OSA's Digital Library

Applied Optics

Applied Optics


  • Vol. 37, Iss. 31 — Nov. 1, 1998
  • pp: 7253–7258

Phase-shifting interferometry and maximum-likelihood estimation theory. II. A generalized solution

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

Applied Optics, Vol. 37, Issue 31, pp. 7253-7258 (1998)

View Full Text Article

Enhanced HTML    Acrobat PDF (98 KB)

Browse Journals / Lookup Meetings

Browse by Journal and Year


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools



A novel means of quantitatively assessing the performance of a phase-shifting interferometer is further investigated. We show how maximum-likelihood estimation theory can be used to estimate the surface profile from the general case of M noisy, phase-shifted measurements. Monte Carlo experiments show that the maximum-likelihood estimator is unbiased and efficient, achieving the theoretical Cramér–Rao lower bound on the variance of the error. We then use Monte Carlo experiments to compare the performance of the maximum-likelihood estimator with that of two conventional algorithms.

© 1998 Optical Society of America

OCIS Codes
(000.5490) General : Probability theory, stochastic processes, and statistics
(100.2650) Image processing : Fringe analysis
(120.0120) Instrumentation, measurement, and metrology : Instrumentation, measurement, and metrology
(120.3180) Instrumentation, measurement, and metrology : Interferometry

Original Manuscript: February 5, 1998
Revised Manuscript: July 8, 1998
Published: November 1, 1998

Eric W. Rogala and Harrison H. Barrett, "Phase-shifting interferometry and maximum-likelihood estimation theory. II. A generalized solution," Appl. Opt. 37, 7253-7258 (1998)

Sort:  Author  |  Year  |  Journal  |  Reset  


  1. E. W. Rogala, H. H. Barrett, “Phase-shifting interferometry and maximum-likelihood estimation theory,” Appl. Opt. 36, 8871–8876 (1997). [CrossRef]
  2. C. Rathjen, “Statistical properties of phase-shift algorithms,” J. Opt. Soc. Am. A 12, 1997–2008 (1995). [CrossRef]
  3. H. L. Van Trees, Detection, Estimation, and Linear Modulation Theory (Wiley, New York, 1968), Part 1.
  4. M. G. Kendall, A. Stuart, The Advanced Theory of Statistics, 3rd ed. (Hafner, New York, 1973), Vol. 2.
  5. B. R. Frieden, Probability, Statistical Optics, and Data Testing, 2nd ed. (Springer-Verlag, New York, 1991). [CrossRef]
  6. D. L. Cohn, J. L. Melsa, Decision and Estimation Theory (McGraw-Hill, New York, 1978).
  7. R. A. Fisher, “Theory of statistical estimation,” Proc. Camb. Phil. Soc. XXII Part 5, 700–725 (1925). [CrossRef]
  8. I. S. Gradshteyn, I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, New York, 1965).
  9. J. H. Bruning, D. R. Herriot, J. E. Gallagher, D. P. Resenfeld, A. D. White, D. J. Bangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” Appl. Opt. 13, 2693–2703 (1974). [CrossRef] [PubMed]
  10. C. J. Morgan, “Least-squares estimation in phase-measurement interferometry,” Opt. Lett. 7, 368–370 (1982). [CrossRef] [PubMed]
  11. J. E. Greivenkamp, “Generalized data reduction for heterodyne interferometry,” Opt. Eng. 23, 350–352 (1984). [CrossRef]
  12. Ref. 5, pp. 378–382.
  13. Ref. 4, pp. 8–18.
  14. Ref. 3, pp. 65–73.
  15. 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.
  16. P. L’Ecuyer, “Efficient and portable combined random number generators,” Commun. ACM 31, 742–774 (1988). [CrossRef]
  17. P. Carré, “Installation et utilisation du comparateur photoelectrique et interferentiel du bureau international des poids de mesures,” Metrologia 2, 13–23 (1966). [CrossRef]
  18. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a simple error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987). [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.


Fig. 1 Fig. 2 Fig. 3
Fig. 4

« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited