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
Examples of implementing these algorithms to industrial software will be shown.