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Applied Optics

Applied Optics

APPLICATIONS-CENTERED RESEARCH IN OPTICS

  • Vol. 37, Iss. 13 — May. 1, 1998
  • pp: 2660–2673

Multiply subtractive Kramers–Kronig analysis of optical data

Kent F. Palmer, Michael Z. Williams, and Ben A. Budde  »View Author Affiliations


Applied Optics, Vol. 37, Issue 13, pp. 2660-2673 (1998)
http://dx.doi.org/10.1364/AO.37.002660


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Abstract

We describe a new, multiply subtractive Kramers–Kronig (MSKK) method to find the optical constants of a material from a single transmittance or reflectance spectrum covering a small frequency domain. The MSKK method incorporates independent measurements of n and k at one or more reference wave-number values to minimize errors due to extrapolations of the data. An unexpected connection between the MSKK equations and the interpolation theory allows us to derive the equations from an interpolation theorem. We found that the locations of the reference points affect the accuracy of the values determined for the optical constants and that the optimal spacing of N reference data points is related to the zeros of a suitably transformed Chebychev polynomial of order N. We discuss our efforts to optimize both the number and the spacing of these reference points and apply our method to some test spectra.

© 1998 Optical Society of America

OCIS Codes
(120.4530) Instrumentation, measurement, and metrology : Optical constants
(160.4760) Materials : Optical properties
(310.6860) Thin films : Thin films, optical properties
(350.5030) Other areas of optics : Phase

History
Original Manuscript: August 7, 1997
Revised Manuscript: December 19, 1997
Published: May 1, 1998

Citation
Kent F. Palmer, Michael Z. Williams, and Ben A. Budde, "Multiply subtractive Kramers–Kronig analysis of optical data," Appl. Opt. 37, 2660-2673 (1998)
http://www.opticsinfobase.org/ao/abstract.cfm?URI=ao-37-13-2660


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References

  1. R. H. Young, “Validity of the Kramers–Kronig transformation used in reflection spectroscopy,” J. Opt. Soc. Am. 67, 520–523 (1977). [CrossRef]
  2. J. S. Plaskett, P. N. Schatz, “On the Robinson and Price (Kramers–Kronig) method of interpreting reflection data taken through a transparent window,” J. Chem. Phys. 38, 612–617 (1963). [CrossRef]
  3. K. F. Palmer, M. Z. Williams, “Optical constant determination of thin films condensed on transmitting and reflecting surfaces,” Technical Report AEDC-TR-83-64 (AD-A140845) (Defense Technical Information Center, Fort Belvoir, Va., 1984).
  4. K. F. Palmer, M. Z. Williams, “Determination of the optical constants of a thin film from transmittance measurements of a single film thickness,” Appl. Opt. 24, 1788–1798 (1985). [CrossRef] [PubMed]
  5. S. Maeda, G. Thyagarajan, P. N. Schatz, “Absolute infrared intensity measurements in thin films: II. Solids deposited on halide plates,” J. Chem. Phys. 38, 3474–3481 (1963). [CrossRef]
  6. E. A. Lupaskho, V. K. Miloslavskii, I. N. Shklyarevskii, “Use of the Kramers–Kronig dispersion relations in determining the phase shift occurring upon reflection of light from thin dielectric layers,” Opt. Spektrosk. 24, 257–262 (1968) [Opt. Spectrosc. 24, 132–134 (1968)].
  7. E. A. Lupaskho, V. K. Miloslavskii, I. N. Shklyarevskii, “Use of the Kramers–Kronig dispersion relationships to calculate the phase of the wave reflected from thin dielectric layers,” Opt. Spektrosk. 29, 789–793 (1970) [Opt. Spectrosc. 29, 419–422 (1970)].
  8. J. S. Toll, “Causality and the dispersion relation: logical foundations,” Phys. Rev. 104, 1760–1770 (1956). [CrossRef]
  9. P.-O. Nilsson, “Determination of optical constants from intensity measurements at normal incidence,” Appl. Opt. 7, 435–442 (1968). [CrossRef] [PubMed]
  10. R. K. Ahrenkiel, “Modified Kramers–Kronig analysis of optical spectra,” J. Opt. Soc. Am. 61, 1651–1655 (1971). [CrossRef]
  11. H. M. Nussenzveig, Causality and Dispersion Relations (Academic, New York, 1972).
  12. T. G. Goplen, D. G. Cameron, R. N. Jones, “The control of errors in infrared spectrophotometry. VI. The evaluation of optical constants by combined transmission and attenuated total reflection measurements,” Appl. Spectrosc. 34, 652–656 (1980). [CrossRef]
  13. P. J. Davis, Interpolation and Approximation (Dover, New York, 1975).
  14. L. D. Landau, E. M. Lifshitz, Electrodynamics of Continuous Media (Pergamon, New York, 1960).
  15. K.-E. Peiponen, E. M. Vartiainen, “Kramers–Kronig relations in optical data inversion,” Phys. Rev. B 44, 8301–8303 (1991). [CrossRef]
  16. E. M. Vartiainen, K. E. Peiponen, T. Asakura, “Maximum entropy model in reflection spectra analysis,” Opt. Commun. 89, 37–40 (1992). [CrossRef]
  17. E. M. Vartiainen, K.-E. Peiponen, T. Asakura, “Comparison between the optical constants obtained by the Kramers–Kronig analysis and the maximum entropy method: infrared optical properties of orthorhombic sulfur,” Appl. Opt. 32, 1126–1129 (1993). [CrossRef] [PubMed]
  18. K. F. Palmer, M. Z. Williams, B. A. Budde, W. T. Bertrand, “Optical analysis methods for material films condensed on cryogenic surfaces of spacecraft,” Technical Report AEDC-TR-94-3 (AD-A284014) (Defense Technical Information Center, Fort Belvoir, Va., 1994).
  19. G. D. Guenther, Modern Optics (Wiley, New York, 1990).
  20. M. Born, E. Wolf, Principles of Optics, 5th ed. (Pergamon, Oxford, 1975).
  21. A. V. Tikhonravov, P. W. Baumeister, K. V. Popov, “Phase properties of multilayers,” Appl. Opt. 36, 4382–4392 (1997). [CrossRef] [PubMed]
  22. K. F. Palmer, J. A. Roux, B. E. Wood, “The infrared optical properties of mixtures of molecular species at 20 K,” Technical Report AEDC-TR-80-30 (AD-A094214) (Defense Technical Information Center, Fort Belvoir, Va., 1981).
  23. R. P. Boas, Invitation to Complex Analysis (Random House, New York, 1987).

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