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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 39, Iss. 25 — Sep. 1, 2000
  • pp: 4557–4568

Determination of optical parameters in general film–substrate systems: a reformulation based on the concepts of envelope extremes and local magnitudes

Juan Carlos Martínez-Antón  »View Author Affiliations


Applied Optics, Vol. 39, Issue 25, pp. 4557-4568 (2000)
http://dx.doi.org/10.1364/AO.39.004557


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Abstract

We present a reformulation of the determination of optical parameters in general film–substrate systems. Developed for interferential films in terms of photometric magnitudes (R, T), the formalism introduced allows us to establish how many parameters can be extracted from a set of measurements and from which type of sample model. These parameters are the refractive index and the absorption of both film and substrate (i.e., ñ1 = n1 - jk1 and ñ2 = n2 - jk2), the thickness of the film (d), the inhomogeneity of the film (Δn1), and the surface roughness of the interfaces (σ1, σ2) delimiting the film. The new formalism leads to some new analytical results and confirms others. Among the new results we have the following: (a) The mathematical condition commonly related with extremes (maxima and minima) in an interference pattern defines in fact a condition for envelope extremes. (b) The refractive index of a film can be obtained without prior knowledge of the thickness or the refractive index of the substrate (provided we have an optical interference film). (c) Absorption can be directly extracted from an interference-free magnitude T/(1 - R). (d) Roughness at the inner surface, inhomogeneity in the film, and absorption are correlated in reflection spectral measurements.

© 2000 Optical Society of America

OCIS Codes
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(120.5240) Instrumentation, measurement, and metrology : Photometry
(240.0310) Optics at surfaces : Thin films
(240.5770) Optics at surfaces : Roughness
(240.6700) Optics at surfaces : Surfaces
(310.1620) Thin films : Interference coatings
(310.6860) Thin films : Thin films, optical properties

History
Original Manuscript: January 31, 2000
Revised Manuscript: May 24, 2000
Published: September 1, 2000

Citation
Juan Carlos Martínez-Antón, "Determination of optical parameters in general film–substrate systems: a reformulation based on the concepts of envelope extremes and local magnitudes," Appl. Opt. 39, 4557-4568 (2000)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-39-25-4557


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