A high-order perturbation approach to profile reconstruction: I. Perfectly conducting gratings

Inverse Problems

Volumn 15, Issue 4, 1999, Pages 1067-1085

  Ito, Kazufumi ^a   Reitich, Fernando ^a  

^a NONE

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0000128521     PISSN: 02665611     EISSN: None     Source Type: Journal    
DOI: 10.1088/0266-5611/15/4/315     Document Type: Article

References (47)

1. Achdou Y and Pironneau O 1991 Optimization of a photocell Opt. Control Applic. Meth. 12 221-46
2. Anand G V and George M K 1986 Normal mode sound propagation in an ocean with sinusoidal surface waves J. Acoust. Soc. Am. 80 238-43
3. Anand G V and George M K 1993 Normal mode sound propagation in an ocean with random narrow-band surface waves J. Acoust. Soc. Am. 94 279-92
4. Baker G A and Graves-Morris P 1996 Padé approximants Encyclopedia of Mathematics and its Applications 2nd edn, vol 59 (Cambridge: Cambridge University Press)
5. Bertsekas D P 1982 Constrained Optimization and Lagrange Multiplier Methods (Paris: Academic)
6. Bliek P, Deleuil R, Breidne M and Maystre D 1981 Microwave verification of a numerical optimization of Fourier gratings Appl. Phys. 24 147-50
7. Bruno O P and Reitich F 1992 Solution of a boundary value problem for Helmholtz equation via variation of the boundary into the complex domain Proc. R. Soc. Edin. A 122 317-40
8. Bruno O P and Reitich F 1993 Numerical solution of diffraction problems: a method of variation of boundaries I J. Opt. Soc. Am. A 10 1168-75
9. Bruno O P and Reitich F 1993 Numerical solution of diffraction problems: a method of variation of boundaries II J. Opt. Soc. Am. A 10 2307-12
10. Bruno O P and Reitich F 1993 Numerical solution of diffraction problems: a method of variation of boundaries III J. Opt. Soc. Am. A 10 2551-62
11. Bruno O P and Reitich F 1994 Approximation of analytic functions: a method of enhanced convergence Math. Comput. 63 195-213
12. Bruno O P and Reitich F 1996 Calculation of electromagnetic scattering via boundary variations and analytic continuation ACES J. 11 17-31
13. Bruno O P and Reitich F 1998 Boundary-variation solutions for bounded-obstacle scattering in three dimensions J. Acoust. Soc. Am. 104 2579-83
14. Colton D and Kress R 1992 Inverse Acoustic and Electromagnetic Scattering Theory (Heidelberg: Springer)
15. Dobson D C 1992 Designing periodic structures with specified low-frequency scattered far-field data Advances in Computer Methods for Partial Differential Equations VII eds R Vichnevetsky, D Knight and G Richter (IMACS) pp 224-30
16. Dobson D C 1993 Exploiting ill-posedness in the design of diffractive optical structures Mathematics in Smart Structures (Proc. Int. Society for Optical Engineering (SPIE)) vol 1919, ed H T Banks (Bellingham, WA: SPIE) pp 248-57
17. Greffet J J 1988 Scattering of electromagnetic waves by rough dielectric surfaces Phys. Rev. B 37 6436-41
18. Greffet J J, Baylard C and Versaevel P 1992 Diffraction of electromagnetic waves by crossed gratings: a series solution Opt. Lett. 17 1740-2
19. Greffet J J and Maassarani Z 1990 Scattering of electromagnetic waves by a grating: a numerical evaluation of the iterative series solution J. Opt. Soc. Am. A 7 1483-93
20. Harper E Y and Labianca F M 1975 Perturbation theory for scattering of sound from a point source by a moving rough surface in the presence of refraction J. Acoust. Soc. Am. 57 1044-51
21. Harper E Y and Labianca F M 1975 Scattering of sound from a point source by a rough surface progressing over an isovelocity ocean J. Acoust. Soc. Am. 58 349-64
