Reconstructing the Optical Parameters of a Layered Medium with Optical Coherence Elastography
Peter Elbau, Leonidas Mindrinos, Leopold Veselka
TL;DR
This work tackles the inverse problem of reconstructing the optical properties of a layered dispersive medium from OCT-based elastography data. It develops a Maxwell-based forward model that accounts for layering and randomly distributed scatterers, and introduces a domain-decomposition and layer-stripping approach to reduce the problem to tractable per-layer subproblems. Using measurements at multiple compression states, the authors show that all essential optical parameters, including layer refractive indices $n_j(\omega)=\sqrt{1+\check\chi_j(\omega)}$, layer boundaries $z_j$, scatterer density $\rho_j$, and particle indices $\nu_j(\omega)$ with their compression derivatives $\nu_j'(\omega)$, can be uniquely recovered. The framework thus provides a principled route to combine optical parameter reconstruction with mechanical properties, enabling quantitative optical coherence elastography in complex layered media with micro-scale scatterers.
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.