Quantitative OCT reconstructions for dispersive media

Abstract

We consider the problem of reconstructing the position and the time-dependent optical properties of a linear dispersive medium from OCT measurements. The medium is multilayered described by a piece-wise inhomogeneous refractive index. The measurement data are from a frequency-domain OCT system and we address also the phase retrieval problem. The parameter identification problem can be formulated as an one-dimensional inverse problem. Initially, we deal with a non-dispersive medium and we derive an iterative scheme that is the core of the algorithm for the frequency-dependent parameter. The case of absorbing medium is also addressed.

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

“…, J, where each successive step is only used to further simplify the operator G 2 from the previous step. This thus leads to a sort of layer stripping algorithm, see, for example, [8], where a similar argument was presented.…”

“…Here, we consider two independent measurements for two different positions of the mirror in order to overcome the problem of phase-less data, see [8]. Thus, we obtain the data…”

“…For Problem 4.2, the situation is more complicated and we settle for an approximate solution for the electric field. For that, we assume (using the same notation as in (8)) that the susceptibility χ (p) j of the random particles does not differ much from the background χ j , so that the difference between the induced field and the incident field becomes small, and we do a first order approximation in the difference χ (p) j − χ j . For that purpose, we write the differential equation ( 4) in the form…”