Uncertainty evaluation of a fiber-based interferometer for the measurement of absolute dimensions

The evaluation of the measurement uncertainty of a robust all-fiber-based low-coherence interferometer for the measurement of absolute thickness of transparent artifacts is described. The performance of the instrument is evaluated by measuring the length of air-gaps in specially constructed artifacts and the observed measurement errors are discussed in the context of the uncertainty associated with them. A description of the construction of the artifacts is presented, accompanied by an uncertainty analysis to estimate the uncertainty associated with the artifacts. This analysis takes into account the dimensional uncertainty of the artifacts (including wringing effects), thermal effects, and effects of the environment on refractive index. The ‘out-of-the-box’ performance of the instrument is first evaluated. A maximum error of 350 nm for an air-gap of 10.1 mm is observed. A linear trend between the measured length and the error is also observed. The relative magnitude of the errors and the uncertainty associated with the error suggests that this trend is real and that a performance enhancement can be expected by mapping the error. Measurements of the artifacts are used to develop an error map of the instrument. The uncertainty associated with the predicted error is determined based on the uncertainty associated with the error. This analysis suggests that the uncertainty in the predicted error at the 2σ level may be conservatively estimated to be (2.9L+37.5) nm, where L is in units of mm.