OSA's Digital Library

Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN 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)
http://dx.doi.org/10.1364/AO.23.004477


View Full Text Article

Enhanced HTML    Acrobat PDF (1037 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

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

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

Citation
Berge Tatian, "Fitting refractive-index data with the Sellmeier dispersion formula," Appl. Opt. 23, 4477-4485 (1984)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-23-24-4477


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  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]

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