# Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm

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## Abstract

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## 1. Introduction

## 2. Principles and Methods

#### 2.1. Design of 7 × 7 DOE with Uniform Energy Distribution

#### 2.2. Point Matching in Structured-Light 3D Imaging and Target Reconstruction

## 3. Results

#### 3.1. Design of 7 × 7 DOE with Uniform Energy Distribution

#### 3.2. Structured-Light 3D Imaging and Target Reconstruction

## 4. Discussion

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## 5. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 1.**Optimization flow of Vector IFTA. First, the initial solution is obtained by the revised GS algorithm, and vector electromagnetic simulation is performed on it. Then, optimized results are judged according to the evaluation function and the number of iterations. Finally, the quasi-continuous-phase metasurface with diffraction uniform is obtained.

**Figure 2.**The optimization process of the 7 × 7 DOE. (

**A**) Evaluation function EF versus the number of iterations K. The diffraction efficiencies at all orders of the initial and final solutions are also shown. (

**B**) Phase distributions of the initial solution, final solution, and the difference between them. (

**C**) The electron microscope scanning images of the 7 × 7 DOE.

**Figure 3.**Principles and results of structured-light 3D imaging and target reconstruction. (

**A**) Setup of the binocular vision system. DOE and the VSCEL are integrated together and placed between the two cameras. The target objects are a full-face mask and a white paper plane with different depths and heights. (

**B**) Principle of acquiring depth information and point matching for the binocular vision system. (

**C**) Result of structured-light 3D reconstruction with different viewing directions.

Parameter | Result | |
---|---|---|

Camera—Left | Internal Reference Matrix | $\left[\begin{array}{ccc}2870.553& -0.061& 1269.105\\ 0& 2871.493& 941.98\\ 0& 0& 1\end{array}\right]$ |

Distortion Factor | −0.197, 0.183, −0.156, −0.00007, 0.00065 | |

Camera—Right | Internal Reference Matrix | $\left[\begin{array}{ccc}2869.618& -0.097& 1278.367\\ 0& 2869.667& 949.371\\ 0& 0& 1\end{array}\right]$ |

Distortion Factor | −0.1897, 0.093, 0.1385, −0.00001, −0.0002 | |

System | Rotation Matrix | $\left[\begin{array}{ccc}1& 0.001& -0.003\\ -0.0005& 1& 0.002\\ 0.003& -0.002& 1\end{array}\right]$ |

Translation Matrix | $\left[\begin{array}{ccc}105.76& -0.0041& 0.9302\end{array}\right]$ |

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## Share and Cite

**MDPI and ACS Style**

Zhang, R.; Qiao, S.; Luo, Y.; Guo, Y.; Li, X.; Zhang, Q.; Fan, Y.; Zhao, Z.; Luo, X.
Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm. *Nanomaterials* **2024**, *14*, 929.
https://doi.org/10.3390/nano14110929

**AMA Style**

Zhang R, Qiao S, Luo Y, Guo Y, Li X, Zhang Q, Fan Y, Zhao Z, Luo X.
Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm. *Nanomaterials*. 2024; 14(11):929.
https://doi.org/10.3390/nano14110929

**Chicago/Turabian Style**

Zhang, Runzhe, Siyuan Qiao, Yixiong Luo, Yinghui Guo, Xiaoyin Li, Qi Zhang, Yulong Fan, Zeyu Zhao, and Xiangang Luo.
2024. "Structured-Light 3D Imaging Based on Vector Iterative Fourier Transform Algorithm" *Nanomaterials* 14, no. 11: 929.
https://doi.org/10.3390/nano14110929