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ABSTRACT: A semi-infinite space Green's function of the time-dependent radiative transfer equation is derived based upon an exact solution for anisotropic scattering in infinite space and the approximated extrapolated boundary condition. The obtained solution is compared to Monte Carlo simulations and used for retrieving the optical parameters of simulated data in a nonlinear fit. It is shown that the solution performs well for boundaries with mismatched refractive indices. The relative errors in the fitted optical parameters are considerably smaller than by using the diffusion theory.
Journal of Biomedical Optics 01/2013; 18(1):15001. · 3.16 Impact Factor
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ABSTRACT: A darkfield scattering microscope has been constructed that enables both angular and spectrally resolved measurements of elastic scattering patterns. The comparison of the angular and spectral resolution modes is shown in detail. Angular patterns of the backscattered light by homogeneous polystyrene spheres were measured at 57 wavelengths and the diameters of the single spheres were determined by using Mie theory at each wavelength. The mean diameter values were estimated in the angular mode with a relative standard deviation of 0.25% or less. Spectral scattering patterns of the same beads were investigated and the diameters were determined and compared with the results of the angular measurements. The estimated diameter values in the angular and the spectral mode were in an excellent agreement with deviations of less than 0.20%.
Journal of Biomedical Optics 11/2012; 17(11):117006. · 3.16 Impact Factor
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ABSTRACT: The three-dimensional radiative transfer equation is solved in the spatial frequency domain for modeling the light propagation due to a spatially modulated light source obliquely incident on a semi-infinite uniform medium. The dependence of the derived solution on the spatial frequencies as well as on position and direction is found analytically. The main computational procedure arises from the determination of several constants obtained by a system of linear equations. The obtained equations are verified and illustrated by comparisons with Monte Carlo simulations and the diffusion approximation, respectively.
Optics Letters 10/2012; 37(19):4158-60. · 3.40 Impact Factor
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ABSTRACT: The time-dependent radiative transport equation is solved for the three-dimensional spatially uniform infinite medium which is illuminated by a point unidirectional source using a spherical harmonics transform under rotation. Apart from the numerical evaluation of a spherical Hankel transform which connects the spatial distance with the radial distance in Fourier space, the dependence on all variables is found analytically. For the special case of a harmonically modulated source, even the spherical Hankel transform can be carried out analytically. Additionally, a special solution for the isotropically scattering infinite medium is given. The Monte Carlo method is used for a successful verification of the derived solution.
Physical Review E 09/2012; 86(3-2):036603. · 2.26 Impact Factor
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ABSTRACT: 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 Maxwell's equations. The essential features of the measured images including the Hunter-Schreger bands could be explained by the simulations.
Optics Letters 08/2012; 37(15):3246-8. · 3.40 Impact Factor
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ABSTRACT: The three-dimensional radiative transfer equation is solved for modeling the light propagation in anisotropically scattering semi-infinite media such as biological tissue, considering the effect of internal reflection at the interfaces. The two-dimensional Fourier transform and the modified spherical harmonics method are applied to derive the general solution to the associated homogeneous problem in terms of analytical functions. The obtained solution is used for solving boundary-value problems, which are important for applications in the biomedical optics field. The derived equations are successfully verified by comparisons with Monte Carlo simulations.
Journal of the Optical Society of America A 07/2012; 29(7):1475-81. · 1.56 Impact Factor
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ABSTRACT: We present a new approach to the analysis of radiance in turbid media. The approach combines data from spectral, angular and spatial domains in a form of spectro-angular maps. Mapping provides a unique way to visualize details of light distribution in turbid media and allows tracking changes with distance. Information content of experimental spectro-angular maps is verified by a direct comparison with simulated data when an analytical solution of the radiative transfer equation is used. The findings deepen our understanding of the light distribution in a homogenous turbid medium and provide a first step toward applying the spectro-angular mapping as a diagnostic tool for tissue characterization.
Journal of Biomedical Optics 06/2012; 17(6):067007. · 3.16 Impact Factor
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ABSTRACT: 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.
Journal of Biomedical Optics 04/2012; 17(4):045003. · 3.16 Impact Factor
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ABSTRACT: We present a method for the determination of the absorption coefficient of turbid media in a broad wavelength range with high spectral resolution using a dual step method. First, the reduced scattering coefficient is determined for a few wavelengths with spatially resolved reflectance measurements. The reduced scattering coefficient for the intermediate wavelengths is interpolated by fitting a power law. Second, the absorption coefficient is obtained from measurements of the total reflectance using the a priori knowledge of the reduced scattering coefficient. By applying a white light source and a spectrometer to measure the total reflectance, the absorption coefficient is determined with a high spectral resolution. The methodology is verified by comparing the absorption coefficients determined by the spatially resolved reflectance measurements with those obtained by the dual step method. The influence of an unknown refractive index and phase function on the determination of the optical properties is investigated. In addition, the optical properties of Intralipid/ink phantoms and the fat layer of porcine rind were determined. The absorption coefficient of the investigated phantoms varying by four orders of magnitude could be determined with an average error of less than 10%.
Journal of Biomedical Optics 03/2012; 17(3):037009. · 3.16 Impact Factor
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ABSTRACT: This study contains the derivation of an infinite space Green's function of the time-dependent radiative transfer equation in an anisotropically scattering medium based on analytical approaches. The final solutions are analytical regarding the time variable and given by a superposition of real and complex exponential functions. The obtained expressions were successfully validated with Monte Carlo simulations.
