### Abstract

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.

Original language | English (US) |
---|---|

Pages (from-to) | 7253-7258 |

Number of pages | 6 |

Journal | Applied Optics |

Volume | 37 |

Issue number | 31 |

State | Published - 1998 |

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### ASJC Scopus subject areas

- Atomic and Molecular Physics, and Optics

### Cite this

*Applied Optics*,

*37*(31), 7253-7258.

**Phase-shifting interferometry and maximum-likelihood estimation theory. II. A generalized solution.** / Rogala, Eric W.; Barrett, Harrison H.

Research output: Contribution to journal › Article

*Applied Optics*, vol. 37, no. 31, pp. 7253-7258.

}

TY - JOUR

T1 - Phase-shifting interferometry and maximum-likelihood estimation theory. II. A generalized solution

AU - Rogala, Eric W.

AU - Barrett, Harrison H

PY - 1998

Y1 - 1998

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0011355835&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0011355835&partnerID=8YFLogxK

M3 - Article

C2 - 18301555

AN - SCOPUS:0011355835

VL - 37

SP - 7253

EP - 7258

JO - Applied Optics

JF - Applied Optics

SN - 1559-128X

IS - 31

ER -