# Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing

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## Abstract

**:**

## 1. Introduction

## 2. The Principle of PR

#### 2.1. Gerchberg–Saxton Algorithm

#### 2.2. The Modified PR Algorithm

## 3. The Design of the Experiments

#### 3.1. Measuring Plane Mirror

#### 3.2. Measuring Concave Mirror

#### 3.3. Measuring Spherical Mirror

## 4. Results and Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 6.**The measurement results by removing the first four items. (

**a**) MPR: RMS = 0.0475 λ, PV = 5.3352 λ; (

**b**) ZYGO interferometer: RMS = 0.037 λ, PV = 4.149 λ.

**Figure 7.**The measurement results by removing the first four items and spherical. (

**a**) MPR: RMS = 0.04392 λ, PV = 4.9304 λ; (

**b**) ZYGO interferometer: RMS = 0.03325 λ, PV = 3.7685 λ.

**Figure 10.**The measurement results. (

**a**) MPR: RMS = 2.5322 λ, PV = 15.529 λ; (

**b**) ZYGO interferometer: RMS = 2.5139 λ, PV = 14.119 λ.

**Figure 12.**The measurement results obtained by removing the first four items (piston, tilt X, tilt Y, and power) on spherical mirror II. (

**a**) MPR: RMS = 0.0527 λ, PV = 0.667 λ; (

**b**) ZYGO interferometer: RMS = 0.041 λ, PV = 0.585 λ.

**Figure 13.**The measurement results of aspherical mirror. (

**a**) MPR: RMS = 0.667 λ, PV = 3.027 λ; (

**b**) ZYGO interferometer: RMS = 0.632 λ, PV = 2.155 λ.

The Type of Tested Mirror | Evaluation Index | MPR | ZYGO | RMSD ifference |
---|---|---|---|---|

Plane mirror (removing the first four items) | RMS PV | 0.0475 λ 5.3352 λ | 0.037 λ 4.149 λ | 0.0105 λ |

Plane mirror (removing the first four items and spherical aberration) | RMS PV | 0.04392 λ 4.9304 λ | 0.03325 λ 3.7685 λ | 0.01067 λ |

Spherical concave mirror I | RMS PV | 2.5322 λ 15.529 λ | 2.5139 λ 14.119 λ | 0.0183λ |

Spherical concave mirror II | RMS PV | 0.0527 λ 0.667 λ | 0.041 λ 0.585 λ | 0.0117 λ |

Aspherical mirror | RMS PV | 0.667 λ 3.027 λ | 0.632 λ 2.155 λ | 0.035 λ |

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**MDPI and ACS Style**

Ma, X.; Wang, J.; Wang, B.; Liu, X.; Chen, Y.
Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing. *Micromachines* **2023**, *14*, 1142.
https://doi.org/10.3390/mi14061142

**AMA Style**

Ma X, Wang J, Wang B, Liu X, Chen Y.
Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing. *Micromachines*. 2023; 14(6):1142.
https://doi.org/10.3390/mi14061142

**Chicago/Turabian Style**

Ma, Xinxue, Jianli Wang, Bin Wang, Xinyue Liu, and Yuqiang Chen.
2023. "Research on Optical Metrology for Complex Optical Surfaces with Focal Plane Wavefront Sensing" *Micromachines* 14, no. 6: 1142.
https://doi.org/10.3390/mi14061142