Jan Schäfer

Light scattering by multiple spheres: comparison between Maxwell theory and radiative-transfer-theory calculations

We present a methodology to compare results of classical radiative transfer theory against exact solutions of Maxwell theory for a high number of spheres. We calculated light propagation in a cubic scattering region (20 x 20 x 20 microm(3)) consisting of different concentrations of polystyrene spheres in water (diameter 2 microm) by an analytical solution of Maxwell theory and by a numerical solution of radiative transfer theory. The relative deviation of differential as well as total scattering cross sections obtained by both approaches was evaluated for each sphere concentration. For the considered case, we found that deviations due to radiative transfer theory remain small, even for concentrations up to ca. 20 vol. %.

Multiple scattering of polarized light: comparison of Maxwell theory and radiative transfer theory

For many research areas in biomedical optics, information about scattering of polarized light in turbid media is of increasing importance. Scattering simulations within this field are mainly performed on the basis of radiative transfer theory. In this study a polarization sensitive Monte Carlo solution of radiative transfer theory is compared to exact Maxwell solutions for all elements of the scattering Müller matrix. Different scatterer volume concentrations are modeled as a multitude of monodisperse nonabsorbing spheres randomly positioned in a cubic simulation volume which is irradiated with monochromatic incident light. For all Müller matrix elements effects due to dependent scattering and multiple scattering are analysed. The results are in overall good agreement between the two methods with deviations related to dependent scattering being prominent for high volume concentrations and high scattering angles.

Scattering of light by multiple dielectric cylinders: comparison of radiative transfer and Maxwell theory

We have compared radiative transfer theory with analytical solutions of the Maxwell equations for light scattering by multiple infinitely long parallel cylinders at perpendicular incidence. The calculated scattering cross sections for both methods show large differences, but the angle-dependent differential scattering cross-section results are very similar for small cylinder densities, except close to the forward direction. In contrast to recently published results, it is shown that the radiative transfer equation is a useful approximation for small cylinder concentrations.

Simulating the scanning of a focused beam through scattering media using a numerical solution of Maxwell’s equations

Abstract. A highly efficient method based on Maxwell’s theory was developed, which enables the calculation of the scanning of a focused beam through scattering media. Maxwell’s equations were numerically solved in two dimensions using finite difference time domain simulations. The modeling of the focused beam was achieved by applying the angular spectrum of plane waves method. The scanning of the focused beam through the scattering medium was accomplished by saving the results of the near field obtained from one simulation set of plane waves incident at different angles and by an appropriate post processing of these data. Thus, an arbitrary number of focus positions could be simulated without the need to further solve Maxwell’s equations. The presented method can be used to efficiently study the light propagation of a focused beam through scattering media which is important, for example, for different kinds of scanning microscopes.

Comparison of Monte Carlo simulations with exact Maxwell solutions for polarized light scattering by multiple absorbing spheres

The goal of this study was to investigate the differences between radiative transfer theory and Maxwell theory for simulation of light propagation in a turbid medium. Polarization effects as well as absorbing scatterers with complex index of refraction are taken into account. The simulation volume contained different numbers of scattering and absorbing spheres (radius: 1 μm) and was irradiated from one side with a plane electromagnetic wave (λ = 600 nm). The absorption was varied as well as the concentration of the scatterers. The resulting 16 Muller matrix elements were compared for the Monte Carlo method as well as for the Maxwell method for all scattering angles. An increasing absorption of the spheres resulted in larger differences especially for the intensity results (M11 Muller matrix element) between the two solution methods, while increasing scatterer concentrations led generally to larger differences for all Muller matrix elements. That means that the results of radiative transfer theory have to be treated with care for high scatterer concentrations and large absorption. By using the presented method, differences between the two theories can be investigated for arbitrary particle size parameters (spheres) and optical properties of the scatterers.

Simulated and measured optical coherence tomography images of human enamel.

Optical coherence tomography images of human enamel were simulated and compared to measured images. A Monte Carlo code was implemented, which considered the microstructure of enamel. The prisms, the main scattering structures of the enamel, were described by oscillating cylinders whose scattering functions were obtained by solutions of Maxwells equations. The essential features of the measured images including the Hunter-Schreger bands could be explained by the simulations.

Comparison of Monte Carlo simulations of polarized light propagation in turbid media with exact Maxwell solutions

A Monte Carlo program for simulation of polarized light propagation in scattering media was developed. By comparing the results of this program (angularly resolved independent Müller matrix elements S11, S21, S34 and S44) with analytical solutions of Maxwell equations, a testing method for Monte Carlo programs simulating polarized light propagation was found. A further goal was to quantitatively point out the differences between solutions of radiative transfer theory and Maxwell theory for polarized light.

Multiscale Description of Light Propagation in Biological Tissue

A multiscale description of the light propagation in biological tissue is presented. The Maxwell’s equations, the transport equation, and the diffusion equation are applied for the description on the microscopic, mesoscopic, and macroscopic scale, respectively. The modus operandi of the multiscale approach is illustrated for the case of tendon tissue. It is shown that the aligned microstructure of tendon strongly influences the light propagation in the tissue.

FDTD-Simulation of Multiple Light Scattering in Dentin

A two-dimensional finite difference time domain software has been developed to simulate light propagation in biological tissue. The phase functions of dentin slabs of various thicknesses were calculated, predicting the appearance of an interference peak.

Parallel FDTD Simulation of the Scattering of Light in Media Containing Cylindrical Scatterers

We have implemented a parallel two-dimensional finite difference time domain (FDTD) method to investigate the propagation of light in biological tissue. In particular we want to examine the dependence of the light propagation on the microstructure of tissue containing cylindrical scatterers. Therefore we performed simulations for a series of various tissue models of randomly distributed cylinders embedded in dielectric media with varying cylinder concentrations and tissue probe thickness.