Scattering from fractally corrugated surfaces
JOSA A, Vol. 7, Issue 6, pp. 1131-1139 (1990)
http://dx.doi.org/10.1364/JOSAA.7.001131
Enhanced HTML Acrobat PDF (909 KB)
Abstract
We consider the problem of scattering of optical or electromagnetic waves from a family of irregular rough surfaces characterized by band-limited fractal functions. This method provides a unified and realistic method for examining rough surfaces without the use of random or periodic functions. We relate the angular distribution and the amount of energy in the specularly scattered field to the fractal characteristics of the surfaces by finding their analytical expressions under the Kirchhoff limit and calculating the scattering patterns.
© 1990 Optical Society of America
Citation
Dwight L. Jaggard and Xiaoguang Sun, "Scattering from fractally corrugated surfaces," J. Opt. Soc. Am. A 7, 1131-1139 (1990)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-7-6-1131
Sort: Year | Journal | Reset
References
- B. B. Mandelbrot, The Fractal Geometry of Nature (Freeman, San Francisco, Calif., 1983), 1–34.
- D. L. Jaggard and X. Sun, "Scattering from bandlimited fractal fibers," IEEE Trans. Antennas Propag. 37,1591–1597 (1989). [CrossRef]
- P. Beckmann and A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces (Pergamon, New York, 1963).
- F. T. Ulaby, R. K. Moore, and A. K. Fung, Microwave Remote Sensing: Active and Passive (Artech, Dedham, Mass., 1982), Vol. 2, Chap. 12.
- D. P. Winebrenner and A. Ishimaru, "Application of the phase-perturbation technique to randomly rough surfaces," J. Opt. Soc. Am. A 2, 2285–2294 (1985). [CrossRef]
- M. F. Chen and A. K. Fung, "A numerical study of the regions of validity of the Kirchhoff and small-perturbation rough surface scattering models," Radio Sci. 23, 163–170 (1988). [CrossRef]
- E. I. Thorsos, "The validity of the Kirchhoff approximation for rough surface scattering using a Gaussian roughness spectrum," J. Acoust. Soc. Am. 83, 78–92 (1988). [CrossRef]
- J. M. Soto-Crespo and M. Nieto-Vesperinas, "Electromagnetic scattering from very rough random surfaces and deep reflection gratings," J. Opt. Soc. Am. A 6,367–384 (1989). [CrossRef]
- D. L. Jordan, R. C. Hollins, and E. Jakeman, "Experimental measurements of non-Gaussian scattering by a fractal diffuser," Appl. Phys. B 31, 179–186 (1983). [CrossRef]
- Note that this roughness fractal function is related to but different from the Weierstrass function that has been used previously by the authors and others (e.g., Refs. 2 and 16). The functionthat is used here becomes a simple smooth sine function in the limit where D → 1.
- The formulations of this section are correct for observation angles in the x-z plane. Equation (6) [and hence Eqs. (12)-(14)] should be multiplied by smc(v_{y}L_{y}) for angles outside the x-z plane, where 2L_{y} is the patch size in the y direction. For this more general case, v_{x} = fe(sin sin θ_{S} cos ø_{S}), v_{y} = -k sin θS, and vz remains the same.
- The validity of the Kirchhoff approximation for the chosen parameters in the numerical calculation has been checked against the Kirchhoff criterion, λ^{2}h/Λ3 « cos θ (Ref. 3, page 48). Since small-rms-height (0.05X) surfaces are considered, the solution is clearly valid except at large scattering angles.
- See, e.g., A. R. Mickelson and D. L. Jaggard, "Electromagnetic wave propagation in almost periodic media," IEEE Trans. Antenna Propag. AP-27, 34-40 (1979); D. L. Jaggard and A. R. Mickelson, "The reflection of electromagnetic waves from almost periodic structures," Appl. Phys. 19,405–418 (1979). [CrossRef]
- J. Teixeira, "Experimental methods for studying fractal aggregates," in On Growth and Form, H. E. Stanley and N. Os-trowsky, eds. (Nijhoff, Boston, Mass., 1986).
- Here, our model is a one-dimensional cut through a surface, while in Ref. 14 the dimension Ds is a surface fractal dimension. The relation is given by Ds = D + 1.
- D. L. Jaggard and Y. Kim, "Diffraction by bandlimited fractal screens," J. Opt. Soc. Am. A 4, 1055–1062 (1987). [CrossRef]
- D. L. Jaggard, "On fractal electrodynamics," in Recent Advances in Electromagnetic Research, H. N. Kritikos and D. L. Jaggard, eds. (Springer-Verlag, New York, 1990). [CrossRef]
- D. H. Berman, "Scintillation behind non-Gaussian fractal phase screens," J. Acoust. Soc. Am. 76, Suppl. 1, S94 (A) (1984). [CrossRef]
Cited By |
Alert me when this paper is cited |
OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.
OSA is a member of CrossRef.