# Mesoscopic States of Light for the Detection of Weakly Absorbing Objects

## Abstract

**:**

## 1. Introduction

## 2. The Theoretical Model

## 3. Materials and Methods

## 4. Results

## 5. Discussion

## 6. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

GI | ghost imaging |

PNR | photon number resolving |

CMOS | complementary metal oxide semiconductor |

BS | beam splitter |

HPD | hybrid photodetector |

## References

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**Figure 1.**R as a function of the mean number of photons for $t=0.9$, $\mu =1$, and $\eta =0.25$ in the case of a multi-mode twin-beam state (black curve) and a multi-mode pseudothermal state (red curve). The gray dashed line at $R=1$ defines the boundary condition between classical and quantum correlations.

**Figure 2.**Sketch of the experimental setup. M: mirror; L${}_{1}$: 200 mm-focal-length lens; GD: rotating ground-glass disk; L${}_{2}$: 200 mm-focal-length lens; PH: pin-hole; I: variable iris; BS: balanced beam splitter; OBJ: object; L: achromatic doublet; MF: multi-mode optical fiber; HPD: hybrid photodetector.

**Figure 3.**Photon-number distributions of detected photons in semi-log scale for almost the same mean value and three different choices of $\mu $. In Panel (

**a**), $\langle m\rangle =0.53$ and $\mu =1.00\pm 0.02$; in (

**b**), $\langle m\rangle =0.49$ and $\mu =2.65\pm 0.04$; in (

**c**), $\langle m\rangle =0.54$ and $\mu =5.12\pm 0.07$.

**Figure 4.**R as a function of the mean number of photons per mode for three different values of $\mu $. The data are shown as colored dots + error bars, while the theoretical curves according to Equation (6) are shown as colored lines. From the fitting procedure, we obtain the value of t. In particular, in Panel (

**a**), $t=0.54\pm 0.02$ (case $\mu =1.03\pm 0.01$), in Panel (

**b**), $t=0.46\pm 0.01$ (case $\mu =2.8\pm 0.1$), and in Panel (

**c**), $t=0.45\pm 0.03$ (case $\mu =6.2\pm 0.3$).

**Figure 5.**R as a function of the mean number of photons for $\mu =2.8\pm 0.1$ (Panel (

**a**)) and $\mu =6.2\pm 0.3$ (Panel (

**b**)). The data are shown as colored dots + error bars, while the theoretical curves according to Equation (8) are shown as colored lines. From the fitting procedure, we obtain the value of t. In particular, in Panel (

**a**), $t=0.55\pm 0.02$, and in Panel (

**b**), $t=0.56\pm 0.03$. The other parameters are $\langle {m}_{\mathrm{N}}\rangle =0.09\pm 0.03$ and ${\mu}_{\mathrm{N}}=1.0\pm 0.1$ in Panel (

**a**) and $\langle {m}_{\mathrm{N}}\rangle =0.15\pm 0.03$ and ${\mu}_{\mathrm{N}}=2.5\pm 0.3$ in Panel (

**b**).

**Figure 7.**R as a function of the mean number of photons per mode for two different values of $\mu $. The data are shown as colored dots + error bars, while the theoretical curves according to Equation (6) are shown as colored lines. From the fitting procedure, we obtain the value of t. In particular, in Panel (

**a**), $t=0.81\pm 0.03$ (case $\mu =1.05\pm 0.02$), and in Panel (

**b**), $t=0.78\pm 0.03$ (case $\mu =3.7\pm 0.1$).

**Figure 8.**Values of t obtained fitting the data according to Equation (6) as a function of the number of modes. The gray dashed line represents the expected value $t=0.804$.

**Figure 9.**Values of t obtained fitting the data according to Equation (6) as a function of the number of modes, in the case in which the mean number of photons per mode is constant. The gray dashed line represents the expected value $t=0.804$.

**Figure 10.**R as a function of the mean number of photons per mode for $\mu =1.08\pm 0.02$. The data are shown as black dots + error bars, while the theoretical curve according to Equation (6) is shown as a black line. From the fitting procedure, we obtain $t=0.92\pm 0.09$.

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**MDPI and ACS Style**

Allevi, A. Mesoscopic States of Light for the Detection of Weakly Absorbing Objects. *Photonics* **2022**, *9*, 819.
https://doi.org/10.3390/photonics9110819

**AMA Style**

Allevi A. Mesoscopic States of Light for the Detection of Weakly Absorbing Objects. *Photonics*. 2022; 9(11):819.
https://doi.org/10.3390/photonics9110819

**Chicago/Turabian Style**

Allevi, Alessia. 2022. "Mesoscopic States of Light for the Detection of Weakly Absorbing Objects" *Photonics* 9, no. 11: 819.
https://doi.org/10.3390/photonics9110819