Institute For Lasertechnologien In Der Medizin Und Messtechnik

Neu-Ulm, Germany

Institute For Lasertechnologien In Der Medizin Und Messtechnik

Neu-Ulm, Germany
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Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Optics Express | Year: 2010

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 δ-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. © 2010 Optical Society of America.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Optics Express | Year: 2010

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 (≈ 10ms) for the case of equal reduced scattering coefficients and refractive indices in all layers. © 2010 Optical Society of America.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Optics Letters | Year: 2012

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. © 2012 Optical Society of America.


Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Foschum F.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Optics Express | Year: 2011

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. © 2011 Optical Society of America.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Optics Letters | Year: 2010

We derived analytical solutions of the simplified spherical harmonics equations, an approximation of the radiative transfer equation, for infinitely extended scattering media. The derived equations are simple (sum of exponential functions) and quickly evaluated. We compared the solutions with Monte Carlo simulations in the steady-state and time domains and found much better agreement compared to solutions of the diffusion equation, especially for large absorption coefficients, short time values, and small distances from the source. © 2010 Optical Society of America.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Biomedical Optics Express | Year: 2012

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. © 2012 Optical Society of America.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Journal of the Optical Society of America A: Optics and Image Science, and Vision | Year: 2012

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. © 2012 Optical Society of America.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Physical Review A - Atomic, Molecular, and Optical Physics | Year: 2011

This Brief Report presents the derivation of analytical expressions for the fluence of the steady state radiative transfer equation in an infinitely extended and anisotropically scattering medium in arbitrary dimensions for different source types. The fluence, which is composed of an infinite sum of diffusion-like Green's functions, was compared to the Monte Carlo method. Within the stochastic nature of the Monte Carlo simulations, an exact agreement was found in the steady state and time domains. It is shown that the use of low-order approximations is sufficient for many relevant cases. © 2011 American Physical Society.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Journal of Biomedical Optics | Year: 2010

We deal with light diffusion in mismatched N-layered turbid media having a finite or an infinitely thick N'th layer. We focus on time-resolved light propagation in both the frequency and time domains. Based on our results for the steady-state domain, solutions of the N-layered diffusion equations in the frequency and time domains are obtained by applying the Fourier transform technique. Different methods for calculation of the inverse Fourier transform are studied to validate the solutions, showing relative differences typically smaller than 10 -6. The solutions are compared to Monte Carlo simulations, revealing good agreement. Finally, by applying the Laplace and Fourier transforms we derive a fast (≈1 ms) and accurate analytical solution for the time domain reflectance from a two-layered turbid medium having equal reduced scattering coefficients and refractive indices in both layers. © 2010 Society of Photo-Optical Instrumentation Engineers.


Liemert A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik | Kienle A.,Institute For Lasertechnologien In Der Medizin Und Messtechnik
Physical Review E - Statistical, Nonlinear, and Soft Matter Physics | Year: 2011

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. © 2011 American Physical Society.

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