1. Articles from Peter Elbau

    1-6 of 6
    1. Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography

      Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography

      In this work we consider the inverse problem of reconstructing the optical properties of a layered medium from an elastography measurement where optical coherence tomography is used as the imaging method. We hereby model the sample as a linear dielectric medium so that the imaging parameter is given by its electric susceptibility, which is a frequencyand depth-dependent parameter. Additionally to the layered structure (assumed to be valid at least in the small illuminated region), we allow for small scatterers which we consider to be randomly distributed, a situation which seems more realistic compared to purely homogeneous layers. We then show ...

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    2. The inverse scattering problem for orthotropic media in polarization-sensitive optical coherence tomography

      The inverse scattering problem for orthotropic media in polarization-sensitive optical coherence tomography

      In this paper we provide for a first time, to our knowledge, a mathematical model for imaging an anisotropic, orthotropic medium with polarization-sensitive optical coherence tomography. The imaging problem is formulated as an inverse scattering problem in three dimensions for reconstructing the electrical susceptibility of the medium using Maxwell’s equations. Our reconstruction method is based on the second-order Born-approximation of the electric field

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    3. Quantitative reconstructions in multi-modal photoacoustic and optical coherence tomography imaging

      Quantitative reconstructions in multi-modal photoacoustic and optical coherence tomography imaging

      In this paper we perform quantitative reconstruction of the electric susceptibility and the Gr¨uneisen parameter of a non-magnetic linear dielectric medium using measurement of a multi-modal photoacoustic and optical coherence tomography system. We consider the mathematical model presented in [11], where a Fredholm integral equation of the first kind for the Gr¨uneisen parameter was derived. For the numerical solution of the integral equation we consider a Galerkin type method.

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    4. Inverse Problems of Combined Photoacoustic and Optical Coherence Tomography

      Inverse Problems of Combined Photoacoustic and Optical Coherence Tomography

      Optical coherence tomography (OCT) and photoacoustic tomography (PAT) are emerging non-invasive biological and medical imaging techniques. It is a recent trend in experimental science to design experiments that perform PAT and OCT imaging at once. In this paper we present a mathematical model describing the dual experiment. Since OCT is mathematically modelled by Maxwell's equations or some simplifications of it, whereas the light propagation in quantitative photoacoustics is modelled by (simplifications of) the radiative transfer equation, the first step in the derivation of a mathematical model of the dual experiment is to obtain a unified mathematical description, which in ...

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    5. Mathematical Methods of Optical Coherence Tomography (Book Chapter)

      Mathematical Methods of Optical Coherence Tomography (Book Chapter)

      In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high-resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for different positions of the mirror. Different approaches are addressed depending on the ...

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    6. Mathematical Modelling of Optical Coherence Tomography

      Mathematical Modelling of Optical Coherence Tomography

      In this chapter a general mathematical model of Optical Coherence Tomography (OCT) is presented on the basis of the electromagnetic theory. OCT produces high resolution images of the inner structure of biological tissues. Images are obtained by measuring the time delay and the intensity of the backscattered light from the sample considering also the coherence properties of light. The scattering problem is considered for a weakly scattering medium located far enough from the detector. The inverse problem is to reconstruct the susceptibility of the medium given the measurements for di erent positions of the mirror. Di erent approaches are addressed ...

      Read Full Article
    1-6 of 6
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    Mathematical Modelling of Optical Coherence Tomography Mathematical Methods of Optical Coherence Tomography (Book Chapter) Inverse Problems of Combined Photoacoustic and Optical Coherence Tomography Quantitative reconstructions in multi-modal photoacoustic and optical coherence tomography imaging The inverse scattering problem for orthotropic media in polarization-sensitive optical coherence tomography Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography Optical coherence tomography angiography (OCTA) findings in Serpiginous Choroiditis Changes in retinal layer thickness with maturation in the dog: an in vivo spectral domain - optical coherence tomography imaging study Optical coherence tomography angiography analysis of fabry disease An unsupervised hierarchical approach for automatic intra‐retinal cyst segmentation in spectral‐domain optical coherence tomography images Towards quantitative assessment of burn based on photoacoustic and optical coherence tomography Cellular Scale Imaging of Transparent Retinal Structures and Processes Using Adaptive Optics Optical Coherence Tomography