Dr. Manuel J. Mestre Profile

Dr. Manuel J. Mestre

at Ecole Normale Superieure Paris-Saclay

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Proceedings Article | 18 June 2007 Paper

Reaching lambda/100 resolution in static fringes interferometry using linear prediction

Manuel Mestre, Didier Pasquelin, Peter Flug

Proceedings Volume 6616, 661610 (2007) https://doi.org/10.1117/12.726037

KEYWORDS: Wavefronts, Photovoltaics, Reconstruction algorithms, Interferometry, Interferometers, Metrology, Phase shifts, Monte Carlo methods, Fringe analysis, Turbulence

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Both in industrial close-to-production quality control and in laboratory metrology, measuring optical components and systems with high precision and resolution (typically lambda/100 ptv) is currently achieved by phase-shifting interferometry devices. The main drawbacks of such devices compared to static fringes systems lie in a higher cost, and a greater the sensitivity to the environment, both vibration and air turbulence; the latter becomes unacceptable for large components and large cavity interferometers. Conversely, static fringes metrology usually lacks precision and resolution. Particularly, the lateral resolution is an issue, due to the sampling theorem. This paper shows how a linear prediction of a random function (with a Bayesian approach) makes it possible to tackle a lambda/100 resolution for the estimated wavefront, being the mathematical expectation of the prediction, i.e. the most probable form with respect to the fringe data. Incidentally, the prediction increases robustness by detecting and correcting aberrant fringe data with a high reliability. Furthermore, a Monte-Carlo simulation performed on the whole conditional probability density of the wavefront, provides a stochastic sub-fringe-spacing interpolation. As a result, confidence intervals for any parameter of interest (such as ptv, rms, ptv of slopes...) can be estimated over the whole aperture, which is novel worldwide. These algorithms have also been adapted to wavefront reconstruction from gradient data for Shack-Hartmann and for moiré devices. Examples of implementing these algorithms to industrial software will be shown.

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