Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Quantitative OCT reconstructions for dispersive media

Peter Elbau, Leonidas Mindrinos, Leopold Veselka

TL;DR

This work develops a quantitative OCT framework for reconstructing the position, thickness, and optical properties of multi-layer dispersive media from time- and frequency-domain OCT data. It integrates an iterative layer-stripping approach with Maxwell-based forward models, handling non-dispersive, dispersive, and absorbing media, and uses phase retrieval strategies (including phase from multiple reference-mirror positions and Kramers-Kronig relations) to recover complex refractive indices. The contributions include explicit forward-model formulations, time-domain and frequency-domain inverse schemes, and numerical demonstrations showing accurate reconstructions and robustness to noise. The approach advances OCT by enabling quantitative, depth-resolved recovery of frequency-dependent optical properties, with potential applications in tissue diagnostics and material characterization.

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 multi-layered 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.

Quantitative OCT reconstructions for dispersive media

TL;DR

This work develops a quantitative OCT framework for reconstructing the position, thickness, and optical properties of multi-layer dispersive media from time- and frequency-domain OCT data. It integrates an iterative layer-stripping approach with Maxwell-based forward models, handling non-dispersive, dispersive, and absorbing media, and uses phase retrieval strategies (including phase from multiple reference-mirror positions and Kramers-Kronig relations) to recover complex refractive indices. The contributions include explicit forward-model formulations, time-domain and frequency-domain inverse schemes, and numerical demonstrations showing accurate reconstructions and robustness to noise. The approach advances OCT by enabling quantitative, depth-resolved recovery of frequency-dependent optical properties, with potential applications in tissue diagnostics and material characterization.

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 multi-layered 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.

Paper Structure

This paper contains 16 sections, 8 theorems, 100 equations, 8 figures, 3 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. The forward problem
  3. Non-dispersive medium
  4. Dispersive medium
  5. The inverse problem
  6. Phase retrieval and OCT
  7. Reconstructions in time domain
  8. Reconstructions in frequency domain
  9. Dispersive medium
  10. Absorbing medium
  11. Numerical Implementation
  12. Reconstructions from phase-less data in time domain
  13. Reconstructions having phase information in frequency domain
  14. Non-dispersive medium
  15. Dispersive medium
  16. ...and 1 more sections

Key Result

Proposition 1

Let $L = (z_1, \, z_2)$ be a single-layer medium, and let the refractive index be given by If the initial wave $f_0,$ see l1, satisfies $\mathop{\mathrm{supp}}\nolimits f_0\subset (-\infty,z_1),$ then the solution of l53, together with $u(t<0,z) = f_0,$ is given by with $U_1, \, U_2,$ and $U_3$ defined as before.

Figures (8)

  • Figure 1: Experimental data obtained from a frequency-domain OCT system of a three-layer medium with piece-wise constant refractive index. Courtesy of Ryan Sentosa and Lisa Krainz, Medical University of Vienna.
  • Figure 2: Wave propagation. The reflection and transmission operators for the sub-problem \ref{['l2']} (left) and the sub-problem \ref{['l10']} (right).
  • Figure 3: Left: The intersection points of the circles $\hat{m} (r_1 ; \omega_1) \in \mathbbm{C}$ (red) and $\hat{m}_s (\omega_1) \in \mathbbm{C}$ (blue). Right: The intersection points of the circles $\hat{m} (r_1 ; \omega_2) \in \mathbbm{C}$ (red), $\hat{m} (r_2 ; \omega_2) \in \mathbbm{C}$ (green) and $\hat{m}_s (\omega_2) \in \mathbbm{C}$ (blue). The red asterisk indicates the unique solution. The setup is the same as the one in the third example in Sec. \ref{['sec4']}.
  • Figure 4: The simulated data (absolute value) in the time-domain for the first example (left) and in the frequency-domain for the second example (right).
  • Figure 5: The function $\phi(\omega),$ for $\omega \in [\underline{\omega},\overline{\omega}],$ at the first (left) and the last (right) iteration step of Algorithm \ref{['alg2']}.
  • ...and 3 more figures

Theorems & Definitions (17)

  • Proposition 1
  • Proof 1
  • Example 1
  • Proposition 2
  • Proposition 3
  • Proof 2
  • Remark 1
  • Lemma 2.1
  • Proof 3
  • Proposition 4
  • ...and 7 more