OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 40, Iss. 16 — Jun. 1, 2001
  • pp: 2618–2625

Noninvasive Characterization of Continuous-Profile Blazed Diffraction Gratings

Anu Huttunen, Ilkka Kallioniemi, and Jyrki Saarinen  »View Author Affiliations

Applied Optics, Vol. 40, Issue 16, pp. 2618-2625 (2001)

View Full Text Article

Acrobat PDF (1373 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



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

OCIS Codes
(000.4430) General : Numerical approximation and analysis
(050.1970) Diffraction and gratings : Diffractive optics
(120.4290) Instrumentation, measurement, and metrology : Nondestructive testing
(120.5820) Instrumentation, measurement, and metrology : Scattering measurements
(290.3200) Scattering : Inverse scattering

Anu Huttunen, Ilkka Kallioniemi, and Jyrki Saarinen, "Noninvasive Characterization of Continuous-Profile Blazed Diffraction Gratings," Appl. Opt. 40, 2618-2625 (2001)

Sort:  Author  |  Year  |  Journal  |  Reset


  1. H. P. Herzig, ed., Micro-Optics: Elements, Systems, and Applications (Taylor & Francis, Bristol, UK, 1997).
  2. J. Turunen and F. Wyrowski, eds., Diffractive Optics for Industrial and Commercial Applications (Akademie Verlag, Berlin, 1997).
  3. M. T. Gale, M. Rossi, J. Pedersen, and H. Schutz, “Fabrication of continuous-relief micro-optical elements by direct laser writing in photoresist,” Opt. Eng. 33, 3556–3566 (1994).
  4. K. S. Urquhart, R. Stein, and S. H. Lee, “Computer-generated holograms fabricated by direct write of positive electron-beam resist,” Opt. Lett. 18, 308–310 (1993).
  5. W. Däschner, P. Long, R. Stein, C. Wu, and S. H. Lee, “Cost-effective mass fabrication of multilevel diffractive optical elements by use of a single exposure with a gray-scale mask on high-energy beam-sensitive glass,” Appl. Opt. 36, 4675–4680 (1997).
  6. R. Petit, ed., Topics in Current Physics: Electromagnetic Theory of Gratings (Springer-Verlag, Berlin, 1980).
  7. J. W. Goodmann, Introduction to Fourier Optics, 2nd ed. (McGraw-Hill, San Francisco, Calif., 1996).
  8. B. W. Smith, “Strategies toward sub-0.25 μm lithography,” Opt. Photon. News 8, (March 1997), pp. 23–27.
  9. P. Rai-Choudhury, ed., Handbook of Microlithography, Micromachining, and Microfabrication: Volume 1: Microlithography (SPIE Optical Engineering Press, Bellingham, Wash., 1997).
  10. H. Giovannini, C. Deumie, H. Akhouayri, and C. Amra, “Angle-resolved polarimetric phase measurement for the characterization of gratings,” Opt. Lett. 21, 1619–1621 (1996).
  11. N. Garcia and 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).
  12. J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, and G. A. Petersen, “Scatterometry applied to microelectronics processing—part 1,” Solid State Technol. 36, 29–32 (1993).
  13. J. R. McNeil, S. S. H. Naqvi, S. M. Gaspar, K. C. Hickman, K. P. Bishop, L. M. Milner, R. H. Krukar, and G. A. Petersen, “Scatterometry applied to microelectronics processing—part 2,” Solid State Technol. 36, 53–56 (1993).
  14. D. J. Search, C. A. Hobson, J. T. Atkinson, and 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, and F. Y. Wu, eds., Proc. SPIE 2183, 170–179 (1994).
  15. R. Krukar, A. Kornblit, L. A. Clark, J. Kruskal, D. Lambert, E. A. Reitman, and 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).
  16. Z. R. Hatab, S. L. Prins, S. S. H. Naqvi, and J. R. McNeil, “16 MB DRAM trench depth characterization using dome scatterometry,” Appl. Surf. Sci. 86, 597–599 (1995).
  17. S. S. H. Naqvi, S. Gaspar, K. Hickman, K. Bishop, and J. R. McNeil, “Linewidth measurement of gratings on photomasks: a simple technique,” Appl. Opt. 31, 1377–1384 (1992).
  18. S. S. H. Naqvi, R. H. Krukar, J. R. McNeil, J. E. Franke, T. M. Niemczyk, D. M. Haaland, R. A. Gottscho, and A. Kornblit, “Etch depth estimation of large-period silicon gratings with multivariate calibration of rigorously simulated diffraction profiles,” Appl. Opt. 11, 2485–2493 (1994).
  19. C. M. Bishop, Neural Networks for Pattern Recognition (Clarendon, Oxford, 1996).
  20. I. Kallioniemi, J. Saarinen, and E. Oja, “Optical scatterometry of subwavelength diffraction gratings: neural-network approach,” Appl. Opt. 37, 5830–5835 (1998).
  21. I. Kallioniemi, J. Saarinen, and E. Oja, “Characterization of diffraction gratings in a rigorous domain with optical scatterometry: hierarchical neural-network model,” Appl. Opt. 38, 5920–5930 (1999).
  22. Th. Hessler, M. Rossi, R. E. Kunz, and M. T. Gale, “Analysis and optimization of fabrication of continuous-relief diffractive optical elements,” Appl. Opt. 37, 4069–4079 (1998).
  23. I. Kallioniemi, Th. Ammer, and M. Rossi, “Optimization of continuous-profile blazed gratings using rigorous diffraction theory,” Opt. Commun. 177, 15–24 (2000).
  24. M. G. Moharam and T. K. Gaylord, “Rigorous coupled-wave analysis of planar-grating diffraction,” J. Opt. Soc. Am. 71, 811–818 (1981).

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.

CrossCheck Deposited