Interferometric technique for microstructure metrology using an index matching liquid

Non-null interferometry offers a viable alternative to traditional interferometric testing of aspheric micro-lenses since computer generated holograms or null optics whose fabrication and testing are very expensive, are not required. However, due to the violation of the Nyquist sampling theorem these non-null tests provide limited dynamic range. The dynamic range of these non-null tests can be extended by implementing an index liquid which allows the measurement of micro-lenses with several microns of departure from a sphere. The first objective of this dissertation was to test important micro-lens properties such as the sag, radius of curvature and form errors for a micro-lens by using an index liquid. The results compared favorably to measurements taken on a Twyman-Green interferometer, a contact profilometer and an optical non-contact profilometer. Also, retrace errors, which are aberrations caused by altered ray paths of the test beam through a micro-lens were investigated. Reverse ray-trace and reverse optimization techniques are typically used to calibrate retrace errors, but in depth knowledge of the interferometer optics is assumed, and hence cannot be used for systems containing commercial optics. In this dissertation, re-trace errors are quantified and a novel calibration procedure derived to experimentally compensate for these errors. This retrace error calibration led to agreement of within 1% for the sag values between the index liquid technique and a profilometer. The second objective of this dissertation was to enable measurements of arbitrary geometries and to reduce testing time compared to profilometry. The index liquid technique was applied to faceted microstructured optical products which are becoming more widespread due to advances in manufacturing. Many of these structures contain faceted surfaces with steep slopes. Adequate metrology for such surfaces is lacking. The use of the index liquid technique achieved high quality, high speed measurements of such faceted microstructures. Refraction is accounted for at the interfaces, rather than consider only optical path length changes due to the index liquid, and this significantly improves the facet angle measurement. The technique is demonstrated with the measurement of an array of micro-pyramids and show that our results are in good agreement with measurements taken on a contact profilometer. The index liquid measurements took approximately five seconds to complete compared to a measurement time of six hours for the contact profilometer. The technique was also extended to measure opaque micro-corner cubes by implementing an intermediate replication step. This allowed a measurement of the angle between facets of a nickel micro-corner cube hexagonal array, a combination not previously demonstrated in the literature. A first order uncertainty analysis was carried out on the index liquid technique to determine any limiting factors that need to be taken into account when assessing such parameters as the sag and facet angle. The uncertainties in the sag and facet angle were found to be well below 1%. Lastly secondary factors such interferometer bias, refraction, masking effects and pixel calibration were investigated to understand the possible implications on the sag and facet angle calculation.