Ellipse fitting by nonlinear constraints to demodulate
quadrature homodyne interferometer signals and to determine the
statistical uncertainty of the interferometric phase

J 2014

Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase

KONING, Rainer; Gejza WIMMER a Viktor WITKOVSKÝ

Základní údaje

Originální název

Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase

Autoři

KONING, Rainer; Gejza WIMMER a Viktor WITKOVSKÝ

Vydání

MEASUREMENT SCIENCE & TECHNOLOGY, BRISTOL, IOP PUBLISHING LTD, 2014, 0957-0233

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

20102 Construction engineering, Municipal and structural engineering

Stát vydavatele

Velká Británie a Severní Irsko

Utajení

není předmětem státního či obchodního tajemství

Odkazy

Full Text

Impakt faktor

Impact factor: 1.433

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/14:00080210

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Heydemann correction; homodyne interferometry; demodulation of quadrature homodyne interferometer signals; measurement uncertainty

Štítky

AKR, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 19. 12. 2019 11:15, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

Optical interferometers are widely used in dimensional metrology applications. Among them are many quadrature homodyne interferometers. These exhibit two sinusoidal interference signals shifted, in the ideal case, by 90 degrees to allow a direction sensitive detection of the motion responsible for the actual phase change. But practically encountered signals exhibit additional offsets, unequal amplitudes and a phase shift that differs from 90 degrees. In order to demodulate the interference signals the so called Heydemann correction is used in almost all cases, i.e. an ellipse is fitted to both signals simultaneously to obtain the offsets, amplitude and the phase lag. Such methods are typically based on a simplified least squares fit that leads to a system of linear equations, which can be solved directly in one step. Although many papers related to this subject have been published already only a few of them consider the uncertainties related to this demodulation scheme. In this paper we propose a new method for fitting the ellipse, based on minimization of the geometric distance between the measured and fitted signal values, which provides locally best linear unbiased estimators (BLUEs) of the unknown model parameters, and simultaneously also estimates of the related statistical uncertainties, including the uncertainties of estimated phases and/or displacements.

Citovat

KONING, Rainer; Gejza WIMMER a Viktor WITKOVSKÝ. Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase. MEASUREMENT SCIENCE & TECHNOLOGY. BRISTOL: IOP PUBLISHING LTD, 2014, roč. 25, č. 11, s. "nestrankovano", 11 s. ISSN 0957-0233. Dostupné z: https://doi.org/10.1088/0957-0233/25/11/115001.

@article{1297995,
   author = {Koning, Rainer and Wimmer, Gejza and Witkovský, Viktor},
   article_location = {BRISTOL},
   article_number = {11},
   doi = {https://doi.org/10.1088/0957-0233/25/11/115001},
   keywords = {Heydemann correction; homodyne interferometry; demodulation of quadrature homodyne interferometer signals; measurement uncertainty},
   language = {eng},
   issn = {0957-0233},
   journal = {MEASUREMENT SCIENCE & TECHNOLOGY},
   title = {Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase},
   url = {https://iopscience.iop.org/article/10.1088/0957-0233/25/11/115001/pdf},
   volume = {25},
   year = {2014}
}

TY  - JOUR
ID  - 1297995
AU  - Koning, Rainer - Wimmer, Gejza - Witkovský, Viktor
PY  - 2014
TI  - Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase
JF  - MEASUREMENT SCIENCE & TECHNOLOGY
VL  - 25
IS  - 11
SP  - "nestrankovano"
EP  - "nestrankovano"
PB  - IOP PUBLISHING LTD
SN  - 09570233
KW  - Heydemann correction
KW  - homodyne interferometry
KW  - demodulation of quadrature homodyne interferometer signals
KW  - measurement uncertainty
UR  - https://iopscience.iop.org/article/10.1088/0957-0233/25/11/115001/pdf
N2  - Optical interferometers are widely used in dimensional metrology applications. Among them are many quadrature homodyne interferometers. These exhibit two sinusoidal interference signals shifted, in the ideal case, by 90 degrees to allow a direction sensitive detection of the motion responsible for the actual phase change. But practically encountered signals exhibit additional offsets, unequal amplitudes and a phase shift that differs from 90 degrees. In order to demodulate the interference signals the so called Heydemann correction is used in almost all cases, i.e. an ellipse is fitted to both signals simultaneously to obtain the offsets, amplitude and the phase lag. Such methods are typically based on a simplified least squares fit that leads to a system of linear equations, which can be solved directly in one step. Although many papers related to this subject have been published already only a few of them consider the uncertainties related to this demodulation scheme. In this paper we propose a new method for fitting the ellipse, based on minimization of the geometric distance between the measured and fitted signal values, which provides locally best linear unbiased estimators (BLUEs) of the unknown model parameters, and simultaneously also estimates of the related statistical uncertainties, including the uncertainties of estimated phases and/or displacements.
ER  -

KONING, Rainer; Gejza WIMMER a Viktor WITKOVSKÝ. Ellipse fitting by nonlinear constraints to demodulate quadrature homodyne interferometer signals and to determine the statistical uncertainty of the interferometric phase. \textit{MEASUREMENT SCIENCE \&{}amp; TECHNOLOGY}. BRISTOL: IOP PUBLISHING LTD, 2014, roč.~25, č.~11, s.~''nestrankovano'', 11 s. ISSN~0957-0233. Dostupné z: https://doi.org/10.1088/0957-0233/25/11/115001.

Přehled o publikaci