Biomedical Optics Express 03/2012; 3(3):543-51. · 2.33 Impact Factor
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ABSTRACT: In this study, Green's function of the two-dimensional radiative transfer equation is derived for an infinitely extended anisotropically scattering medium, which is illuminated by a unidirectional source distribution. In the steady-state domain, the final results, which are based on eigenvalues and eigenvectors, are given analytically apart from the eigenvalues. For the time-dependent case an additional numerical inverse Fourier transform is required. The obtained solutions were successfully validated with another exact analytical solution in the time domain for isotropically scattering and with the Monte Carlo method for anisotropically scattering media.
Journal of Physics A Mathematical and Theoretical 11/2011; 44(50):505206. · 1.56 Impact Factor
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ABSTRACT: In this study, the third-order simplified spherical harmonics equations (SP3), an approximation of the radiative transfer equation, are solved for a semi-infinite geometry considering the exact simplified spherical harmonics boundary conditions. The obtained Green's function is compared to radiative transfer calculations and the diffusion theory. In general, it is shown that the SP3 equations provide better results than the diffusion approximation in media with high absorption coefficient values but no improvement is found for small distances to the source.
Optics Letters 10/2011; 36(20):4041-3. · 3.40 Impact Factor
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ABSTRACT: Analytical solutions of the diffusion equation for a radially N-layered cylinder were derived in the steady-state, frequency, and time domains. Solutions for axially infinite and finite cylinders are presented. The derived formulas were compared to a known solution of the diffusion equation for a layered semi-infinite geometry and to Monte Carlo simulations, showing excellent and good agreement, respectively. The analytical solutions were applied to calculate the light propagation in models of the forearm and the finger, demonstrating the improvement in analysis of hemodynamics measurements compared to the formulas used so far.
Physical Review E 10/2011; 84(4 Pt 1):041911. · 2.26 Impact Factor
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ABSTRACT: A scattering microscope was developed to investigate single cells and biological microstructures by light scattering measurements. The spectrally resolved part of the setup and its validation are shown in detail. The analysis of light scattered by homogenous polystyrene spheres allows the determination of their diameters using Mie theory. The diameters of 150 single polystyrene spheres were determined by the spectrally resolved scattering microscope. In comparison, the same polystyrene suspension stock was investigated by a collimated transmission setup. Mean diameters and standard deviations of the size distribution were evaluated by both methods with a statistical error of less than 1nm. The systematic errors of both devices are in agreement within the measurement accuracy.
Biomedical Optics Express 09/2011; 2(9):2665-78. · 2.33 Impact Factor
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ABSTRACT: We investigated the performance of a neural network for derivation of the absorption coefficient of the brain from simulated non-invasive time-resolved reflectance measurements on the head. A five-layered geometry was considered assuming that the optical properties (except the absorption coefficient of the brain) and the thickness of all layers were known with an uncertainty. A solution of the layered diffusion equation was used to train the neural network. We determined the absorption coefficient of the brain with an RMS error of <6% from reflectance data at a single distance calculated by diffusion theory. By applying the neural network to reflectance curves obtained from Monte Carlo simulations, similar errors were found.
Physics in Medicine and Biology 06/2011; 56(11):N139-44. · 2.83 Impact Factor
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ABSTRACT: An analytical solution of the radiative transfer equation for the radiance caused by an isotropic source which is located in an infinitely extended medium was derived using the P{N} method. The results were compared with Monte Carlo simulations and excellent agreement was found. In addition, the radiance of the SP{N} approximation for the same geometry was derived. Comparison with Monte Carlo simulations showed that the SP{N} radiance, although being more exact than the radiance derived from diffusion theory, has relatively large errors in many relevant cases.
Physical Review E 03/2011; 83(3 Pt 2):036605. · 2.26 Impact Factor
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ABSTRACT: The time-honored Lambert law is widely applied for describing the angle resolved reflectance from illuminated turbid media. We show that this law is only exactly fulfilled for a very special set of geometrical and optical properties. In contrast to what is believed so far, we demonstrate theoretically and experimentally that huge deviations from the Lambert law are ubiquitous. This finding is important for many applications such as those in biomedical optics.
Optics Express 02/2011; 19(5):3881-9. · 3.59 Impact Factor
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ABSTRACT: This paper is the second of two dealing with light diffusion in a turbid cylinder. The diffusion equation was solved for an N-layered finite cylinder. Solutions are given in the steady-state, frequency, and time domains for a point beam incident at an arbitrary position of the first layer and for a circular flat beam incident at the middle of the cylinder top. For special cases the solutions were compared to other solutions of the diffusion equation showing excellent agreement. In addition, the derived solutions were validated by comparison with Monte Carlo simulations. In the time domain we also derived a fast solution ( approximately 10ms) for the case of equal reduced scattering coefficients and refractive indices in all layers.
Optics Express 04/2010; 18(9):9266-79. · 3.59 Impact Factor
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ABSTRACT: This paper is the first of two dealing with light diffusion in a turbid cylinder. The diffusion equation was solved for a homogeneous finite cylinder that is illuminated at an arbitrary location. Three solutions were derived for an incident delta -light source in the steady-state, frequency, and time domains, respectively, applying different integral transformations. The performance of these solutions was compared with respect to accuracy and speed. Excellent agreement between the solutions, of which some are very fast (< 10ms), was found. Six of the nine solutions were extended to a circular flat beam which is incident onto the top side. Furthermore, the validity of the solutions was tested against Monte Carlo simulations.
Optics Express 04/2010; 18(9):9456-73. · 3.59 Impact Factor
