# Proof of Principle for Direct Reconstruction of Qualitative Depth Information from Turbid Media by a Single Hyper Spectral Image

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## Abstract

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## 1. Introduction

## 2. Methods

#### 2.1. Set-Up and Phantom

#### 2.2. Depth Effect on Reflectance Spectrum

#### 2.3. Reconstruction of Depth Information

## 3. Results

#### 3.1. Depth Effect on Reflectance Spectrum

#### 3.2. Reconstruction of Depth Information

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

**Figure A1.**Reflectance spectrum from barium sulfate measured by the hyper-spectral camera before normalization. The drop of intensity in the blue and the red region is caused by the spectral efficiency of the grating and the camera.

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**Figure 1.**(

**A**): Sample phantom with inclusions filled with a red ink water solution. The green rectangle shows the part of the phantom for which the data analysis is done. Only the upper inclusion was used for the analysis as the lower one would be prone to boundary effects. The inclusion has a diameter of two millimeters and it is drilled from the top to the bottom surface. On the right part, it crosses the top surface (closer to camera) while in the left part, it crosses the bottom surface (further away from the camera). (

**B**): Set-up. The phantom is illuminated from the side and imaged with the hyper-spectral camera (adapted from [18]). (

**C**): Schematic of the set-up of the hyper-spectral camera.

**Figure 2.**Spectra for different x-directions and, therefore, different inclusion depths as a function of the ink concentration inside the inclusions. The lower the x-position, the deeper the inclusion is. The green arrow symbolizes the spectra for deeper inclusions and the red circle symbolizes the position of the iso-point (10% ink) or the position there is nearly not depth effect (1% ink). With water inside the inclusion, there is no iso-point.

**Figure 3.**Comparison of the inclusion measured by OCT and caliper (

**top left**) with the hyper-spectral signal at 550 nm (

**bottom left**) and the hyper-spectral signal at the iso-point at 575 nm (

**top right**) with the depth map (

**bottom right**).

**Figure 4.**HSI depth parameter along the inclusion for different positions perpendicular to the inclusion and the lower and upper depth of the inclusion. The left y-axis shows the depth parameter and the right y-axis the results from the real depth. In all cases, the depth parameter acts linear (marked by red ellipses) with the actual depth up to a maximal depth depending on the optical properties. The green and orange graphs represent the real depth, measured by an OCT and a caliper.

**Figure 5.**HSI depth parameter perpendicular to the inclusion for different positions along the inclusion and the lower and upper depth of the inclusion. The left y-axis shows the depth parameter and the right y-axis the results from the real depth. The green and orange graphs represent the real depth, measured by an OCT and a caliper.

**Figure 6.**HSI depth parameter in the linear regime and the exponential regime over the real depth of the bottom channel with the according fits.

**Figure 7.**HSI depth parameter in the linear regime and the exponential regime over the real depth of the bottom channel with the according fits for the central part of the inclusion.

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**MDPI and ACS Style**

Hohmann, M.; Hecht, D.; Lengenfelder, B.; Späth, M.; Klämpfl, F.; Schmidt, M.
Proof of Principle for Direct Reconstruction of Qualitative Depth Information from Turbid Media by a Single Hyper Spectral Image. *Sensors* **2021**, *21*, 2860.
https://doi.org/10.3390/s21082860

**AMA Style**

Hohmann M, Hecht D, Lengenfelder B, Späth M, Klämpfl F, Schmidt M.
Proof of Principle for Direct Reconstruction of Qualitative Depth Information from Turbid Media by a Single Hyper Spectral Image. *Sensors*. 2021; 21(8):2860.
https://doi.org/10.3390/s21082860

**Chicago/Turabian Style**

Hohmann, Martin, Damaris Hecht, Benjamin Lengenfelder, Moritz Späth, Florian Klämpfl, and Michael Schmidt.
2021. "Proof of Principle for Direct Reconstruction of Qualitative Depth Information from Turbid Media by a Single Hyper Spectral Image" *Sensors* 21, no. 8: 2860.
https://doi.org/10.3390/s21082860