Resolution and accuracy of nonlinear regression of point spread function with artificial neural networks

Matthias Lehmann; Christian Wittpahl; Hatem Ben Zakour; Alexander Braun

doi:10.1117/1.OE.58.4.045101

9 April 2019 Resolution and accuracy of nonlinear regression of point spread function with artificial neural networks

Matthias Lehmann, Christian Wittpahl, Hatem Ben Zakour, Alexander Braun

Author Affiliations +

Optical Engineering, Vol. 58, Issue 4, 045101 (April 2019). https://doi.org/10.1117/1.OE.58.4.045101

Abstract

We had already demonstrated a numerical model for the point spread function (PSF) of an optical system that can efficiently model both the experimental measurements and the lens design simulations of the PSF. The novelty lies in the portability and the parameterization of this model, which allow for completely new ways to validate optical systems, which is especially interesting not only for mass production optics such as in the automotive industry but also for ophthalmology. The numerical basis for this model is a nonlinear regression of the PSF with an artificial neural network (ANN). After briefly describing both the principle and the applications of the model, we then discuss two optically important aspects: the spatial resolution and the accuracy of the model. Using mean squared error (MSE) as a metric, we vary the topology of the neural network, both in the number of neurons and in the number of hidden layers. Measurement and simulation of a PSF can have a much higher spatial resolution than the typical pixel size used in current camera sensors. We discuss the influence this has on the topology of the ANN. The relative accuracy of the averaged pixel MSE is below ^{10 − 4}, thus giving confidence that the regression does indeed model the measurement data with good accuracy. This article is only the starting point, and we propose several research avenues for future work.

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Matthias Lehmann, Christian Wittpahl, Hatem Ben Zakour, and Alexander Braun "Resolution and accuracy of nonlinear regression of point spread function with artificial neural networks," Optical Engineering 58(4), 045101 (9 April 2019). https://doi.org/10.1117/1.OE.58.4.045101

Received: 19 August 2018; Accepted: 19 March 2019; Published: 9 April 2019

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