Coupled distance sensor systems for high-accuracy topography measurement: Accounting for scanning stage and systematic sensor errors

Scanning topography measurements using systems of coupled distance sensors suffer from the presence of scanning stage and systematic sensor errors. While scanning stage errors can be estimated for suitably-designed sensor systems, it is usually not possible to simultaneously estimate both scanning stage and systematic sensor errors. Additional angular scanning stage measurements can solve this problem, and potentials and limitations of such a proceeding will be assessed. shown that perfect topography reconstruction can be achieved in the presence of systematic sensor and certain scanning stage errors provided that the measurements are noise-free and no further systematic errors emerge. In general, the topography is reconstructed by the application of least-squares, and the uncertainty associated with the reconstructed topography is derived. Resulting topography accuracies are evaluated for different noise levels of the distance sensor and angular scanning stage measurements, and practical considerations are discussed. The gain in accuracy due to accounting for scanning stage and systematic sensor errors can be large, and high accuracies can be reached.