In the context of autonomous driving, the augmentation of existing data through simulations provides an elegant solution to the challenge of capturing the full range of adverse weather conditions in training datasets. However, existing physics-based augmentation models typically rely on single scattering approximations to predict light propagation under unfavorable conditions, such as fog. This can prevent the reproduction of important signal characteristics encountered in a real-world environment. Consequently, in this work, Monte Carlo simulations are employed to assess the relevance of multiple-scattered light to the detected LiDAR signal in different types of fog, with scattering phase functions calculated from Mie theory considering real particle size distributions. Bidirectional path tracing is used within the self-developed GPU-accelerated Monte Carlo software to compensate for the unfavorable photon statistics associated with the limited detection aperture of the LiDAR geometry. To validate the Monte Carlo software, an analytical solution of the radiative transfer equation for the time-resolved radiance in terms of scattering orders is derived, thereby providing an explicit representation of the double-scattered contributions. The results of the simulations demonstrate that the shape of the detected signal can be significantly impacted by multiple-scattered light, depending on LiDAR geometry and visibility. In particular, double-scattered light can dominate the overall signal at low visibilities. This indicates that considering higher scattering orders is essential for improving AI-based perception models.

In this work, we introduce a novel variance reduction approach utilising the integral formulation of the radiative transfer equation to calculate the radiance in a planar symmetric slab geometry. Due to its integral nature, our method offers a fundamental advantage over well-established variance reduction methods such as the local estimate technique. As opposed to the local estimate procedure, photons add to the overall radiance not only at specific points of interaction but also throughout each consecutive path element; hence, our variance reduction approach can be thought of as an integral local estimate method. This facilitates a substantial enhancement in statistical efficiency, especially in scenarios where only a small number of scattering events or a high attenuation along the detection paths is to be anticipated. To evaluate the overall performance of the integral approach, we incorporated it into a self-developed GPU-accelerated Monte Carlo software, together with a conventional local estimate implementation adapted to slab geometry for a comprehensive comparison.

We derived a semianalytical solution for the time-dependent temperature distribution in a three-layered laterally infinite scattering and absorbing slab illuminated by an obliquely incident collimated beam of light. The light propagation was modeled by the low-order $$P_1$$P 1 and $$P_3$$P 3 approximations to the radiative transfer equation with closed form expressions for eigenvalues and eigenvectors, yielding a quickly computable solution, while the heat conduction was modeled by the Fourier equation. The solution was compared to a numerical solution using a Monte Carlo simulation for the light propagation and an FEM method for the heat conduction. The results showed that using the $$P_3$$P 3 solution for the light propagation offers a large advantage in accuracy with only a moderate increase in calculation time compared to the $$P_1$$P 1 solution. Also, while the $$P_3$$P 3 solution is not a very good approximation for the spatially resolved absorbance itself, its application as a source term for the heat conduction equation does yield a very good approximation for the time-dependent temperature.

The spherical harmonics method ($P_N$ method) is often used for solving the radiative transport equation in terms of analytical functions. A severe and unsolved problem in this context was the evaluation of the angle-resolved radiance near sources and boundaries, which is a serious limitation of this method in view of concrete applications, e.g., in biomedical optics for investigating the different types of optical microscopy, within NIR spectroscopy, such as for the determination of ingredients in foods or in pharmaceuticals, and within physics-based rendering. In this article, we report on a hybrid method that enables accurate evaluation of the angle-resolved radiance directly at the boundary of an anisotropically scattering medium, avoiding the problems of the traditional $P_N$ methods. The derived integral equation needed for the realization of the hybrid $P_N$ method is formally valid for an arbitrary convex bounded medium. The proposed approach can be evaluated with practically the same computational effort as the traditional $P_N$ method while being far more accurate.

Wavefront shaping is a well-known method of restoring a focus deep within scattering media by manipulating the incident light. However, the achievable focus enhancement depends on and is limited by the optical and geometrical properties of the medium. These properties contribute to the number of linearly independent transmission channels for light propagating through the turbid medium. Correlations occur when the number of incident waves coupled into the scattering medium exceeds this finite number of transmission channels. This paper investigates the wavefront shaping of such correlated electric fields. The influence of the observed correlations persists even though the average electric field distribution at positions in the focal plane follows a circular complex Gaussian. We show that correlations of the transmitted electric fields reduce the achievable intensity enhancement, even deep in the turbid medium. The investigations are carried out using a Monte Carlo algorithm. It is based on the speckle statistics of independent waves and introduces correlations of neighbouring electric fields via a Cholesky decomposition of the covariance matrix. Additional investigations include scenarios where the electric fields are not completely randomized, such as for ballistic or insufficiently scattered light. Significant contributions from such little-scattered light are observed to reduce the intensity enhancement further. Data from simulations solving Maxwell’s equations are compared with the results obtained from the Monte Carlo simulations for validation throughout this paper.

Lidar systems are of major importance for driver assistance systems and autonomous driving, but their obstacle detection range can be heavily impaired by adverse weather conditions like fog. To mitigate the effects of fog, the use of polarized light has been proposed. We simulated a polarized lidar system, taking Mie theory-based scattering functions for different fog types at several wavelengths into account, and investigated the possible increase in contrast between fog backscattering and target returns for different surface types, depending on the target orientation and the polarizer configuration. Fog is modeled as an infinite, homogeneous, scattering, and absorbing medium. The simulated detector registers the time-dependent radiance, resolved by scattering order. Our findings show that the suitable choice of illumination and detection polarization allows the amount of single-scattered light detected to be reduced by two to four orders of magnitude and the contrast between fog and target to be increased significantly. Crucially, this approach delivers robust contrast enhancement regardless of whether the target surface is depolarizing Lambertian or perfectly reflecting.