Equivalent functions for the Fresnel integral

Umul, Yusuf Ziya

doi:10.1364/opex.13.008469

Cited by 67 publications

(27 citation statements)

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“…where the first term is the exact GO and the second one is the exact diffracted waves [3]. I hope this example will be enough to enlighten Hacivelioglu and co-authors on the terminology that I used in [2].…”

Section: Our Rebuttals On Wave Terminologymentioning

confidence: 94%

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Reply to the ``Comment on `Fringe Waves in an Impedance Half-Plane'"

Basdemir¹

2014

PIER Letters

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In [1], Hacivelioglu and co-authors criticize my paper, named "Fringe waves in an impedance halfplane" [2]. Unfortunately, the general scenario of the criticisms is based on misconceptions and lack of basic knowledge in the diffraction theory. Below we give our detailed rebuttals on their comments. Our Rebuttals on Wave TerminologyIn general, the objections of Hacivelioglu and co-authors are related with their misinterpretations on the basic concepts of the diffraction theory and bedevil the redear. For example 1) The term "asymptotic exact" is used in the beginning of p. 572 of [2]. It is clear from the whole sentence that the statement means the asymptotic form of the exact solution, which is the Maliuzhinetz's in this case if one does not scissor the phrase from the whole sentence as the authors do.2) The objection of Hacivelioglu and co-authors to the phrase "exact geometrical optics (GO)" proves their real level of knowledge on the diffraction theory. The GO waves are exact, because they are directly obtained from the exact solution without any approximation. We can give the example of the exact reflected scattered waves from a half-plane with the Neumann boundary condition as(1) for k is the wavenumber, φ 0 angle of incidence. F is the Fresnel integral,and(1) can be decomposed exactly aswhere the first term is the exact GO and the second one is the exact diffracted waves [3]. I hope this example will be enough to enlighten Hacivelioglu and co-authors on the terminology that I used in [2]. Hacivelioglu and co-workers mention the GO wave as an asymptotic field in their comments. This shows that their interpretation of the diffraction theory is incorrect.3) The uniform or nonuniform fringe currents mean that the fields that approach to infinity or have finite value at the transition regions respectively. The authors should have read the explanation, after Eq. (25) in p. 576 of [2] in order to understand the meaning of our terminology on uniform and nonuniform diffracted fields. I also advice them to read fundamental text books on the uniform theory of diffraction (UTD) in order to learn the basic terminology, used in the diffraction theory. As a result, I stress the authors' lack of basic knowledge in the criticisms on my terminology.

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Section: Our Rebuttals On Wave Terminologymentioning

confidence: 94%

“…b) Hacivelioglu and co-workers try to support their claims with false references. For example References [3] and [6] of [1]. In those references, Umul does not deal with PTD or fringe fields, but authors cite these papers in order to support their wrong claims about Eq.…”

Section: Rebuttal Of Examplesmentioning

confidence: 99%

Reply to the ``Comment on `Fringe Waves in an Impedance Half-Plane'"

Basdemir¹

2014

PIER Letters

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“…On the other hand, to evaluate Fresnel integrals for high values of | |, the solution is resort to the expansion in terms of Bessel functions [14,15]. Besides, in [16], one of the performed approximations was made by the sum of the first term of the Fresnel integrals asymptotic expansion and an exponential function which approaches infinity at the zero of Fresnel function argument.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Approximation of Fresnel Integrals with Applications to Diffraction Problems

Sandoval-Hernandez

Vázquez-Leal

Hernandez-Martinez

et al. 2018

Mathematical Problems in Engineering

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This article introduces two approximations that allow the evaluation of Fresnel integrals without the need for using numerical algorithms. These equations accomplish the characteristic of being continuous in the same interval as Fresnel. Both expressions have been determined applying the least squares method to suitable expressions. Accuracy of equations improves as increases; as for small values of , it is possible to achieve an absolute error less than 8 × 10 −5 . To probe the efficiency of the equations, two case studies are presented, both applied in the optics field. The first case is related to the semi-infinite opaque screen for Fresnel diffraction. In this case study Fresnel integrals are evaluated with the proposed equations to calculate the irradiance distribution and the Cornu spiral for diffraction computations of the Fresnel diffraction; obtained results show a good accuracy. The second case is related to the double aperture problem for Fresnel diffraction.

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“…The incident field will become in the positive x 1 and negative y 1 directions. It has the expression of u i (P) = e −jk cos( 1 +˛0) (19) in terms of the second face's coordinate system. Note that a minus sign does not added in the amplitude of the incident wave, because it is not image.…”

Section: Wedge With Double Faces Illuminatedmentioning

confidence: 99%

“…with this aim for x 1 [18,19]. sign(x) is the signum function, which is equal to 1 for x > 0 and −1 otherwise.…”

Section: Asymptotic Evaluation Of the Scattering Integralsmentioning

confidence: 99%