High-dimensional sensitivity analysis of complex optronic systems by experimental design: applications to the case of the design and the robustness of optical coatings
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We present the advantages of experimental design in the sensitivity analysis of optical coatings with a high number of layers by limited numbers of runs of the code. This methodology is effective in studying the uncertainties propagation, and to qualify the interactions between the layers. The results are illustrated by various types of filters and by the influence of two monitoring techniques on filter quality. The sensitivity analysis by experimental design of optical coatings is useful to assess the potential robustness of filters and give clues to study complex optronic systems. OCIS codes: 310.0310, 220.0220, 120.0120. doi: 10.3788/COL201008S1.0021. The study of complex optronic systems entails sensitivity analysis with a large number of parameters. Very often the response depends on synergies or interactions between these parameters. Due to interference characteristics of multilayer filters, optical coatings make possible the evaluation of methods that can explore highdimensional space parameters and the presence of interactions between parts of these parameters. For coatings production with a high number of layers, sensitivity analysis is an efficient way to determine the most critical layers of an optical coating [1] . Refractive index errors or thickness errors during the manufacturing of these layers can induce dramatic consequences on the desired optical properties [2] . We present the advantages of using the method of experimental design [3] , which is used for metamodel constructions and high-dimensional code explorations with limited numbers of runs of the code, particularly in the case of coatings with a high number of layers. This methodology is more effective in studying uncertainties propagation (refractive index or thickness values) to determine the influence of errors on the optical properties, and to quantify the interactions between the errors of each layer. The results are illustrated by various types of filters, particularly bandpass filters and multiple halfwave filters. Different designs such as factorial, fractional factorial, and space-filling designs are used to present the results. Furthermore, we study the influence of two monitoring techniques, and show the most critical coating layers and the dependency of these layers with future manufacturing. The results show that the study of thin-film filters is very useful in examining the interactions of highdimensional systems due to the filter’s adjustable number of layers, and the existence of interactions between these layers. Finally, we demonstrate that sensitivity analysis of optical coatings by experimental design is useful in assessing the potential robustness of filters, and gives clues to study complex optronic systems. The codes to study complex phenomena become more and more realistic with a larger input data set. However, due to the complexity of the mathematical system underlying the computer simulation tools, there are often no explicit input-output formulas. Although computer power has significantly increased in the past years, the evaluation of a particular setting of the design parameters may still be very time-consuming. The simulator is often replaced by a metamodel to approximate the relationship between the code and the design parameters. These metamodels are built using numerical designs of experiments that can indicate interactions between the parameters. The choice of an underlying empirical model (depending on accuracy and interactions level) can be written as Y = Cste + ∑ i biXi + ∑ i
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