) 
Relationships among ray optical, Gaussian beam, and fractional Fourier transform descriptions of firstorder optical systems
(Elsevier BV * NorthHolland, 19971101)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 ...