# Holographic Three-Dimensional Imaging of Terra-Cotta Warrior Model Using Fractional Fourier Transform

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Principle of The Proposed Method

#### 2.1. Spatial Coordinate Transformation for Calculating Holograms of Terra-Cotta Warrior Model

_{0}in the coordinate system $\left({x}^{\prime}{y}^{\prime}{z}^{\prime}\right)$. We calculate the holograms of the model along a circle route line, with 60 viewpoints at intervals of 6 degrees [17].

_{0}.

#### 2.2. FRT and Hologram Generation

_{1}, and the distance from the second layer to the lens is d

_{2}. The distance between the two planes can be expressed as

_{i}, and the standard focal length ${f}_{e}$ are given, the fractional order p

_{i}of the ith object plane can be expressed as

## 3. Digital Reconstruction and Electro-Optical Reconstruction Experiment

#### 3.1. Digital Reconstruction

#### 3.2. Electro-Optical Reconstruction Experiment

#### 3.3. Image Quality Evaluation

#### 3.4. Electro-Optical Reconstruction of Kinoforms

#### 3.5. Relationship Between Computational Distance and Imaging Quality

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**Digital reconstructed images at different viewing angles with kinoform sequence scheme II.

**Figure 7.**Layering Terra-Cotta Warrior model, thickness of layering set at 5 mm, and the inappropriate fringes are redisplayed on the model.

**Figure 10.**(

**a**) Speckle index (SI) of reconstructed image from single hologram calculated by different random phases. (

**b**) SI of superposed reconstructed images from different number of holograms.

**Figure 11.**Electro-optical reconstructed images at different viewing angles with kinoform sequence scheme I.

**Figure 12.**Electro-optical reconstructed images at different viewing angles with kinoform sequence scheme II.

**Figure 15.**The Relationship between Computational Distance and Image Quality of 10 Superimposed Images.

Viewing Angle | 0° | 6° | … | 354° |

Scheme I$({H}_{\theta ,t})$ | ${H}_{0,1}$ | ${H}_{6,1}$ | … | ${H}_{354,1}$ |

Scheme II$({H}_{\theta ,t})$ | ${H}_{0,1},{H}_{0,2},{H}_{0,3},\dots ,{H}_{0,T}$ | ${H}_{6,1},{H}_{6,2},{H}_{6,3},\dots ,{H}_{6,T}$ | … | ${H}_{354,1},{H}_{354,2},{H}_{354,3},\dots ,{H}_{354,T}$ |

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**MDPI and ACS Style**

Gao, Z.-F.; Zheng, H.-D.; Yu, Y.-J.
Holographic Three-Dimensional Imaging of Terra-Cotta Warrior Model Using Fractional Fourier Transform. *J. Imaging* **2019**, *5*, 67.
https://doi.org/10.3390/jimaging5080067

**AMA Style**

Gao Z-F, Zheng H-D, Yu Y-J.
Holographic Three-Dimensional Imaging of Terra-Cotta Warrior Model Using Fractional Fourier Transform. *Journal of Imaging*. 2019; 5(8):67.
https://doi.org/10.3390/jimaging5080067

**Chicago/Turabian Style**

Gao, Zhi-Fang, Hua-Dong Zheng, and Ying-Jie Yu.
2019. "Holographic Three-Dimensional Imaging of Terra-Cotta Warrior Model Using Fractional Fourier Transform" *Journal of Imaging* 5, no. 8: 67.
https://doi.org/10.3390/jimaging5080067