A frequentistic and a bayesian approach for optimal optical filter design
This report discusses three merit functions to optimize optical interference filter coatings. The applications of these filters are intentionally optical 3D sensors, e.g. a chromatic confocal triangulation sensor. Optimizing these optical filters is done by minimizing the measurement uncertainty of the sensor. The measurement task is handled as a parameter estimation problem and the sensor is considered as a physical experiment. As part of the experimental design, the optical filters are optimized to achieve measurements with lower uncertainty. The first merit function is based on a frequentistic statistic utilizing the Cramér-Rao lower bound. An example is used to point out disadvantages and two alternative merit functions are proposed. Instead of a lower bound, the other merit functions incorporate a specific estimator function.