OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A


  • Vol. 16, Iss. 2 — Feb. 1, 1999
  • pp: 364–370

Representation of the transparent layer–arbitrary substrate system parameters through the Fourier coefficients of the ellipsometric function

Stoyan C. Russev  »View Author Affiliations

JOSA A, Vol. 16, Issue 2, pp. 364-370 (1999)

View Full Text Article

Enhanced HTML    Acrobat PDF (303 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A system of transparent layers on top of an arbitrary underlying subsystem is considered. It is shown that the layer refractive index and the subsystem generalized Fresnel coefficients can be expressed in a simple and explicit way by the Fourier coefficients of the ellipsometric function ρ with the layer thickness as an expansion parameter. Thus the inverse ellipsometric problem is reduced to a much simpler and well-defined problem of finding these Fourier coefficients. Analysis shows that the ellipsometric inverse task must be considered separately, depending on whether the modulus of the s-polarization Fresnel coefficient for the ambient–layer interface is smaller than, equal to, or greater than that for the layer–substrate system.

© 1999 Optical Society of America

OCIS Codes
(070.2590) Fourier optics and signal processing : ABCD transforms
(100.3190) Image processing : Inverse problems
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(160.4760) Materials : Optical properties

Original Manuscript: December 24, 1997
Revised Manuscript: August 18, 1998
Manuscript Accepted: October 12, 1998
Published: February 1, 1999

Stoyan C. Russev, "Representation of the transparent layer–arbitrary substrate system parameters through the Fourier coefficients of the ellipsometric function," J. Opt. Soc. Am. A 16, 364-370 (1999)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. R. M. A. Azzam, N. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  2. D. E. Aspnes, “Minimal-data approaches for determining outer-layer dielectric responses of films from kinetic reflectometric and ellipsometric measurements,” J. Opt. Soc. Am. A 10, 974–983 (1993). [CrossRef]
  3. D. E. Aspnes, “New developments in spectroellipsometry: the challenge of surfaces,” in Proceedings of the 1st International Conference on Spectroscopic Ellipsometry (Elsevier, New York, 1993), pp. 1–8.
  4. T. Easwarakhanthan, S. Ravelet, P. Renard, “An ellipsometric procedure for the characterization of very thin surface films on absorbing substrates,” Appl. Surf. Sci. 90, 251–259 (1995). [CrossRef]
  5. A. A. Antippa, R. M. Leblanc, D. Ducharme, “Multiple-wavelength ellipsometry in thin uniaxial nonabsorbing films,” J. Opt. Soc. Am. A 3, 1794–1802 (1986). [CrossRef]
  6. R. M. A. Azzam, A.-R. M. Zaghloul, N. Bashara, “Ellipsometric function of a film–substrate system: applications to the design of reflection-type optical devices and to ellipsometry,” J. Opt. Soc. Am. 65, 252–260 (1975). [CrossRef]
  7. R. M. A. Azzam, A.-R. M. Zaghloul, N. Bashara, “Polarizer-surface-analyzer null ellipsometry for film–substrate systems,” J. Opt. Soc. Am. 65, 1464–1471 (1975). [CrossRef]
  8. F. Scandonne, L. Ballerini, “Théorie de la transmission et de la réflexion dans les systèmes de couches minces multiples,” Nuovo Cimento 5, 81–91 (1946).
  9. Z. Knittl, Optics of Thin Films (Wiley, New York, 1976).
  10. H. Jeffreys, B. Swirles, Methods of Mathematical Physics (Cambridge U. Press, Cambridge, UK, 1966).
  11. R. E. Edwards, Fourier Series: A Modern Introduction (Springer-Verlag, Berlin, 1979).
  12. R. M. A. Azzam, “Ellipsometry of unsupported and embedded thin films,” J. Phys. (France) C10, 67–70 (1983).
  13. J. Lekner, “Ellipsometry of a thin film between similar media,” J. Opt. Soc. Am. A 5, 1041–1043 (1988). [CrossRef]
  14. J. Lekner, “Analytic inversion of ellipsometric data for an unsupported nonabsorbing uniform layer,” J. Opt. Soc. Am. A 7, 1875–1877 (1990). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited