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.

The increasing use of colored materials in 3D printing enables the creation of complex structures with realistic color appearances. Ensuring that the printed colors match the design requires advanced rendering methods to accurately predict the final product. We use a fully optical property-based pipeline for rendering the physically correct color of 3D-printed objects, achieving results nearly indistinguishable compared to the final printed samples. Our approach is based entirely on the intrinsic optical properties of the printing materials: the reduced scattering coefficient, absorption coefficient, refractive index, and scattering anisotropy factor. First, we employed an integrating sphere setup to measure the spectrally resolved absorption and reduced scattering coefficients of the base materials. This method was extended to handle both highly scattering and nearly non-scattering materials with precision. Next, a spectral Monte Carlo path tracing simulation was used to compute light transfer through the printed object, fully modeling the physics of light propagation in heterogeneous turbid media. Our results achieved CIE Δ E ₂₀₀₀ values below 2.0, with renderings accurately reproducing the colors of the specially designed validation samples printed using a Stratasys PolyJet system. This pipeline provides a robust tool for predicting and optimizing the color appearance of 3D-printed objects. It offers broad applicability across various printing systems and material compositions while eliminating the need for time- and cost-intensive trial-and-error test prints.

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.

Accurately recreating the appearance of translucent materials poses a substantial challenge in physically based rendering, primarily due to limitations in capturing complex light transport, especially subsurface scattering. Current methods often rely on approximations of radiative transfer theory and lack detailed characterization of material optical properties, limiting physical accuracy. Here, we introduce a comprehensive workflow that captures the full physical complexity needed to achieve true physical fidelity in translucent object rendering. Using a calibrated photo box environment, we validate our approach by comparing rendered scenes to their physical counterparts. Across a range of test materials, from silicon phantoms to everyday media like milk, our results show imperceptible color deviations, with ΔE values consistently below 1. By bridging the gap between real-world light behavior and digital simulations, our method enhances predictive rendering realism, paving the way for precise digital representations in medical and technical applications.

Optical diagnostic techniques represent an attractive complement to conventional pulp vitality tests, as they can provide direct information about the vascular status of the pulp. However, the complex, multi-layered structure of a tooth significantly influences the detected signal and, ultimately, the diagnostic decision. Despite this, the impact of the various dental components on light propagation within the tooth, particularly in the context of diagnostic applications, remains insufficiently studied. To help bridge this gap and potentially enhance diagnostic accuracy, this study employs digital optical twins based on the Monte Carlo method. Using incisor and molar models as examples, the influence of tooth and pulp geometry, blood concentration, and pulp composition, such as the possible presence of pus, on spectrally resolved transmission signals is demonstrated. Furthermore, it is shown that gingival blood absorption can significantly overlay the pulpal measurement signal, posing a substantial risk of misdiagnosis. Strategies such as shifting the illumination and detection axes, as well as time-gated detection, are explored as potential approaches to suppress interfering signals, particularly those originating from the gingiva.