# Real-Time Correction of a Laser Beam Wavefront Distorted by an Artificial Turbulent Heated Airflow

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## Abstract

**:**

## 1. Introduction

## 2. The Fast Adaptive Optical System

#### 2.1. Deformable Mirror

#### 2.2. Shack–Hartmann Wavefront Sensor

#### 2.3. Adaptive Optical System Control Loop

## 3. Experimental Setup

## 4. Processing the Results of the Experiment

^{(−5/3)}corresponds to the Kolmogorov spectrum. The sampling duration of the focal spot coordinates was 10 s (at a frequency of 2000 Hz, 20,000 samples were recorded), which provided a resolution along the frequency axis of 0.1 Hz.

- A sample of the offset coordinates of the focal spots of the lens array of the WFS with a duration of 10 s was recorded. This made it possible to achieve a resolution along the frequency axis of 0.1 Hz. At a frequency of 2000 Hz, a total of 20,000 values of coordinate offsets of each focal spot were recorded
- The transition was carried out from sampling by coordinates to sampling by the coefficients of the wavefront expansion by Zernike polynomials. In this work, we used a set of 24 Zernike polynomials in Wyant indices [23] (1 and 2—tilts, 3—defocus, 4 and 5—astigmatism, 6 and 7—coma, 8—spherical, etc.).
- Using the Fourier transform, the transition from the time domain to the frequency domain was carried out for sampling each Zernike polynomial;
- The power spectral density was calculated for each mode;
- Further, by integrating the spectral power density, the spectral energy was calculated.

## 5. Discussion

- The combination of FPGA performance and a bimorph wavefront corrector in an adaptive optical system allows correction of artificially created turbulence in real time. The correction frequency in the experiments was chosen to be equal to 2000 Hz. Such a stable correction frequency is almost impossible to obtain using a conventional PC. The PC, unlike the FPGA, performs I/O at the driver level, thereby increasing the time of the closed correction cycle. FPGA exchanges data between external devices (wavefront sensor and corrector control unit) directly. In addition, the FPGA performs parallel processing of information, which has significant limitations in the case of using a PC.
- The speed of the AOS controlled by the FPGA made it possible to analyze the effectiveness of aberration correction up to the 23rd Zernike polynomial, whose bandwidth is about 100 Hz, in detail.
- The bimorph WFC does not have the ability to correct for the slopes of the WF. Accordingly, the correction efficiency of the first two Zernike polynomials is negative, i.e., there is an increase in the amplitude of the initial slopes. To eliminate the slopes, it is necessary to use either a separate beam position stabilization system (see, for example, [25]), or to install a mirror in a tip–tilt mount. In this case, the virtual slopes used in the experiment become real and the voltages calculated during operation are applied to the control drives of the tip–tilt mount.
- WFC used in the experiments has three rings of electrodes and cannot reproduce a spherical aberration of the third order (polynomial # 24), since this aberration has four extremums (max–min). To reduce the aberration # 24, a higher spatial resolution WFC is required.
- The aberrations from 3 to 23 are compensated well enough by this WFC. However, because the initial amplitude of the polynomial # 24 is small compared to other aberrations, the undercompensating of this aberration can be neglected.

## 6. Conclusions

## Author Contributions

## Funding

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Bimorph mirror used in experiments: (

**a**) Mirror photo; (

**b**) electrodes structure. The numbers indicate the channels of the mirror. The first electrode, conventionally shown in the lower-left corner, has the dimensions of the mirror aperture and is used to control the defocusing of the wavefront.

**Figure 4.**FPGA timing diagram. The total time of one closed cycle is 500 microseconds, which corresponds to an operating frequency of 2000 Hz.

**Figure 5.**Adaptive optical system experimental setup. WFS—wavefront sensor; mirror CU—mirror control unit.

**Figure 6.**Spectral power density of the oscillation of the X coordinate of the WFS lens array focal spot.

Parameter | Value |
---|---|

Clear aperture | 50 mm |

Electrodes number | 31 |

Control voltage range | −200 V ± 300 V |

Maximal stroke | ±10 µm |

First resonant frequency | 8.3 kHz |

Coating | Protected silver |

Size | Ø 70 mm × 68 mm |

Weight | 320 g |

Parameter | Value |
---|---|

Sensor | Alexima LUX19HS |

Spectral bandwidth | 350–1100 nm |

Dynamic Range (Tilt) | ±50λ |

Accuracy of measurements | λ/90 |

Frame rate | 2500 fps @ 1920 × 1080 |

~4000 fps @ 480 × 480 | |

Interface | Fiber Optic 40 Gb/s |

Lenslet array focal length | 12 mm |

Number of working sub-apertures | 20 × 20 |

Input light beam size | 4.8 × 4.8 mm |

Resolution | 8 bit |

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**MDPI and ACS Style**

Rukosuev, A.; Nikitin, A.; Toporovsky, V.; Sheldakova, J.; Kudryashov, A. Real-Time Correction of a Laser Beam Wavefront Distorted by an Artificial Turbulent Heated Airflow. *Photonics* **2022**, *9*, 351.
https://doi.org/10.3390/photonics9050351

**AMA Style**

Rukosuev A, Nikitin A, Toporovsky V, Sheldakova J, Kudryashov A. Real-Time Correction of a Laser Beam Wavefront Distorted by an Artificial Turbulent Heated Airflow. *Photonics*. 2022; 9(5):351.
https://doi.org/10.3390/photonics9050351

**Chicago/Turabian Style**

Rukosuev, Alexey, Alexander Nikitin, Vladimir Toporovsky, Julia Sheldakova, and Alexis Kudryashov. 2022. "Real-Time Correction of a Laser Beam Wavefront Distorted by an Artificial Turbulent Heated Airflow" *Photonics* 9, no. 5: 351.
https://doi.org/10.3390/photonics9050351