1 Introduction

With optical-infrared interferometry becoming more mature, the quality of visibility measurements have become an issue. Single-mode interferometers (see Sect. 2.3) allow one to eliminate non-stationary effects by filtering out the spatial modes of turbulence. The response of interferometers is therefore very stable and the issue of estimating the accuracies of non-biased data is raised. The final visibility estimate is a complex quantity as it is a non-linear mix of noisy measurements and of parameter estimates with their own uncertainties. Estimating the stability of the instrument, a crucial point for calibration, and the final error on visibilities is therefore non-trivial and must be considered with caution. Moreover, data analysis mainly consists of model fitting the final visibilities and the matter of their potential correlations becomes important, especially if some very faint structures are looked for, as is the case in extra-solar planet detection.

In this Paper I propose a method to meet these challenges. The method has been tested and elaborated along with the FLUOR interferometer, the first single-mode interferometer. This method was first published in Perrin (1996) and used in Perrin et al. (1998). It is updated and improved in this paper by accounting for correlations.