Phase-shifting interferometry and maximum-likelihood estimation theory

Eric W. Rogala, Harrison H. Barrett

Research output: Contribution to journalArticlepeer-review

17 Scopus citations


A novel means of quantitatively assessing the performance of a phase-shifting interferometer is presented. We show how maximum-likelihood estimation theory can be used to estimate the surface-height profile from four noisy phase-shifted measurements. Remarkably, the analytical expression for the maximum-likelihood estimator is identical to the classical four-step algorithm, thereby rooting the traditional method on a statistically sound foundation. Furthermore, a Monte Carlo experiment shows the maximum-likelihood estimator is unbiased and efficient, achieving the theoretical Cramer-Rao lower bound on the variance of the error. This technique is then used to show that the performance is a function of the ratio of the irradiances from each arm, with the optimal performance occurring, not surprisingly, when the irradiances from the two arms are equal.

Original languageEnglish (US)
Pages (from-to)8871-8876
Number of pages6
JournalApplied optics
Issue number34
StatePublished - Dec 1 1997


  • Cramer-Rao lower bounds
  • Jackknifing
  • Maximum-likelihood estimation theory
  • Phase-shifting interferometry

ASJC Scopus subject areas

  • Atomic and Molecular Physics, and Optics
  • Engineering (miscellaneous)
  • Electrical and Electronic Engineering


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