Abstract

Smooth, continuous-profile diffractive optical elements and other regular microstructures demand advanced characterization methods. Here the problem of reconstructing the profiles with optical scatterometry is addressed for the first time to our knowledge. We represent the profile of a blazed grating with an analytic Chebyshev series. The coefficients of the series are inferred from the far-field diffraction pattern, when the grating profile is illuminated with coherent light. An advanced neural-network model is used as a nonlinear statistical estimator. The reconstruction error is found to be less than 4% as normalized to the depth of the profile, even with realistic measurement errors included in the simulations.

© 2001 Optical Society of America

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    [Crossref]
  16. Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
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    [Crossref] [PubMed]
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    [Crossref]
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2000 (1)

I. Kallioniemi, Th. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[Crossref]

1999 (1)

1998 (2)

1997 (2)

1996 (1)

1995 (2)

N. Garcia, M. Nieto-Vesperinas, “Direct solution to the inverse scattering problem for surfaces from near-field intensities without phase retrieval,” Opt. Lett. 20, 949–951 (1995).
[Crossref] [PubMed]

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[Crossref]

1994 (2)

M. T. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

1993 (4)

K. S. Urquhart, R. Stein, S. H. Lee, “Computer-generated holograms fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
[Crossref] [PubMed]

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

1992 (1)

1981 (1)

Akhouayri, H.

Ammer, Th.

I. Kallioniemi, Th. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[Crossref]

Amra, C.

Atkinson, J. T.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[Crossref]

Bishop, C. M.

C. M. Bishop, Neural Networks for Pattern Recognition (Clarendon, Oxford, 1996).

Bishop, K.

Bishop, K. P.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

Clark, L. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Däschner, W.

Deumie, C.

Franke, J. E.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

Gale, M. T.

Th. Hessler, M. Rossi, R. E. Kunz, M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069–4079 (1998).
[Crossref]

M. T. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

Garcia, N.

Gaspar, S.

Gaspar, S. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

Gaylord, T. K.

Giovannini, H.

Goodmann, J. W.

J. W. Goodmann, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996).

Gottscho, R. A.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Haaland, D. M.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

Hatab, Z. R.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[Crossref]

Hessler, Th.

Hickman, K.

Hickman, K. C.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

Hobson, C. A.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[Crossref]

Kallioniemi, I.

Kornblit, A.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Krukar, R.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Krukar, R. H.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

Kruskal, J.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Kunz, R. E.

Lambert, D.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Lee, S. H.

Long, P.

McNeil, J. R.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[Crossref]

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

S. S. H. Naqvi, S. Gaspar, K. Hickman, K. Bishop, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[Crossref] [PubMed]

Milner, L. M.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

Moharam, M. G.

Naqvi, S. S. H.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[Crossref]

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

S. S. H. Naqvi, S. Gaspar, K. Hickman, K. Bishop, J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
[Crossref] [PubMed]

Niemczyk, T. M.

S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).

Nieto-Vesperinas, M.

Oja, E.

Pearson, J. D.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[Crossref]

Pedersen, J.

M. T. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

Petersen, G. A.

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

Prins, S. L.

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[Crossref]

Reitman, E. A.

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

Rossi, M.

I. Kallioniemi, Th. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[Crossref]

Th. Hessler, M. Rossi, R. E. Kunz, M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069–4079 (1998).
[Crossref]

M. T. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

Saarinen, J.

Schutz, H.

M. T. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

Search, D. J.

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[Crossref]

Smith, B. W.

B. W. Smith, “Strategies toward sub-0.25 µm lithography,” Opt. Photon. News 8, (March1997), pp. 23–27.

Stein, R.

Urquhart, K. S.

Wu, C.

Appl. Opt. (6)

Appl. Surf. Sci. (1)

Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
[Crossref]

J. Appl. Phys. (1)

R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, R. A. Gottscho, “Reactive ion etching profile and depth characterization using statistical and neural network analysis of light scattering data,” J. Appl. Phys. 74, 3698–3706 (1993).
[Crossref]

J. Opt. Soc. Am. (1)

Opt. Commun. (1)

I. Kallioniemi, Th. Ammer, M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
[Crossref]

Opt. Eng. (1)

M. T. Gale, M. Rossi, J. Pedersen, H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
[Crossref]

Opt. Lett. (3)

Opt. Photon. News (1)

B. W. Smith, “Strategies toward sub-0.25 µm lithography,” Opt. Photon. News 8, (March1997), pp. 23–27.

Solid State Technol. (2)

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).

J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).

Other (7)

D. J. Search, C. A. Hobson, J. T. Atkinson, J. D. Pearson, “Diffraction pattern analysis for automatic defect classification in manufactured electronic assemblies,” in Machine Vision Applications in Industrial Inspection II, B. M. Dawson, S. S. Wilson, F. Y. Wu, eds., Proc. SPIE2183, 170–179 (1994).
[Crossref]

C. M. Bishop, Neural Networks for Pattern Recognition (Clarendon, Oxford, 1996).

P. Rai-Choudhury, ed., Handbook of Microlithography, Micromachining, and Microfabrication: Volume 1: Microlithography (SPIE Optical Engineering Press, Bellingham, Wash., 1997).

R. Petit, ed., Topics in Current Physics: Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
[Crossref]

J. W. Goodmann, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996).

H. P. Herzig, ed., Micro-Optics: Elements, Systems, and Applications (Taylor & Francis, Bristol, UK, 1997).

J. Turunen, F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, Berlin, 1997).

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Figures (6)

Fig. 1
Fig. 1

Geometry of the ideal blazed grating is characterized by period d and depth h. The grating is illuminated at normal incidence with coherent light (wavelength λ), which is diffracted into transmitted orders m. The refractive index of the grating is n 1 and that of the surrounding medium n 0.

Fig. 2
Fig. 2

Smoothed blazed-grating profile p(x) (solid curve) and its approximation with a finite Chebyshev series (x) (dashed curve), as given in Eq. (2). The number of Chebyshev polynomials used is C = 19.

Fig. 3
Fig. 3

To find the optimal number of Chebyshev polynomials C for the approximation of the blazed-grating profiles, (a) the error E and (b) the maximum deviation E max are determined as functions of C. The definitions of E and E max are given in Eqs. (4) and (5), respectively. The curves are formed by averaging over 100 profiles randomly chosen from the range of interest of grating profiles.

Fig. 4
Fig. 4

Generation of smoothed blazed-grating profiles. (a) First an ideal blazed grating with random values of d and h is defined at S sampling points, with an interval of 33.3 nm. (b) The profile is divided into slots of length s x = 400 nm consisting of 12 sampling points. The depth of each slot is the mean of the depth values at the sampling points in the slot. (c) A random number of maximum ±5% of h is added to the slot depths, producing a randomly shaped profile. (d) The profile is convolved with the Gaussian distribution in Eq. (1) with w = 500 nm.

Fig. 5
Fig. 5

Four target profiles (solid curves) from the test set are shown together with the profiles predicted by the neural networks. The dashed curves show the results for diffraction data with a noise component of ς2 = 0% and the dotted curves with a noise component of ς2 = 3%. The profiles in (a) and (b) represent third-order gratings, whereas those in (c) and (d) represent second-order gratings.

Fig. 6
Fig. 6

Intensities of the diffraction orders of the four grating profiles in the test set depicted in Fig. 5. Black columns, normalized diffraction intensities of the diffraction orders m = -1–5 of the target profiles, when illuminated with coherent light of the wavelength λ = 514.5 nm. Gray and white columns, normalized diffraction patterns of the corresponding predicted profiles characterized from data with a noise component of ς2 = 0% and ς2 = 3%, respectively.

Tables (1)

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Table 1 Errors of Prediction E for Four Grating Profiles from the Test Set Inferred from Scattering Data Without Noise (ς2 = 0%) and with Noise (ς2 = 3%)a

Equations (6)

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Ix=2wln 2w1/2 exp-2 ln 2xw2,
p˜x=i=1C ciTi-1x,
Tnx=cosn arccos x
E=1hi=1S|pxi-p˜xi|S,
Emax=1/h max|pxi-p˜xi|,  i=1,  , S
ho,m=mλ/n1-n0,

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