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

Abstract

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.

Reconstruction of refractive index maps using photogrammetry

“…A photogrammetry system's ability to measure accurately depends on many factors including the ability to take into account atmospheric effects such as temperature, pressure, refractive index and humidity [10,11]. If we extend the measured volume to that of an industrial setting, we must address light refraction due to temperature variations within the volume; a factory environment does not have a constant temperature as machines and operators emit heat.…”

“…This therefore means that the first-order approximation which says that rays of light move in straight lines are not applicable [5]. This bending of light rays introduces errors in the received measurements (that is, the angle measurements of the photogrammetry system) and consequently, as the volume measured increases, these errors grow and can severely affect the accuracy of the co-ordinate positioning [10]. Accounting for the refractive index effects is a key step to improving the accuracy and quantifying uncertainties.…”