## Profile reconstruction of periodic interface |

JOSA A, Vol. 31, Issue 5, pp. 1083-1089 (2014)

http://dx.doi.org/10.1364/JOSAA.31.001083

Enhanced HTML Acrobat PDF (428 KB)

### Abstract

The reconstruction problem for periodic (arbitrary profiled within a period) boundary between two homogeneous media is considered. Our approach to the solution of the inverse problem is based on the Tikhonov regularization technique, which requires successive selection of the boundaries on the basis of multiple solutions of the direct problem of wave diffraction by the candidate boundaries. The analytical numerical C method has been chosen as a simple but rather efficient tool for the direct problem solving. The scheme for numerical tests of algorithms and criteria for reconstruction accuracy have been suggested and verified. Results of numerical experiments that prove the validity of the approach are presented.

© 2014 Optical Society of America

**OCIS Codes**

(000.3860) General : Mathematical methods in physics

(050.1950) Diffraction and gratings : Diffraction gratings

(050.2770) Diffraction and gratings : Gratings

(100.3190) Image processing : Inverse problems

(050.1755) Diffraction and gratings : Computational electromagnetic methods

**ToC Category:**

Diffraction and Gratings

**History**

Original Manuscript: December 27, 2013

Revised Manuscript: March 19, 2014

Manuscript Accepted: March 20, 2014

Published: April 21, 2014

**Citation**

Petr Melezhik, Anatoliy Poyedinchuk, Nataliya Yashina, and Gérard Granet, "Profile reconstruction of periodic interface," J. Opt. Soc. Am. A **31**, 1083-1089 (2014)

http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-31-5-1083

Sort: Year | Journal | Reset

### References

- L. Rayleigh, “On the dynamical theory of gratings,” Proc. R. Soc. Lond. A 79, 399–416 (1907). [CrossRef]
- R. Petit, ed., Electromagnetic Theory of Gratings (Springer, 1980).
- G. Bao, L. Cowsar, and W. Masters, Mathematical Modeling in Optical Science, SIAM Frontiers in Applied Math Series(SIAM: Society for Industrial and Applied Mathematics, 2001).
- Y. K. Sirenko and S. Strom, eds., Modern Theory of Gratings. Resonant Scattering: Analysis Techniques and Phenomena (Springer, 2010).
- V. Lakshmi, “Remote sensing of soil moisture. Review article,” ISRN Soil Sci. 2013, 424178 (2013). [CrossRef]
- Y. Sirenko, S. Strom, and N. Yashina, Modeling and Analysis of Transient Processes in Open Resonant Structures (Springer, 2007).
- A. Malcolm and D. P. Nicholls, “A boundary perturbation method for recovering interface shapes in layered media,” Inverse Probl. 27, 095009 (2011). [CrossRef]
- J. Elschner and G. Hu, “An optimization method in inverse elastic scattering for one-dimensional grating profiles,” Commun. Comput. Phys. 12, 1434–1460 (2012).
- H. Gross, J. Richter, A. Rathsfeld, and M. Bär, “Investigations on a robust profile model for the reconstruction of 2D periodic absorber lines in scatterometry,” J. Eur. Opt. Soc. Rapid Publ. 5, 10053 (2010).
- Y. Altuncu, A. Yapar, and I. Akduman, “Numerical computation of the Green’s function of a layered media with rough interface,” Microw. Opt. Technol. Lett. 49, 1204–1209 (2007).
- G. Bruckner and J. Elschner, “The numerical solution of an inverse periodic transmission problem,” Math. Methods Appl. Sci. 28, 757–778 (2005).
- J. Elschner and M. Yamamoto, “Uniqueness results for an inverse periodic transmission problem,” Inverse Probl. 20, 1841–1852 (2004). [CrossRef]
- G. Bao, K. Huang, and G. Schmidt, “Optimal design of nonlinear diffraction gratings,” J. Comput. Phys. 184, 106–121 (2003). [CrossRef]
- T. Arens and A. Kirsch, “The factorization method in inverse scattering from periodic structures,” Inverse Probl. 19, 1195–1211 (2003). [CrossRef]
- J. Chandezon, A. Poyedinchuk, Y. Tuchkin, and N. Yashina, “Mathematical modeling of electromagnetic wave scattering by wavy periodic boundary between two media,” Prog. Electromagnet. Res. 38, 130–143 (2002).
- A. Tikhonov and Y. Arsenin, Methods for the Solution of Ill-Posed Problems (Wiley, 1977).
- P. Melezhik, A. Poyedinchuk, N. Yashina, and G. Granet, “Periodic boundary of metamaterial: eigen regimes and resonant radiation,” J. Opt. A 9, S403–S409 (2007). [CrossRef]
- A. Sveshnikov, “Radiation principal,” Doklady SSSR 73, 917–920 (1950).
- A. Sveshnikov, “Principal of limiting absorption,” Doklady SSSR 80, 345–347 (1951).
- A. A. Kirilenko, A. Y. Poyedinchuk, and N. P. Yashina, “Non-destructive control of dielectrics: mathematical models based on analytical regularization,” in Progress in Analysis. Proceeding of the Third International ISSAC Congress (World Scientific, 2001), Vol. II, pp. 1359–1367.
- V. Ivanov, V. Vasin, and V. Talanov, Theory of Linear Ill-Posed Problems and Its Applications (Nauka, 1978) (in Russian).
- A. Tikhonov, A. Goncharsky, V. Stepanov, and A. Yagola, Numerical Methods for the Solution of Ill-Posed Problems (Kluwer Academic, 1995).
- V. Hadson and J. Pim, Application of Functional Analyses for the Operator Theory (Mir, 1987) (in Russian).

## 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.

« Previous Article | Next Article »

OSA is a member of CrossRef.