Deep neural networks for computational optical form measurements

Abstract

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.

Uncertainty Quantification by Ensemble Learning for Computational Optical Form Measurements

“…[7], [11] or [19]). Therefore, we chose the U-Net as network architecture similar to [18]. An example of the network structure is shown in Figure 4.…”

“…In total, almost 40, 000 (virtual) topogaphies are generated for training and about 2, 000 are generated for testing. The mean root mean squared deviation to the design In [18], the training data were generated without including reference planes to the model of the optical system, and simulated data were considered constructed under the assumption of a perfect model for the optical system. In this paper, systematic investigations on the impact of calibration errors are carried out.…”

“…The novelty of the paper is twofold. First, we extend a previous deep learning approach for this application [18] to incorporate an uncertainty quantification of its predictions. This is achieved through ensemble learning.…”

“…This is achieved through ensemble learning. In contrast to [18], the networks are trained on a calibrated data set which will be discussed in more detail later. Second, we systematically insert an increasing out-of-distribution calibration error into the system and analyze its effect on the reliability of the developed uncertainty quantification.…”

A framework for benchmarking uncertainty in deep regression

“…Examples comprise the diagnosis of cancer [1], autonomous driving [2] or language processing [3,4]. Physical and engineering sciences also benefit increasingly from deep learning and current applications range from optical form measurements [5] over image quality assessment in mammography [6,7] or medical imaging in general [8] to applications in weather forecasts and climate modeling [9,10].…”