Proceedings Article | 28 October 2021
KEYWORDS: Wavefronts, Turbulence, Monte Carlo methods, Statistical analysis, Metrology, Interferometry, Tolerancing, Optical components, Signal to noise ratio, Statistical modeling
Air turbulence is a major environmental factor that degrades the precision of optical part interferometric metrology. For large optics with a long cavity, turbulence effects become critical. Reducing those effects by protecting the cavity with mechanical means is necessary, though not sufficient. Averaging wavefronts is a simple, classic, and efficient remedy. However averaging leaves unanswered the following issues: How many wavefronts should be averaged? What is the resulting uncertainty on the parameters of interest (RMS, PTV...)? What is the risk for a parameter to be over tolerance? For addressing those issues, the Xonox X-fringe® interferometry software is fitted with an advanced "Average Statistics" function. Reading a given number of phase data maps, the function computes the average phase map and estimates the significant statistical characteristics of the turbulence, namely its space and time auto-correlation function (ACF), as well as the ACF of the sample average. The latter provides a covariance matrix, applied to Monte-Carlo random trial simulations. On each of those random trials, a parameter of interest is computed. For a high number of trials, the frequency histogram of this parameter tends towards its probability density. Finally, this density yields confidence intervals of the parameter (i.e., uncertainty with a confidence level), and above all, the risk that the parameter could be over tolerance. The user can create templates defining, for a given set of Zernike, the parameter of interest (PTV, RMS, Strehl), or that of the residual wavefront. The software evaluates the signal-to-noise ratio and the measurement reliability.
