  Training autonomous vehicles requires lots of driving sequences in all
situations\cite{zhao2016}. Typically a simulation environment
(software-in-the-loop, SiL) accompanies real-world test drives to
systematically vary environmental parameters. A missing piece in the optical
model of those SiL simulations is the sharpness, given in linear system theory
by the point-spread function (PSF) of the optical system. We present a novel
numerical model for the PSF of an optical system that can efficiently model
both experimental measurements and lens design simulations of the PSF. The
numerical basis for this model is a non-linear regression of the PSF with an
artificial neural network (ANN). The novelty lies in the portability and the
parameterization of this model, which allows to apply this model in basically
any conceivable optical simulation scenario, e.g. inserting a measured lens
into a computer game to train autonomous vehicles. We present a lens
measurement series, yielding a numerical function for the PSF that depends only
on the parameters defocus, field and azimuth. By convolving existing images and
videos with this PSF model we apply the measured lens as a transfer function,
therefore generating an image as if it were seen with the measured lens itself.
Applications of this method are in any optical scenario, but we focus on the
context of autonomous driving, where quality of the detection algorithms
depends directly on the optical quality of the used camera system. With the
parameterization of the optical model we present a method to validate the
functional and safety limits of camera-based ADAS based on the real, measured
lens actually used in the product.
