### 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) |
---|---|

Pages (from-to) | 8871-8876 |

Number of pages | 6 |

Journal | Applied Optics |

Volume | 36 |

Issue number | 34 |

State | Published - 1997 |

### Fingerprint

### 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.

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

Research output: Contribution to journal › Article

*Applied Optics*, vol. 36, no. 34, pp. 8871-8876.

}

TY - JOUR

T1 - Phase-shifting interferometry and maximum-likelihood estimation theory

AU - Rogala, Eric W.

AU - Barrett, Harrison H

PY - 1997

Y1 - 1997

N2 - 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.

AB - 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.

KW - Cramer-rao lower bounds

KW - Jackknifing

KW - Maximum-likelihood estimation theory

KW - Phase-shifting interferometry

UR - http://www.scopus.com/inward/record.url?scp=0000645860&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000645860&partnerID=8YFLogxK

M3 - Article

C2 - 18264438

AN - SCOPUS:0000645860

VL - 36

SP - 8871

EP - 8876

JO - Applied Optics

JF - Applied Optics

SN - 1559-128X

IS - 34

ER -