Investigation into the limitations of straightness interferometers using a multisensor-based error separation method

Abstract

The uncertainty of a straightness interferometer is independent of the component used to introduce the divergence angle between the two probing beams, and is limited by three main error sources, which are linked to each other: their resolution, the influence of refractive index gradients and the topography of the straightness reflector. To identify the configuration with minimal uncertainties under laboratory conditions, a fully fibre-coupled heterodyne interferometer was successively equipped with three different wedge prisms, resulting in three different divergence angles (4°, 8° and 20°). To separate the error sources an independent reference with a smaller reproducibility is needed. Therefore, the straightness measurement capability of the Nanometer Comparator, based on a multisensor error separation method, was improved to provide measurements with a reproducibility of 0.2 nm. The comparison results revealed that the influence of the refractive index gradients of air did not increase with interspaces between the probing beams of more than 11.3 mm. Therefore, over a movement range of 220 mm, the lowest uncertainty was achieved with the largest divergence angle. The dominant uncertainty contribution arose from the mirror topography, which was additionally determined with a Fizeau interferometer. The measured topography agreed within ±1.3 nm with the systematic deviations revealed in the straightness comparison, resulting in an uncertainty contribution of 2.6 nm for the straightness interferometer.