Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography
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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.
KeywordsOptical coherence tomography Optical coherence elastography Inverse problem Parameter identification
MSC:65J22 65M32 78A46
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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