A Quantitative Model for Optical Coherence Tomography

TL;DR

A first step to a quantitative model is made by considering the measured intensity as a combination of back-scattered Gaussian beams affected by the system, which includes system relevant parameters, such as the position of the focus and the spot size of the incident laser beam, which allow a precise prediction of the OCT data.

Abstract

Optical coherence tomography (OCT) is a widely used imaging technique in the micrometer regime, which gained accelerating interest in medical imaging in the last twenty years. In up-to-date OCT literature [5,6] certain simplifying assumptions are made for the reconstructions, but for many applications a more realistic description of the OCT imaging process is of interest. In mathematical models, for example, the incident angle of light onto the sample is usually neglected or a plane wave description for the light-sample interaction in OCT is used, which ignores almost completely the occurring effects within an OCT measurement process. In this article, we make a first step to a quantitative model by considering the measured intensity as a combination of back-scattered Gaussian beams affected by the system. In contrast to the standard plane wave simplification, the presented model includes system relevant parameters such as the position of the focus and the spot size of the incident laser beam, which allow a precise prediction of the OCT data and therefore ultimately serves as a forward model. The accuracy of the proposed model - after calibration of all necessary system parameters - is illustrated by simulations and validated by a comparison with experimental data obtained from a 1300 nm swept-source OCT system.

Figures (9)

• Figure 1: OCT setup: Insight: 1300nm swept-source; 25/75 % fiber coupler; PC: polarization control; C: circulator; 50/50 % fiber coupler for light recombination; FC: fiber collimator; M1, M2: mirrors; Gx, Gy scanning galvanometers; SL: scan lens; S: sample; DBD: dual-balance detector.
• Figure 2: Modeling of the separate parts of the OCT experiment: We start by describing the light beam produced by the laser (the red box) in Section \ref{['se:Gaussian']}, we give a representation for the beam in the sample arm which is backscattered from the sample (the orange box) in Section \ref{['se:sampleField']} and is then coupled back into the fiber system via the scan lens (the yellow box) in Section \ref{['se:scanlens']}. This is afterwards recombined with the beam from the reference arm (the green box) in Section \ref{['se:referenceField']} and detected by the dual balance detector (the blue box) in Section \ref{['se:dbd']}.
• Figure 3: The near-field for different positions of the focus (red, blue, green) vs. the far-field (black) regime for different positions of the surface. At the dotted lines, indicating where the surface and focus position coincide, the intensities of near- and far-field regime are equal.
• Figure 4: Comparison between the power meter measurements for different angular steps of the mirror (blue dashed curve) as in Section \ref{['subsec:data_prep']} and the simulation (red curve) for \ref{['eq:scatt']}.
• Figure 5: Comparison of averaged maximum values for all B-scans (of different sample locations) of the experimental data (black with errorbars) and the simulated data points (red) for the mirror experiment.

Theorems & Definitions (10)

• Theorem 1
• Theorem 2
• Lemma 4.1
• Lemma 4.2
• Proof 1: Proof of Theorem \ref{['thm:thm1']}
• Lemma 8.1
• Proof 2
• Proof 3: Proof of Theorem \ref{['thm:first_order']}
• Proof 4: Proof of Lemma \ref{['lem:integral_approximation']}
• Proof 5: Proof of Lemma \ref{['lem:maximum']}