This article [J. Biomed. Opt.. 19, , 071404 (2014)] was originally published online on 6 January 2014 with Figs. 2 and 3 reversed, though the captions were correct. The corrected figures and captions are reprinted below.
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.
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.
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.
Propagation of light in a cubic scattering region containing different concentrations of polystyrene spheres in
water was calculated. Therefore an analytical solution of Maxwell theory was applied, as well as a numerical
solution of radiative transfer theory. Apart from differences in the calculated differential scattering cross sections
at small and large scattering angles, a comparison of both methods showed only small deviations for almost the
whole angle range. This indicates the usefulness of radiative transfer theory for concentrations up to 20% as a
fast approximative method to describe multisphere scattering.
We implemented a two-dimensional finite-difference time-domain (FDTD) method for the calculation of the
scattering by turbid slabs containing cylindrical scatterers. We present validation results of the FDTD method
used for the calculation of the scattering by an infinite dielectric cylinder. In particular the error caused by
numerical dispersion due to an expansion of the simulation grid is discussed. Finally, an analytical solution of
the scattering by an infinite cylinder has been used to analyze the error caused by the discrete near- to far-field
transformation.
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