Optical metrology to support the next generation of nanopositioning

Abstract

This thesis develops methods for the analysis and elimination of non-linearities, defined as errors in the measured displacement that are periodic with some harmonic of the illuminating wavelength, in homodyne displacement measuring optical interferometers. A particular focus is placed on phase-quadrature coating based interferometers. A novel modelling technique is described, allowing the effects of cavity formation within networks of polarising optics to be analysed. This modelling technique is applied to investigate the sources higher order non-linearities introduced by unwanted cavity formation within the optics of the NPL plane plane mirror differential interferometer. Some non-linearities may be eliminated through improved optical design, however, this is not always possible, or practical. Three novel correction algorithms are therefore proposed, aiming to correct for non-linearities in situations where existing correction algorithms fail. The first, the two-wavelength non-linearity correction aims to correct for higher order non-linearities in cases where the displacement covers several optical fringes. Compared to a standard Heydemann ellipse fitting correction, the two-wavelength approach is shown to reduce estimated residual non-linearity amplitude from 84 pm to 11 pm. The second algorithm, the multiple intensity reference correction, aims to correct for non-linearities in cases where the displacement covers a small portion of the optical fringe. This algorithm is shown to reduce the amplitude of elliptical non-linearity harmonics to below the 10 pm level. Finally, the measurement arm normalisation correction also aims to correct for certain sources of higher order non-linearities, but reduced optical, electrical and data processing complexity as compared to the two-wavelength correction. Based on the findings of modelling work in combination with experimental non-linearity measurements, an improvement to an existing NPL interferometer design, utilising the measurement arm normalisation correction, is developed and tested. Peak-to-peak residual non-linearities of (23:0 ± 0:6) pm are achieved, reduced from (56:8 ± 0:4) pm by application of the measurement arm normalisation algorithm.