Abstract
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 frequency- and 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 that a unique reconstruction of the susceptibility of the medium (after averaging over the small scatterers) can be achieved from optical coherence tomography measurements for different compression states of the medium.
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Acknowledgements
This work was made possible by the greatly appreciated support of the Austrian Science Fund (FWF) via the special research programme SFB F68 “Tomography Across the Scales”: Peter Elbau and Leopold Veselka have been supported via the subproject F6804-N36 “Quantitative Coupled Physics Imaging”, and Leonidas Mindrinos acknowledges support from the subproject F6801-N36.
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Elbau, P., Mindrinos, L., Veselka, L. (2020). Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography. In: Beilina, L., Bergounioux, M., Cristofol, M., Da Silva, A., Litman, A. (eds) Mathematical and Numerical Approaches for Multi-Wave Inverse Problems. CIRM 2019. Springer Proceedings in Mathematics & Statistics, vol 328. Springer, Cham. https://doi.org/10.1007/978-3-030-48634-1_8
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DOI: https://doi.org/10.1007/978-3-030-48634-1_8
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