Comparison of light scattering models for diffuse optical tomography

González-Rodríguez, Pedro; Kim, Arnold D.

doi:10.1364/oe.17.008756

Cited by 27 publications

(18 citation statements)

References 16 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…There have been several studies on the asymptotic behavior of (7.1) with forward-peaked scattering leading to the Fokker-Planck approximation [35] and its generalizations [37,29]. Solving the radiative transfer equation (7.1) with these approximate scattering operators has led to useful physical insight [25,26,16]. However, for most scattering models used for applications, the Fokker-Planck approximation is inaccurate.…”

Section: Extension To Forward-peaked Scattering In Radiative Transfermentioning

confidence: 99%

Asymptotic Approximations for the Close Evaluation of Double-Layer Potentials

Carvalho¹,

Khatri²,

Kim³

2020

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

When using the boundary integral equation method to solve a boundary value problem, the evaluation of the solution near the boundary is challenging to compute because the layer potentials that represent the solution are nearly-singular integrals. To address this close evaluation problem, we apply an asymptotic analysis of these nearly singular integrals and obtain an asymptotic approximation. We derive the asymptotic approximation for the case of the double-layer potential in two and three dimensions, representing the solution of the interior Dirichlet problem for Laplace's equation. By doing so, we obtain an asymptotic approximation given by the Dirichlet data at the boundary point nearest to the interior evaluation point plus a nonlocal correction. We present numerical methods to compute this asymptotic approximation, and we demonstrate the efficiency and accuracy of the asymptotic approximation through several examples. These examples show that the asymptotic approximation is useful as it accurately approximates the close evaluation of the double-layer potential while requiring only modest computational resources.

show abstract

Section: Extension To Forward-peaked Scattering In Radiative Transfermentioning

confidence: 99%

Asymptotic Approximations for the Close Evaluation of Double-Layer Potentials

Carvalho¹,

Khatri²,

Kim³

2020

SIAM J. Sci. Comput.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Mathematical models were developed describing light transport inside tissue employing finite element methods (FEM) or Monte Carlo simulations for image reconstruction to determine differences in absorption and scattering coefficients [12][13][14][15][16][17][18]. The implementation of those methods is strongly simplified due to recent developments in software toolboxes like TOAST 1 or NIRFAST² offering a broad variety of adjustable parameters [19].…”

Section: Reconstruction Of Inner Tissue Structurementioning

confidence: 99%

3D-surface reconstruction method for diffuse optical tomography phantoms and tissues using structured and polarized light

et al. 2011

View full text Add to dashboard Cite

In recent years optical methods became increasingly popular for pre-clinical research and small animal imaging. One main field in biomedical optics research is the diffuse optical tomography (DOT). Many new systems were invented for small animal imaging and breast cancer detection. In combination with the progress in the development of optical markers, optical detectors and near infrared light sources, these new systems have become a formidable source of information. Most of the systems detect the transmitted light which passes through an object and one observes the intensity variations on the detector side. The biggest challenge for all diffuse optical tomography systems is the enormous scattering of light in tissues and tissue-like phantoms resulting in loss of image information. Many systems work with contact gels and optical fibers that have direct contact with the object to neglect the light path between surface and detector. Highly developed mathematic models and reconstruction algorithms based on FEM and Monte Carlo simulations describe the light transport inside tissues and determine differences in absorption and scattering coefficients inside.The proposed method allows a more exact description of the orientation of surface elements from semi-transparent objects towards the detector. Using Polarization Difference Imaging (PDI) in combination with structured light 3D-scanning, it is possible to separate information from the surface from that of the subsurface. Thus, the actual surface shape can be determined. Furthermore, overlaying byproducts caused by inter-reflections and multiple scattering can be filtered from the basic image information with this method. To enhance the image quality, the intensity dispersion between surface and camera is calculated and the creation of 3D-FEM-meshes simplified.

show abstract

“…Here, we have considered M discrete directions defined as h m ¼ ðm À 1ÞDh with Dh ¼ 2p=M, and the weights have been chosen to be [9,25] …”

Section: Directional Discretizationmentioning

confidence: 99%