OSA's Digital Library

Applied Optics

Applied Optics


  • Editor: James C. Wyant
  • Vol. 45, Iss. 22 — Aug. 1, 2006
  • pp: 5636–5641

Fourier transform approach for thickness estimation of reflecting interference filters

Pierre G. Verly  »View Author Affiliations

Applied Optics, Vol. 45, Issue 22, pp. 5636-5641 (2006)

View Full Text Article

Enhanced HTML    Acrobat PDF (91 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



An empirical procedure based on optical-density-bandwidth products was recently proposed for thickness estimation of dielectric thin film reflectors. A parallel is established with new results derived from the Fourier transform thin film synthesis technique. Two Fourier-transform approaches are proposed and justified by numerical examples.

© 2006 Optical Society of America

OCIS Codes
(230.4040) Optical devices : Mirrors
(230.4170) Optical devices : Multilayers
(310.0310) Thin films : Thin films
(310.1620) Thin films : Interference coatings
(310.6860) Thin films : Thin films, optical properties
(350.2460) Other areas of optics : Filters, interference

ToC Category:
Thin Films

Original Manuscript: November 28, 2005
Manuscript Accepted: February 7, 2006

Pierre G. Verly, "Fourier transform approach for thickness estimation of reflecting interference filters," Appl. Opt. 45, 5636-5641 (2006)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. H. A. Macleod, Thin-Film Optical Filters (Macmillan, 1986). [CrossRef]
  2. P. W. Baumeister, Optical Coating Technology (SPIE Optical Engineering Press, 2004). [CrossRef]
  3. R. R. Willey, "Estimating the number of layers required and other properties of blocker and dichroic optical thin films," Appl. Opt. 35, 4982-4986 (1996). [CrossRef] [PubMed]
  4. R. R. Willey, "Predicting achievable design performance of broadband antireflection coatings," Appl. Opt. 32, 5447-5451 (1993). [CrossRef] [PubMed]
  5. J. A. Dobrowolski, "Subtractive method of optical thin-film interference filter design," Appl. Opt. 12, 1885-1893 (1973). [CrossRef] [PubMed]
  6. J. A. Dobrowolski, A. V. Tikhonravov, M. K. Trubetskov, B. T. Sullivan, and P. G. Verly, "Optimal single-band normal-incidence antireflection coatings," Appl. Opt. 35, 644-658 (1996). [CrossRef] [PubMed]
  7. E. Delano, "Fourier synthesis of multilayer filters," J. Opt. Soc. Am. 57, 1529-1553 (1967). [CrossRef]
  8. L. Sossi, "A method for the synthesis of multilayer dielectric interference coatings," Eesti NSV Tead. Akad. Toim. Fuus. , Mat. 23, 229-237 (1974). An English translation is available from the Translation Services of the Canada Institute for Scientific and Technical Information, National Research Council of Canada, Ottawa, Ontario, Canada K1A 0R6.
  9. J. A. Dobrowolski and D. Lowe, "Optical thin film synthesis program based on the use of Fourier transforms," Appl. Opt. 17, 3039-3050 (1978). [CrossRef] [PubMed]
  10. P. G. Verly, J. A. Dobrowolski, W. J. Wild, and R. L. Burton, "Synthesis of high rejection filters with the Fourier transform method," Appl. Opt. 28, 2864-2875 (1989). [CrossRef] [PubMed]
  11. P. G. Verly and J. A. Dobrowolski, "Iterative correction process for optical thin film synthesis with the Fourier transform method," Appl. Opt. 29, 3672-3684 (1990). [CrossRef] [PubMed]
  12. P. G. Verly, "Design of inhomogeneous and quasi-inhomogeneous optical coatings at the NRC," in Inhomogeneous and Quasi-Inhomogenous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 36-45 (1993).
  13. P. G. Verly, J. A. Dobrowolski, and R. R. Willey, "Fourier transform method for the design of wideband antireflection coatings," Appl. Opt. 31, 3836-3846 (1992). [CrossRef] [PubMed]
  14. B. G. Bovard, "Derivation of a matrix describing a rugate dielectric thin film," Appl. Opt. 27, 1998-2005 (1988). [CrossRef] [PubMed]
  15. H. Fabricius, "Gradient-index filters: conversion into a two-index solution by taking into account dispersion," Appl. Opt. 31, 5216-5220 (1992). [CrossRef] [PubMed]
  16. P. V. Bulkin, P. L. Swart, and B. M. Lacquet, "Fourier-transform design and electron cyclotron resonance plasma-enhanced deposition of lossy graded-index optical coatings," Appl. Opt. 35, 4413-4419 (1996). [CrossRef] [PubMed]
  17. P. G. Verly, A. V. Tikhonravov, and A. D. Poezd, "Multiple solutions to the synthesis of graded index optical coatings," in Inhomogeneous and Quasi-Inhomogeneous Optical Coatings, J.A.Dobrowolski and P.G.Verly, eds., Proc. SPIE 2046, 9-16 (1993).
  18. P. G. Verly, "Fourier transform approach for the estimation of optical thin film thickness," in Technical Digest of Topical Meeting on Optical Interference Coatings (Optical Society of America, 2001), pp. TuA9 1-3.
  19. Equation (5) is more general than stated in Ref. 18; an equal proportion of the high and low refractive index is not necessary.

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