Contribution of the Refractive Index Fluctuations to the Length Noise in Displacement Interferometry

We report on investigations of how fast changes of the refractive index influence the uncertainty of interferometric displacement measurements. Measurement of position within a limited range is typical for precise positioning of coordinate measuring systems, such as nanometrology standards combined with scanning probe microscopy (SPM). The varying refractive index of air contributes significantly to the overall uncertainty; it plays a role especially in case of longer-range systems. In our experiments we have observed that its fast variations, seen as length noise, are not linearly proportional to the measuring beam path and play a significant role only over distances longer than 50 mm. Thus, we found that over longer distances the length noise rises proportionally. The measurements were performed under conditions typical for metrology SPM systems.