The influence of diffraction in length-measuring imaging interferometers

To provide gauge blocks as SI-traceable primary length standards, they are measured using imaging interferometry. In this paper, we theoretically investigate the influence of diffraction in this context. The calculations consider a rectangular mirror located at a distance from the object plane within the measurement arm of an imaging interferometer. Both light propagation to the object plane and the optical imaging process are described by well known diffraction integrals in the Fresnel approximation and are calculated using Mathematica®. An approximation formula for the maximum effect of diffraction on lateral phase averages within suitable image regions is proposed. For experimental validation, length measurements were performed in a vacuum on a 35 mm long gauge block positioned at distances ranging from 0 to 400 mm from the object plane—using various sizes of imaging apertures. The key conclusion drawn from the quantitative theoretical and experimental investigations is that the diffraction effect in this context is well-controlled and negligible within the scope of the relevant measurement uncertainty for gauge block measurements.