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Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 2 — Feb. 1, 1998
  • pp: 538–548

Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface

Eric W. Rogala and Harrison H. Barrett  »View Author Affiliations


JOSA A, Vol. 15, Issue 2, pp. 538-548 (1998)
http://dx.doi.org/10.1364/JOSAA.15.000538


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Abstract

A novel interferometer based on a conventional phase-shifting design is presented. This interferometer is capable of measuring both the real and the imaginary parts of the complex index of refraction and the surface profile of a test surface, n,k, and h, respectively. Maximum-likelihood-estimation theory is shown to be a viable means of extracting the three parameters of interest from the measured data. A Monte Carlo simulation showed limited success in estimating the complex index parameters. The results exhibited bias or deviation from the true values for the system configuration examined. The estimate on the surface profile showed excellent agreement with the true value, although the error in the estimate was an order of magnitude worse than in the case in which only the surface profile is to be estimated.

© 1998 Optical Society of America

OCIS Codes
(050.5080) Diffraction and gratings : Phase shift
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.3180) Instrumentation, measurement, and metrology : Interferometry
(120.5710) Instrumentation, measurement, and metrology : Refraction

History
Original Manuscript: May 1, 1997
Revised Manuscript: September 12, 1997
Manuscript Accepted: September 25, 1997
Published: February 1, 1998

Citation
Eric W. Rogala and Harrison H. Barrett, "Phase-shifting interferometer/ellipsometer capable of measuring the complex index of refraction and the surface profile of a test surface," J. Opt. Soc. Am. A 15, 538-548 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-2-538


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References

  1. J. E. Greivenkamp, J. H. Bruning, “Phase-Shifting Interferometers,” in Optical Shop Testing, 2nd ed., D. Malacara, ed. (Wiley, New York, 1992), pp. 501–598.
  2. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
  3. Y. Liu, C. W. See, M. G. Somekh, “Common path interferometric microellipsometry,” in Optical Inspection and Micromeasurements, C. Gorecki, ed., Proc. SPIE2782, 635–645 (1996). [CrossRef]
  4. S. V. Shatalin, R. Juskaitis, J. B. Tan, T. Wilson, “Reflection conoscopy and microellipsometry of isotropic thin-film structures,” J. Microsc. 179, pt. 3, 241–252 (1995). [CrossRef]
  5. A. Rosencwaig, J. Opsal, D. L. Willenborg, S. M. Kelso, J. T. Fanton, “Beam profile reflectometry: a new technique for dielectric film measurements,” Appl. Phys. Lett. 60, 11,1301–1303 (1992). [CrossRef]
  6. N. Gold, D. Willenborg, J. Opsal, A. Rosencwaig, “Method and apparatus for measuring thickness of thin films,” U.S. Patent No.4,999,014 (1991).
  7. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  8. M. Pluta, Advanced Light Microscopy (Elsevier, New York, 1989).
  9. H. L. Van Trees, Detection, Estimation, and Linear Modulation Theory, Part 1 (Wiley, New York, 1968).
  10. M. G. Kendall, A. Stuart, The Advanced Theory of Statistics, Vol. 2, 3rd ed. (Hafner, New York, 1973).
  11. B. R. Frieden, Probability, Statistical Optics, and Data Testing, 2nd ed. (Springer-Verlag, New York, 1991).
  12. D. L. Cohn, J. L. Melsa, Decision and Estimation Theory (McGraw-Hill, New York, 1978).
  13. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 394–455.
  14. W. H. Press, S. A. Teukolsky, W. T. Vetterling, B. P. Flannery, Numerical Recipes in C, 2nd ed. (Cambridge U. Press, New York, 1992), pp. 274–328.
  15. S. K. Park, K. W. Miller, “Random number generators: good ones are hard to find,” Commun. ACM 31, 1192–1201 (1988). [CrossRef]
  16. P. L’Ecuyer, “Efficient and portable combined random number generators,” Commun. ACM 31, 742–749 (1988). [CrossRef]
  17. B. R. Freiden, Probability, Statistical Optics, and Data Testing, 2nd ed. (Springer-Verlag, New York, 1991), p. 165.
  18. M. Quenouille, “Approximate tests of correlation in time series,” J. R. Statist. Soc. Ser. B, 11, 18–84 (1949).
  19. J. Tukey, “Bias and confidence in not quite large samples,” Ann. Math. Statist. Soc. Ser. B, 29, 614 (1958).
  20. B. Efron, The Jackknife, the Bootstrap and Other Resampling Plans (Society for Industrial and Applied Mathematics, Philadelphia, 1982).
  21. K. M. Wolter, Introduction to Variance Estimation (Springer-Verlag, New York, 1985), pp. 153–200.
  22. F. Mostellar, J. W. Tukey, Data Analysis and Regression: A Second Course in Statistics (Addison-Wesley, Reading, Mass., 1977), pp. 119–162.
  23. E. W. Rogala, H. H. Barrett, “Maximum-likelihood estimation theory and phase-shifting interferometry,” Appl. Opt. 36, 8871–8876.

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