Surface shape determination with a stitching Michelson interferometer and accuracy evaluation

Stitching methods are increasingly used for determining the surface shape of large and high precision optical elements used in synchrotron beamlines. They consist in reconstructing the surface topography from multiple measurements on overlapping parts of the optics aperture by various algorithms. This paper is an attempt to investigate how true and accurate such a reconstruction can be. Error sources are identified and evaluated throughout the acquisition and processing steps. The analysis is based on the example SOLEIL Michelson interferometer for nano-topography, a dedicated measurement bench for stitching interferometry. We propose a method for determining the error made on the estimate of the interferometric reference surface from the stitching dataset. This determination is made before and independently of the stitching procedure itself.