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Uncertainty quantification by ensemble learning is explored in terms of an application known from the field of computational optical form measurements. The application requires solving a large-scale, nonlinear inverse problem. Ensemble learning is used to extend the scope of a recently developed deep learning approach for this problem in order to provide an uncertainty quantification of the solution to the inverse problem predicted by the deep learning method. By systematically inserting out-of-distribution errors as well as noisy data, the reliability of the developed uncertainty quantification is explored. Results are encouraging and the proposed application exemplifies the ability of ensemble methods to make trustworthy predictions on the basis of high-dimensional data in a real-world context.

Abstract. Deep neural networks have been successfully applied in many different fields like computational imaging, healthcare, signal processing, or autonomous driving. In a proof-of-principle study, we demonstrate that computational optical form measurement can also benefit from deep learning. A data-driven machine-learning approach is explored to solve an inverse problem in the accurate measurement of optical surfaces. The approach is developed and tested using virtual measurements with a known ground truth.

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