# Lensless Scheme for Measuring Laser Aberrations Based on Computer-Generated Holograms

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Algorithm for Measuring Wavefront Aberrations

- Selection of $\left\{{\alpha}_{n}\right\}$ and calculation of temporary wavefront model ${\psi}_{t}\left(x,y\right);$
- Synthesis of CGH structure;
- Displaying the CGH structure by SLM;
- Capturing of output intensity distribution by CCD camera;
- Searching for correlation peak position and determining the optimization function value;
- Checking the termination condition of the algorithm. If condition is satisfied, go to step 7, otherwise repeat steps 1–6;
- Decision.

#### 2.2. Modified Wavefront Aberration Measurement Algorithm

## 3. Results and Discussion

## 4. Conclusions

## Author Contributions

## Funding

## Conflicts of Interest

## References

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**Figure 3.**The optical scheme of the wavefront sensor with a Fourier transform lens (

**a**) and the proposed scheme with a digital Fresnel lens (

**b**).

**Figure 4.**Comparison of the correlation functions obtained via two methods for lenses with a focal length equal to 250 mm (

**a**), 500 mm (

**b**), and 1000 mm (

**c**).

Focal Length | Polynomial Type | $\mathbf{Value}\mathbf{of}\left\{{\mathit{\alpha}}_{\mathit{n}}\right\},\mathsf{\mu}\mathbf{m}$ | $\mathsf{\Delta}\left\{{\mathit{\alpha}}_{\mathit{n}}\right\}$ | |
---|---|---|---|---|

Fourier Lens | Digital Fresnel Lens | |||

250 mm | ${Z}_{2}^{2}$ | 1.52 | 1.50 | λ/50 |

${Z}_{3}^{-1}$ | 1.49 | 1.52 | λ/33 | |

500 mm | ${Z}_{2}^{2}$ | 1.50 | 1.53 | λ/33 |

${Z}_{3}^{-1}$ | 1.52 | 1.53 | λ/100 | |

1000 mm | ${Z}_{2}^{2}$ | 1.49 | 1.49 | λ/100 |

${Z}_{3}^{-1}$ | 1.54 | 1.52 | λ/50 |

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**MDPI and ACS Style**

Krasin, G.; Kovalev, M.; Stsepuro, N.; Ruchka, P.; Odinokov, S.
Lensless Scheme for Measuring Laser Aberrations Based on Computer-Generated Holograms. *Sensors* **2020**, *20*, 4310.
https://doi.org/10.3390/s20154310

**AMA Style**

Krasin G, Kovalev M, Stsepuro N, Ruchka P, Odinokov S.
Lensless Scheme for Measuring Laser Aberrations Based on Computer-Generated Holograms. *Sensors*. 2020; 20(15):4310.
https://doi.org/10.3390/s20154310

**Chicago/Turabian Style**

Krasin, George, Michael Kovalev, Nikita Stsepuro, Pavel Ruchka, and Sergey Odinokov.
2020. "Lensless Scheme for Measuring Laser Aberrations Based on Computer-Generated Holograms" *Sensors* 20, no. 15: 4310.
https://doi.org/10.3390/s20154310