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Applied Optics

Applied Optics


  • Vol. 23, Iss. 24 — Dec. 15, 1984
  • pp: 4477–4485

Fitting refractive-index data with the Sellmeier dispersion formula

Berge Tatian  »View Author Affiliations

Applied Optics, Vol. 23, Issue 24, pp. 4477-4485 (1984)

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The fitting of measured optical index data to the Sellmeier dispersion formula, using the variable projection algorithm, is described. Examples of fits obtained by this method to several Schott optical glasses and non-glass materials are given.

© 1984 Optical Society of America

Original Manuscript: August 19, 1984
Published: December 15, 1984

Berge Tatian, "Fitting refractive-index data with the Sellmeier dispersion formula," Appl. Opt. 23, 4477-4485 (1984)

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  1. O. N. Stavroudis, L. E. Sutton, “Rapid Method for Interpolating Refractive Index Measurements,” J. Opt. Soc. Am. 51, 368 (1961). [CrossRef]
  2. L. E. Sutton, O. N. Stavroudis, “Fitting Refractive Index Data by Least Squares,” J. Opt. Soc. Am. 51, 901 (1961). [CrossRef]
  3. B. Tatian, “Interpolation of Glass Indices with Applications to First Order Axial Chromatic Aberration,” Itek Corp. Report OR-63-20, Lexington, Mass. (1964).
  4. M. Herzberger, “Colour Correction in Optical Systems and a New Dispersion Formula,” Opt. Acta 6, 197 (1959). [CrossRef]
  5. A recent article, P. N. Robb, R. I. Mercado, “Calculation of Refractive Indices Using Buchdahl’s Chromatic Coordinate,” Appl. Opt. 22, 1198 (1983), makes the statement, “A theoretical model should have an accuracy comparable to that of precision glass melts, which can be supplied to an index accuracy of 0.0002.” Even standard precision melt sheets supplied by Schott Optical Glass, Inc. specify the dispersion values to ±2 × 10−5, and high-precision melt sheets give the dispersion to ±2 × 10−6. (Dispersion ≡ Nλ0 − Nλ, where λ0 is a wavelength near the middle of the wavelength band considered.) It is the departure of the nominal index, Nλ0, of the melt from the catalog value that can be as high as ±2 × 10−4. This is about ±10 waves/in. of glass, and an error this large in the dispersion would be totally unacceptable for higher-order color effects. [CrossRef] [PubMed]
  6. G. H. Golub, V. Pereyra, “The Differentiation of Pseudo-Inverses and Nonlinear Least Squares Problems Whose Variables Separate,” Siam J. Numer. Anal. 10, 413 (1973). [CrossRef]
  7. F. T. Krogh, “Efficient Implementation of a Variable Projection Algorithm for Nonlinear Least Squares Problems,” Commun. ACM 17, 167 (1974). [CrossRef]
  8. R. Penrose, “On Best Approximate Solutions of Linear Matrix Equations,” Proc. Cambridge Philos. Soc. 52, 17 (1956). [CrossRef]
  9. Optical Glass Catalog 3111E, Schott Optical Glass, Inc., Duryea, Pa.
  10. Raytran Infrared Materials, Raytheon Co., Research Division, Waltham, Mass.
  11. M. J. Dodge, “Refractive Properties of CVD Zinc Sulfide,” in Proceedings, Symposium on Laser-Induced Damage in Optical Materials (U.S. GPO, Washington, 1977), pp. 83–88.
  12. I. H. Malitson, “Refractive Index of Fused Silica,” J. Opt. Soc. Am. 55, 1205 (1965). [CrossRef]
  13. W. L. Wolfe, Ed., Handbook of Optics (McGraw-Hill, New York, 1978), Chap. 7, p. 7–89.
  14. W. L. Wolfe, Ref. 13, p. 7–102.
  15. I. H. Malitson, “A Redetermination of Some Optical Properties of CaF2,” Appl. Opt. 2, 1103 (1963). [CrossRef]
  16. I. H. Malitson, “Refractive Properties of BaF2,” J. Opt. Soc. Am. 54, 628 (1964). [CrossRef]
  17. I. H. Malitson, “Refraction and Dispersion of Synthetic Sapphire,” J. Opt. Soc. Am. 52, 1377 (1962). [CrossRef]
  18. W. S. Rodney, I. H. Malitson, T. A. King, “Refractive Index of Arsenic Trisulfide,” J. Opt. Soc. Am. 48, 633 (1958). [CrossRef]
  19. W. S. Rodney, “Optical Properties of Cesium Iodide,” J. Opt. Soc. Am. 45, 987 (1955). [CrossRef]
  20. W. S. Rodney, I. H. Malitson, “Refraction and Dispersion of Thallium Bromide-Iodide,” J. Opt. Soc. Am. 46, 956 (1956). [CrossRef]
  21. H. H. Li, “Refractive Index of Alkali Halides and Its Wavelength and Temperature Derivatives,” J. Phys. Chem. Ref. Data 5, 329 (1976). [CrossRef]
  22. B. J. Pernick, “Nonlinear Regression Analysis for the Sellmeier Dispersion Equation of CdS,” Appl. Opt. 22, 1133 (1983). [CrossRef] [PubMed]
  23. F. Vilches, J. M. Guerra, M. S. Gomez, “Nonlinear Regression Analysis of a Sellmeier Equation with Various Resonances: Best Fit of CdS Dispersion,” Appl. Opt. 23, 2044 (1984). [CrossRef] [PubMed]
  24. M. Debenham, “Refractive Indices of Zinc Sulfide in the 0.405–13-μm Wavelength Range,” Appl. Opt. 23, 2238 (1984). [CrossRef] [PubMed]

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