# NIR and SWIR Continuous Wave Diffuse Optical Tomography from a Wearable Device Setup

Julien Wojak, Sydur Rahman, Laurent Alacoque, Jean-Michel Tualle, Dominique Ettori, Xavier Alacoque, Anabela Da Silva

► To cite this version:

Julien Wojak, Sydur Rahman, Laurent Alacoque, Jean-Michel Tualle, Dominique Ettori, et al. NIR and SWIR Continuous Wave Diffuse Optical Tomography from a Wearable Device Setup. European Conference on Biomedical Optics, OPTICA/SPIE, Jun 2025, Munich (Germany), Germany. hal-05194754

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Submitted on 31 Jul 2025

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# NIR and SWIR Continuous Wave Diffuse Optical Tomography from a Wearable Device Setup

Julien Wojak¹*, Sydur Rahman¹, Laurent Alacoque ², Jean-Michel Tualle³,
Dominique Ettori³, Xavier Alacoque⁴ and Anabela Da Silva¹

¹Aix Marseille Univ, CNRS, Centrale Med, Institut Fresnel, Marseille, France

²DOPT Department, Univ. Grenoble Alpes, CEA, Leti Grenoble, France

³LPL, UMR 7538 Université Sorbonne Paris-Nord Villetaneuse, France

⁴Anesthesia, intensive care Oncopole Claudius Regaud Toulouse, France

*julien.wojak@univ-amu.fr

**Abstract:** This paper presents absorption reconstruction by diffuse optical tomography from two infrared wavelength measurements using a reflection configuration proposed on a wearable device dedicated to diffuse imaging of biological tissues. © 2025 The Author(s)

## 1. Introduction

Diffuse Optical Tomography (DOT) is a powerful non-invasive and non-ionizing imaging technique that uses infrared illumination to probe the absorption and scattering properties of biological tissues. It provides access to quantitative 3D measurements of physiological parameters such as oxy/deoxyhemoglobin [1] and potentially others such as glucose. Moreover, the growing interest in the development of wearable devices for continuous monitoring leads to the realization of a dual sensor setup [2] for diffuse imaging. Here, using the reflection configuration given by this dual sensor setup, we investigate the ability to reconstruct absorption parameters in tissues using continuous wave DOT for two wavelengths: 800 nm in Near-Infrared (NIR) window and 1600 nm in Short Wave Infrared (SWIR) window. The dual sensor setup shown in figure (1) consists of 24 SWIR photodiodes and 3 NIR rectangular sensor arrays, each consisting of 174 × 92 photodetectors. Reconstructions are performed sequentially from both the NIR window and the SWIR window measurements. The location of absorption inhomogeneities found from the NIR window reconstruction is used as a spatial prior to perform the reconstruction using the SWIR window measurement.

<figure><img src="image_2.png" /><figcaption>Fig. 1: photographs of the multi-sensors wearable device</figcaption></figure>

## 2. Methodology

### 2.1. Synthetic measurements generation

The scattering of infrared light by biological tissues is well described by the Radiative Transfer Equation (RTE), especially in the SWIR window, where the absorption is not negligible with respect to the diffusion and where the diffusion approximation equation does not hold [3]. Monte Carlo simulations have demonstrated their ability to effectively solve RTE in a wide variety of geometries and wavelengths configurations [4]. Here we study infrared light scattering in a medium that is a simplification of a skin sample with a blood vessel passing through it. The skin sample is represented by a rectangular parallelepiped with a depth of 1.5 cm and a surface area of 2.5 × 2.5 cm². The blood vessel is represented as a cylinder with a length of 2 cm and a radius of 0.1 cm. Using MATLAB [5] as a Monte Carlo RTE solver, light propagation in this sample is modeled on a voxelized grid, and the fluence rate is collected at the sensor location for both NIR and SWIR illumination. Figure (2) shows the modeling of the dual
sensor arrays and a result of light collection on the sensor arrays. A typical set of optical properties used for these simulations is summarized in the table (1).

<table><caption>Table 1: Optical properties of Dermis and Blood at 800 nm and 1600 nm wavelengths.</caption><thead><tr><th>λ (Source)</th><th colspan="2">800 nm (NIR)</th><th colspan="2">1600 nm (SWIR)</th></tr><tr><th>Optical properties</th><th>μ<sub>a</sub></th><th>μ<sub>s</sub></th><th>μ<sub>a</sub></th><th>μ<sub>s</sub></th></tr></thead><tbody><tr><td>Dermis (Homogeneous Medium) (cm<sup>-1</sup>)</td><td>0.14</td><td>100</td><td>1.4</td><td>50</td></tr><tr><td>Blood Vessel (Inhomogeneity) (cm<sup>-1</sup>)</td><td>0.42</td><td>100</td><td>4.2</td><td>50</td></tr></tbody></table>

