### Abstract

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 language | English (US) |
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Pages (from-to) | 8871-8876 |

Number of pages | 6 |

Journal | Applied Optics |

Volume | 36 |

Issue number | 34 |

Publication status | Published - 1997 |

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### Keywords

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

### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Applied Optics*,

*36*(34), 8871-8876.