André Liemert
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View article: Hybrid Method for Solving the Radiative Transport Equation
Hybrid Method for Solving the Radiative Transport Equation Open
The spherical harmonics method (PN 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 so…
View article: Impact of Multi-Scattered LiDAR Returns in Fog
Impact of Multi-Scattered LiDAR Returns in Fog Open
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 phy…
View article: An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations
An Integral-Equation-Based Variance Reduction Method for Accelerated Monte Carlo Simulations Open
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 offe…
View article: Two-layered blood-lipid phantom and method to determine absorption and oxygenation employing changes in moments of DTOFs
Two-layered blood-lipid phantom and method to determine absorption and oxygenation employing changes in moments of DTOFs Open
Near-infrared spectroscopy (NIRS) is an established technique for measuring tissue oxygen saturation (StO 2 ), which is of high clinical value. For tissues that have layered structures, it is challenging but clinically relevant to obtain S…
View article: Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Validations, Second Edition
Light Propagation through Biological Tissue and Other Diffusive Media: Theory, Solutions, and Validations, Second Edition Open
This second edition is completely revised and improved and contains eight new chapters and six new appendixes. In addition to the theoretical background on light propagation through diffusive media, this update also provides new didactical…
View article: Back Matter
Back Matter Open
Diffusive-diffusive interfaces, 129, 592 Diffusive-non-scattering interfaces, 124, 589 Boundary conditions for the diffusion equation, 124 Boundary conditions for the radiative transfer equation, 51 Closed-form solutions, 422 Comparisons M…
View article: Single scattering models for radiative transfer of isotropic and cone-shaped light sources in fog
Single scattering models for radiative transfer of isotropic and cone-shaped light sources in fog Open
The simulation of rare edge cases such as adverse weather conditions is the enabler for the deployment of the next generation of autonomous drones and vehicles into conditions where human operation is error-prone. Therefore, such settings …
View article: Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source
Semianalytical solution for the transient temperature in a scattering and absorbing slab consisting of three layers heated by a light source Open
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 w…
View article: Determination of the optical properties of three-layered turbid media in the time domain using the P<sub>3</sub> approximation
Determination of the optical properties of three-layered turbid media in the time domain using the P<sub>3</sub> approximation Open
The inverse problem in three-layered scattering media is investigated using simulations. Instead of using the common diffusion approximation, the light propagation is modeled using the spherical harmonics ($P_N$PN) approximation in the tim…
View article: Spatial frequency domain imaging using an analytical model for separation of surface and volume scattering
Spatial frequency domain imaging using an analytical model for separation of surface and volume scattering Open
A method to correct for surface scattering in spatial frequency domain imaging (SFDI) is presented. The use of a modified analytical solution of the radiative transfer equation allows calculation of the reflectance and the phase of a rough…
View article: Fractional Schrödinger Equation in the Presence of the Linear Potential
Fractional Schrödinger Equation in the Presence of the Linear Potential Open
In this paper, we consider the time-dependent Schrödinger equation: i ∂ ψ ( x , t ) ∂ t = 1 2 ( − Δ ) α 2 ψ ( x , t ) + V ( x ) ψ ( x , t ) , x ∈ R , t > 0 with the Riesz space-fractional derivative of order 0 < α ≤ 2 in the presence of th…
View article: Quantifying phase function influence in subdiffusively backscattered light
Quantifying phase function influence in subdiffusively backscattered light Open
Light backscattering at short source-detector separations is considerably influenced by the scattering phase function of a turbid medium. We seek to more precisely relate a medium's subdiffusive backscattering to the angular scattering cha…