<figure><img src="image_3.png" /><figcaption>Fig. 2: Left: NIR (rectangular areas) / SWIR (single points) sensors configuration. Middle and right: simulated fluence rate on NIR and SWIR sensors respectively recorded from a continuous wave illumination located at the red cross location.</figcaption></figure>

## 2.2. Reconstruction Algorithm

A perturbation approach (Born approximation) is used to establish a linear dependence between a perturbation on the parameters and one on the measurements [4]:

$$ \Delta\Phi(r_d) = \int G(r_d; r)G(r; r_s)\delta_{\mu_a}(r)dr^3 \quad (1) $$

G are the Green's functions of the RTE, computed for source ($r_s$) and detector ($r_d$) positions. Their product is a sensitivity kernel. They are calculated using Monte Carlo simulations. $\Delta\Phi(\vec{r}_d)$ is the perturbation measurement. It consists of the difference of two consecutive sets of Monte Carlo simulations using the configuration described in paragraph (2.1): one modeling the skin sample without the blood vessel passing through (reference measurements), the other modeling the skin sample with the blood vessel passing through. The reconstruction task is to find $\delta_{\mu_a}(\vec{r})$ that satisfies (1) for both NIR and SWIR illuminations. Reconstruction is performed on a voxelized mesh with a resolution 2.5 times coarser than the simulation mesh. This avoids inversion mesh bias and reduces the number of unknowns.

**NIR Reconstruction:** NIR reconstruction is known to be an ill-posed problem [6]. A common resolution strategy is to minimize the error reconstruction between the light scattering model (1) and measurements, subject to *apriori* constraints on the solution known as regularization. Here the regularization used is the total variation penalization [7]:

$$ \arg\min_{\delta_{\mu_a}} \|y - K\delta_{\mu_a}\|^2 + \lambda \|\nabla(\delta_{\mu_a})\|^2 \quad (2) $$

where $y$ is a simulated vector of perturbed measurements, $K$ is the sensitivity matrix obtained by concatenating the sensitivity kernels of the source-detector pairs, and $\lambda$ is a weight parameter defining the trade-off between the data fidelity term and the regularization term. The use of the total variation term forces the solution of (2) to be a piecewise constant function. This regularization is useful when the object to be reconstructed consists of a fairly homogeneous area (such as a blood vessel) contrasted with a homogenized background.

**SWIR Reconstruction:** SWIR reconstruction is also an ill-posed problem. Its resolution using the sensor configuration described in Section (2.1) is particularly challenging. In fact, the number of SWIR sensors is much smaller than the number of NIR sensors. It requires adding strong *apriori* information in the formulation of the reconstruction problem. Therefore, to constrain the SWIR reconstruction to a small subset of voxels, the NIR reconstruction
information is used. This subset is selected by thresholding and dilating areas where the NIR reconstructions show strong inhomogeneities, such as blood vessels. One has to solve

$$ \arg \min_{\delta_{\mu_a} \in \text{ROI}} \|\mathbf{y} - \mathbf{K}\delta_{\mu_a}\|^2 + \lambda \|\delta_{\mu_a}\|^2 \quad (3) $$

where ROI is the subset of voxels of interest deduced from NIR-window reconstruction. It is worth noting that, since the reconstruction area is quite well defined by the NIR reconstruction, a Tikhonov regulation for the SWIR window reconstruction gives us the best results.

### 3. Results

The tests are performed using the configuration described in Section (2.1). The NIR window reconstruction results show good agreement with the simulated ground truth, especially in location. The NIR reconstructions are used as a spatial prior to perform SWIR window reconstruction. The results of the SWIR window reconstruction are shown in Figure (3), where a simulated blood vessel located between the source and the SWIR sensor is reconstructed. Despite the configuration of SWIR sensor location, which is unfavorable for reconstruction, one can retrieve a good approximation of the absorption perturbation in the tissue.

<figure><img src="image_4.png" /><figcaption>Fig. 3: A SWIR reconstruction result and ground truth (resp. left and right) for a cylindrical shape oriented horizontally between source and detectors.</figcaption></figure>

### 4. Conclusion and perspective

A configuration of two wavelengths, 800 nm and 1600 nm, respectively, in NIR and SWIR windows, reproducing a portable device setup to perform biological imaging is simulated within the perspective to perform absorption inhomogeneities reconstruction by DOT. Reconstructions are performed sequentially in NIR and SWIR windows, and tests on synthetic datasets show promising results. Several reconstruction configurations and algorithm details will be presented at the conference. The step forward to using real measurements will be discussed.

### 5. Acknowledgments

This work benefits of the support of the French National Research Agency (ANR) under grand number ANR-16-CE19-0012

### References

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