Phase-shifting interferometry and maximum-likelihood estimation theory

Eric W. Rogala, Harrison H Barrett

Research output: Contribution to journalArticle

15 Citations (Scopus)

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 languageEnglish (US)
Pages (from-to)8871-8876
Number of pages6
JournalApplied Optics
Volume36
Issue number34
StatePublished - 1997

Fingerprint

Maximum likelihood estimation
Interferometry
Maximum likelihood
interferometry
irradiance
estimators
Phase measurement
Interferometers
Acoustic waves
interferometers
acoustics
Experiments
estimates
profiles

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

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

In: Applied Optics, Vol. 36, No. 34, 1997, p. 8871-8876.

Research output: Contribution to journalArticle

@article{04745888645f43de894bf9fd4f140664,
title = "Phase-shifting interferometry and maximum-likelihood estimation theory",
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.",
keywords = "Cramer-rao lower bounds, Jackknifing, Maximum-likelihood estimation theory, Phase-shifting interferometry",
author = "Rogala, {Eric W.} and Barrett, {Harrison H}",
year = "1997",
language = "English (US)",
volume = "36",
pages = "8871--8876",
journal = "Applied Optics",
issn = "1559-128X",
publisher = "The Optical Society",
number = "34",

}

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 -