Resolution and accuracy of non-linear regression of PSF with artificial neural networks

TL;DR

This paper investigates how the resolution and choice of error metrics affect the performance of neural network models for non-linear PSF regression, enhancing optical system validation methods.

Contribution

It analyzes the impact of spatial resolution and error metrics on ANN-based PSF modeling accuracy and topology, providing insights for improved optical system validation.

Findings

Higher resolution measurements influence ANN topology and performance.

Choice of error metric significantly affects model accuracy.

Modeling non-linear PSFs benefits from considering symmetries and spatial relations.

Abstract

In a previous work we have demonstrated a novel numerical model for the point spread function (PSF) of an optical system that can efficiently model both experimental measurements and lens design simulations of the PSF. The novelty lies in the portability and the parameterization of this model, which allows for completely new ways to validate optical systems, which is especially interesting for mass production optics like in the automotive industry, but also for ophtalmology. The numerical basis for this model is a non-linear regression of the PSF with an artificial neural network (ANN). In this work we examine two important aspects of this model: the spatial resolution and the accuracy of the model. Measurement and simulation of a PSF can have a much higher resolution then the typical pixel size used in current camera sensors, especially those for the automotive industry. We discuss the influence this has on on the topology of the ANN and the final application where the modeled PSF is actually used. Another important influence on the accuracy of the trained ANN is the error metric which is used during training. The PSF is a distinctly non-linear function, which varies strongly over field and defocus, but nonetheless exhibits strong symmetries and spatial relations. Therefore we examine different distance and similarity measures and discuss its influence on the modeling performance of the ANN.