22. Hettlich F and Kirsch A 1997 Schiffer's theorem in inverse scattering theory for periodic structures Inverse Problems 13 351-61
23. Husier A M, Quattropani A and Baltes H D 1982 Construction of grating profiles yielding prescribed diffraction efficiencies Opt. Commun. 41 149-53
24. Ito K and Kunisch K 1990 The augmented Lagrangian method for parameter estimation in elliptic systems SIAM J. Control Optim. 28 113-36
25. Jackson D R, Winebrenner D P and Ishimaru A 1988 Comparison of perturbation theories for rough-surface scattering J. Acoust. Soc. Am. 83 961-9
26. Kuperman W A and Ingenito F 1977 Attenuation of the coherent component of sound propagating in shallow water with rough boundaries J. Acoust. Soc. Am. 61 1178-87
27. Loewen E G, Neviere M and Maystre D 1976 Optimal design for beam sampling mirror gratings Appl. Opt. 15 2937-9
28. Lopez C, Yndurain F J and García N 1978 Iterative series for calculating the scattering of waves from a hard corrugated series Phys. Rev. B 18 970-2
29. Maradudin A A 1983 Iterative solutions for electromagnetic scattering by gratings J. Opt. Soc. Am. 73 759-64
30. Maystre D 1984 Rigorous vector theories of diffraction gratings Progress in Optics ed E Wolf (Amsterdam: North-Holland) pp 3-67
31. Maystre D (ed) 1994 Selected Papers on Diffraction Gratings (SPIE Milestones Series) vol MS 83 (Bellingham, WA: SPIE Optical Engineering Press)
32. Meecham W C 1956 On the use of the Kirchoff approximation for the solution of reflection problems J. Rat. Mech. Anal. 5 323-34
33. Millar R F 1971 On the Rayleigh assumption in scattering by a periodic surface II Proc. Camb. Phil. Soc. 69 217-25
34. Nayfeh A H and Asfar O R 1974 Parallel-plate waveguide with sinusoidally perturbed boundaries J. Appl. Phys. 45 4797-800
35. Petit R (ed) 1980 Electromagnetic Theory of Gratings (Berlin: Springer)
36. Lord Rayleigh 1945 The Theory of Sound vol 2 (New York: Dover)
37. Roger A 1980 Grating profile reconstruction Proc. Int. Society for Optical Engineering (SPIE) 240, Periodic Structures, Gratings, Moiré Patterns and Diffraction Phenomena ed C H Chi, E G Loewen and C L O'Bryan III (Bellingham, WA: SPIE) pp 97-101
38. Roger A 1981 Newton-Kantorovitch algorithm applied to an electromagnetic inverse problem IEEE Trans. Antennas Propagat. 29 232-8
39. Roger A and Breidne M 1980 Grating profile reconstruction by an inverse scattering method Opt. Commun. 35 299-302
40. Roger A and Maystre D 1980 Inverse scattering method in electromagnetic optics: Application to diffraction gratings J. Opt. Soc. Am. 70 1483-95
41. Roginsky J 1991 Derivation of closed-form expressions for the T matrices of Rayleigh-Rice and extinction-theorem perturbation theories J. Acoust. Soc. Am. 90 1130-7
42. Schatzberg A and Devaney A J 1993 Rough surface inverse scattering within the Rytov approximation J. Opt. Soc. Am. A 10 942-50
43. Uretsky J L 1965 The scattering of plane waves from periodic surfaces Ann. Phys. 33 400-27
44. Wait J R 1971 Perturbation analysis for reflection from two-dimensional periodic sea waves Radio Sci. 6 387-91
45. Wirgin A 1989 Scattering from hard and soft corrugated surfaces: Iterative corrections to the Kirchhoff approximation through the extinction theorem J. Acoust. Soc. Am. 85 670-9
46. Wirgin A 1994 Determination of the profile of a hard or soft grating from the scattered field Proc. 1994 IEEE Ultrasonics Symposium (Cannes, 1994) pp 1189-92
47. Wombell R J and DeSanto J A 1991 Reconstruction of rough-surface profiles with the Kirchoff approximation J. Opt. Soc. Am. A 8 1892-7