# Focusing Coherent Light through Volume Scattering Phantoms via Wavefront Shaping

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## Abstract

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## 1. Introduction

## 2. Fabrication and Characterization of Phantoms with Well-Defined Optical Properties

#### 2.1. Volume Scattering Phantoms

#### 2.2. Characterization of the Scattering and Absorption Coefficients

#### 2.3. Calculation of the Angular-Dependent Transmittance via the Hybrid ${P}_{N}$ Method

## 3. Wavefront Shaping Setup

## 4. Results

#### 4.1. Solely Scattering Phantoms

#### 4.2. Influence of Absorption

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Front and side view with a scale bar of length 1 cm of an exemplary phantom made of epoxy resin filled in a 3D-printed flat open ring.

**Figure 2.**Partial angular transmittance ${T}_{NA}$ for the phantoms of set 1 and 2 plotted over thickness in mm, collected with a microscope objective of numerical aperture $NA=0.8$.

**Figure 3.**Partial angular transmittance for a microscope objective with $NA=0.8$ for set 1 (

**a**) and set 2 (

**b**) plotted over thickness in mm. Depicted are the transmittance into the NA without any ballistic contribution ${T}_{NA}-{T}_{NA,ball}$ and the partial angular transmittance ${T}_{NA}$.

**Figure 4.**Wavefront shaping setup including a laser diode emitting at 633 nm, a spatial light modulator (SLM), microscope objectives (MO), a CMOS camera, and a gain-amplified photodiode. Isol., isolator; $\lambda $/2, half-wave plate; P, polarizer; L, lens; A, aperture; BS, beam splitter; M, mirror; TL, tube lens.

**Figure 5.**Measured intensity enhancement $\eta $ as a function of the optimized number of segments N for the phantoms of set 1 with similar effective scattering coefficient ${\mu}_{s}^{{}^{\prime}}$, varying thickness d, and negligible absorption coefficient ${\mu}_{a}$. The experimental uncertainty is in the range of the symbol size [2].

**Figure 6.**Measured intensity enhancement $\eta $ as a function of the optimized number of segments N for the phantoms of set 2 with varying absorption coefficient ${\mu}_{a}$, similar effective scattering coefficients ${\mu}_{s}^{{}^{\prime}}$, and thickness d. The experimental uncertainty is in the range of the symbol size [2].

**Table 1.**Thickness d, effective scattering coefficient ${\mu}_{s}^{{}^{\prime}}$, and absorption coefficient ${\mu}_{a}$ of the two sets of phantoms at $\lambda $ = 633 nm. The values are shown with their respective standard deviations of three measurements at different sample positions.

Set.Sample | d (mm) | ${\mathit{\mu}}_{\mathit{s}}^{{}^{\prime}}$ (mm${}^{-1}$) | ${\mathit{\mu}}_{\mathit{a}}$ (mm${}^{-1}$) |
---|---|---|---|

1.1 | 0.395(9) | 3.688(5) | 0.0034(3) |

1.2 | 0.947(4) | 3.781(2) | 0.0020(1) |

1.3 | 1.514(9) | 3.841(4) | 0.0020(1) |

1.4 | 1.987(3) | 3.817(5) | 0.0019(1) |

2.1 | 0.901(8) | 2.724(3) | 0.0213(1) |

2.2 | 1.045(3) | 2.757(1) | 0.0598(1) |

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**MDPI and ACS Style**

Fritzsche, N.; Ott, F.; Pink, K.; Kienle, A.
Focusing Coherent Light through Volume Scattering Phantoms via Wavefront Shaping. *Sensors* **2023**, *23*, 8397.
https://doi.org/10.3390/s23208397

**AMA Style**

Fritzsche N, Ott F, Pink K, Kienle A.
Focusing Coherent Light through Volume Scattering Phantoms via Wavefront Shaping. *Sensors*. 2023; 23(20):8397.
https://doi.org/10.3390/s23208397

**Chicago/Turabian Style**

Fritzsche, Niklas, Felix Ott, Karsten Pink, and Alwin Kienle.
2023. "Focusing Coherent Light through Volume Scattering Phantoms via Wavefront Shaping" *Sensors* 23, no. 20: 8397.
https://doi.org/10.3390/s23208397