OSA's Digital Library

Journal of the Optical Society of America A

Journal of the Optical Society of America A

| OPTICS, IMAGE SCIENCE, AND VISION

  • Vol. 15, Iss. 6 — Jun. 1, 1998
  • pp: 1670–1685

Assessing and optimizing the performance of a phase-shifting interferometer 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 6, pp. 1670-1685 (1998)
http://dx.doi.org/10.1364/JOSAA.15.001670


View Full Text Article

Enhanced HTML    Acrobat PDF (465 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

Abstract

A novel interferometer based upon a conventional phase-shifting design is further investigated. This interferometer is capable of measuring both the real and imaginary parts of the complex index of refraction and the surface profile of a test surface. Maximum-likelihood estimation theory is shown to be an effective means of extracting the three parameters of interest from the measured data. Cramér–Rao lower bounds are introduced as a means of quantitatively assessing the performance of the system. Furthermore, it is shown that as the design parameters are optimized, the results approach the theoretical performance limit. We conclude by developing the underlying theory behind the relationship of the complex-index-of-refraction estimates to the surface-profile estimate.

© 1998 Optical Society of America

OCIS Codes
(100.2650) Image processing : Fringe analysis
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.2130) Instrumentation, measurement, and metrology : Ellipsometry and polarimetry
(120.3180) Instrumentation, measurement, and metrology : Interferometry

History
Original Manuscript: August 4, 1997
Revised Manuscript: January 5, 1998
Manuscript Accepted: January 20, 1998
Published: June 1, 1998

Citation
Eric W. Rogala and Harrison H. Barrett, "Assessing and optimizing the performance of a phase-shifting interferometer capable of measuring the complex index of refraction and the surface profile of a test surface," J. Opt. Soc. Am. A 15, 1670-1685 (1998)
http://www.opticsinfobase.org/josaa/abstract.cfm?URI=josaa-15-6-1670


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. Y. Liu, C. W. See, M. G. Somekh, “Common path interferometric microellipsometry,” Proc. SPIE 2782, 635–645 (1996). [CrossRef]
  2. R. D. Holmes, C. W. See, M. G. Somekh, “Scanning microellipsometry for extraction of true topography,” Electron. Lett. 31, 358–359 (1995). [CrossRef]
  3. C. W. See, R. K. Appel, M. G. Somekh, “Scanning differential optical profilometer for simultaneous measurement of amplitude and phase variation,” Appl. Phys. Lett. 53, 10–12 (1988). [CrossRef]
  4. Y. Lin, C. Chou, K. Chang, “Real-time interferometric ellipsometry with optical heterodyne and phase lock-in techniques,” Appl. Opt. 29, 5159–5162 (1990). [CrossRef] [PubMed]
  5. 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]
  6. 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, 1301–1303 (1992). [CrossRef]
  7. N. Gold, D. Willenborg, J. Opsal, A. Rosencwaig, “Method and apparatus for measuring thickness of thin films,” U.S. patent4,999,014 (March12, 1991).
  8. H. F. Hazebroek, A. A. Holscher, “Interferometric ellipsometry,” J. Phys. E 6, 822–826 (1973). [CrossRef]
  9. T. Mishima, K. C. Kao, “Detection of thickness uniformity of film layers in semiconductor devices by spatially resolved ellipsometry,” Opt. Eng. 21, 1074–1078 (1982). [CrossRef]
  10. R. M. A. Azzam, N. M. Bashara, Ellipsometry and Polarized Light (North-Holland, Amsterdam, 1977).
  11. M. Pluta, Advanced Light Microscopy (Elsevier, New York, 1989).
  12. E. W. Rogala, H. 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). [CrossRef]
  13. E. W. Rogala, H. H. Barrett, “Phase-shifting interferometry and maximum-likelihood estimation theory,” Appl. Opt. 36, 8871–8876 (1997). [CrossRef]
  14. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. A 12, 1997–2008 (1995). [CrossRef]
  15. K. Creath, “Phase-measurement interferometry techniques,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 349–393.
  16. K. Creath, “Comparison of phase-measurement algorithms,” in Surface Characterization and Testing, K. Creath, ed., Proc. SPIE680, 19–29 (1986). [CrossRef]
  17. D. Apostol, P. C. Logofatu, V. Damian, A. Dobrolu, “Sensitivity analysis of parameter determination from measurements of directly measurable quantities using the Jacobian,” Opt. Eng. (Bellingham) 35, 1288–1291 (1996). [CrossRef]
  18. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Eng. 7, 368–370 (1982).
  19. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984). [CrossRef]
  20. H. Cramer, Mathematical Methods of Statistics (Princeton U. Press, Princeton, N.J., 1946).
  21. C. R. Rao, “Information and accuracy attainable in the estimation of statistical parameters,” Bull. Calcutta Math. Soc. 37, 81–91 (1945).
  22. A. C. Aitkin, H. Silverstone, “On the estimation of statistical parameters,” Proc. R. Soc. Edinburgh Sect. A 61, 186–194 (1942).
  23. R. A. Fisher, “Theory of statistical estimation,” Proc. Cambridge Philos. Soc. 22, 700–725 (1925). [CrossRef]
  24. D. Dugue, “Application des propriétes de la limite au sens de calcul des probabilities a l’étude des diverses questions d’estimation,” Ecol. Poly. 3, 305–372 (1937).
  25. H. L. Van Trees, Detection, Estimation Theory, and Linear Modulation Theory, Part 1 (Wiley, New York, 1968).
  26. E. W. Barankin, “Locally best unbiased estimators,” Ann. Math. Stat. 20, 477–501 (1949). [CrossRef]
  27. A. Bhattacharyya, “On some analogues of the amount of information and their use in statistical estimation,” Sankhya 8, 1–15, 201–218, 315–328 (1946).
  28. 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.

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