Kirchhoff Yaklaşımı İntegralinin Radon Dönüşümü Yorumu ile Zaman Uzayında Belirlenmesi Üzerine
Bu çalışmada, düzlemsel dalga ile aydınlatılmış, yumuşak ve sert saçıcılardan oluşan uzak alandaki akustik saçılmanın, Kirchhoff yaklaşımı (KY) ile zaman uzayında analizinde ortaya çıkan ışıma integralinin kapalı-formda belirlenmesi gösterilmiştir. Özel olarak KY ile ortaya çıkan ışıma integralinin, elektromanyetikteki eşdeğeri olan fiziksel optik (FO) yaklaşımı kullanıldığında oluşan ışıma integrali aynı olduğu gösterilmiştir. Sonuç olarak FO yaklaşımı için Radon dönüşümü yorumu ile geliştirilen kapalı-form ifade doğrudan KY için kullanılabilir. Kapalı-form ifadelerinin doğruluğu bir nümerik örnekle gösterilmiştir.
On the Evaluation of the Kirchhoff Approximation Integral using Radon Transform Interpretation in Time Domain
In this work, closed-form evaluation of the radiation integral to determine the time domain acoustic scattered fields at the far zone for soft and hard scatterers using Kirchhoff approximation (KA) under plane-wave illumination is presented. Specifically, it is shown that the radiation integral for KA is the same as the physical optics (PO) integral, which is the equivalent of KA in electromagnetics, for perfect electrically conducting scatterers. Consequently, the closed-form expression of the PO integral developed using Radon transform interpretation can be used in KA directly. The validity of the closed-form expression is demonstrated via a numerical example.
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- [1] J. J. Bowman, T. B. A. Senior, and P. L. E.
Uslenghi, Electromagnetic and Acoustic
Scattering by Simple Shapes, John Wiley and
Sons, 1969.
- [2] T. B. Hansen and A. D. Yaghjian, Plane-Wave
Theory of Time-Domain Fields: Near-Field
Scanning Applications, Wiley-IEEE Press, 1999.
- [3] D. S. Jones, Acoustic and Electromagnetic
Waves, Oxford: Clarendon Press, 1986.
- [4] W. B. Gordon, “Far-field approximations to the
Kirchoff-Helmholtz representations of
scattered fields,” IEEE T Antenn Propag, vol.
23, no. 4, pp. 590-592, July 1975.
- [5] W. B. Gordon, “High frequency
approximations to the physical optics scattering
integral,” IEEE T Antenn Propag, vol. 42, no. 3,
pp. 427-432, Mar. 1994.
- [6] D. Bölükbaş and A. A. Ergin, “A Radon
transform interpretation of the physical optics
integral,” Microw Opt Technol Lett, vol. 44, no.
3, pp. 284–288, 2005.
- [7] H. A. Serim and A. A. Ergin, “Computation of
the physical optics integral on NURBS surfaces
using a Radon transform interpretation,” IEEE
Antenn Wirel Propag Lett, vol. 7, pp. 70-73,
2008.
- [8] S. Karaca and A. A. Ergin, “Closed-form time
domain PO expressions of the electric field
scattered from PEC objects illuminated by an
electric dipole,” IEEE T Antenn Propag, vol. 63,
no. 10, pp. 4477-4485, Oct. 2015.
- [9] A. Aktepe and H. A. Ülkü, “On the closed-form
evaluation of the PO integral using the Radon
transform interpretation for linear triangles,”
Turk J Electr Eng Comput Sci, vol. 29, no. 5,
Article 17, 2021.
- [10]A. Aktepe and H. A. Ülkü, “Exact evaluation of
time-domain physical optics integral on
quadratic triangular surfaces,” IEEE T Antenn
Propag, vol. 68, no. 11, pp. 7447-7456, Nov.
2020.
- [11]A. Aktepe and H. A. Ülkü, “Exact evaluation of
time domain physical optics integral for high
order triangles,” IEEE T Antenn Propag, vol. 71
(Early Access).
- [12]F. Vico-Bondia, M. Ferrando-Bataller, and A.
Valero-Nogueira, “A new fast physical optics
for smooth surfaces by means of a numerical
theory of diffraction,” IEEE T Antenn Propag,
58 (3), 773–789, 2010.
- [13]Y. M. Wu, L. J. Jiang, W. E. I. Sha, and W. C.
Chew, “The numerical steepest descent path
method for calculating physical optics integrals
on smooth conducting quadratic surfaces,”
IEEE T Antenn Propag, vol. 61, no. 8, pp. 4183-
4193, Aug. 2013.
- [14]H. Kobayashi, K. Hongo, and I. Tanaka,
“Expressions of physical optics integral for
smooth conducting scatterers approximated by
quadratic surfaces,” Electron and Commun in
Japan (Part I: Commun), vol. 83, no. 7, pp. 61–
70, 2000.
- [15]M. Domingo, F. Rivas, J. Perez, R. P. Torres, and
M. F. Catedra, “Computation of the RCS of
complex bodies modeled using NURBS
surfaces,” IEEE Antenn Propag M, vol. 37, no.
6, pp. 36-47, Dec. 1995.
- [16]A. C. Yucel and A. A. Ergin, “Exact evaluation
of retarded-time potential integrals for the
RWG bases,” in IEEE T Antenn Propag, vol. 54,
no. 5, pp. 1496-1502, May 2006.
- [17]H. A. Ülkü and A. A. Ergin, “Analytical
evaluation of transient magnetic fields due to
RWG current bases,” IEEE T Antenn Propag,
vol. 55, no. 12, pp. 3565-3575, Dec. 2007.
- [18]H. A. Ülkü and A. A. Ergin, “Application of
analytical retarded-time potential expressions
to the solution of time domain integral
equations,” IEEE T Antenn Propag, vol. 59, no.
11, pp. 4123-4131, Nov. 2011.
- [19]H. A. Ülkü, A. A. Ergin, and F. Dikmen, “On the
evaluation of retarded-time potentials for SWG
bases,” IEEE Antenn Wirel Propag Lett, vol. 10,
pp. 187-190, 2011.
- [20]F. Dikmen, “On analytical evaluation of
retarded-time potentials for SWG bases,” IEEE
T Antenn Propag, vol. 62, no. 9, pp. 4860-4863,
Sept. 2014.