# System Level Requirement Analysis of Beam Alignment and Shaping for Optical Wireless Power Transmission System by Semi–Empirical Simulation

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## Abstract

**:**

## 1. Introduction

- To propose a methodology based on a simple model to simulate and evaluate system level performance of OWPT in a general configuration;
- To clarify the system level requirements regarding beam alignment and shaping based on a particular parameter set such as the beam divergence angle and the size of the solar array;
- To propose a beam alignment and shaping concept based on derived requirements to assess necessary sensors and components for optics of OWPT.

## 2. Definition of OWPT System Model and Requirement Analysis Study

## 3. Factors of Efficiency in OWPT Systems

## 4. Beam Shaping and Beam Alignment Requirement in Non-Cooperative OWPT

#### 4.1. Geometrical Configuration

#### 4.2. Orthogonal Cylindrical Beam Expander Optics

#### 4.3. Requirement for Focus Adjustment (Beam Size Control)

#### 4.4. Requirement for Beam Alignment

^{5}–8 × 10

^{5}in 40 < L < 100 m. A resolution of 2000 to 5000 in L < 10 m would be feasible by a single mechanism. However, there needs to be a quite accurate single mechanism or a complex combination of various single mechanisms for L > 10 m.

## 5. Beam Shaping and Beam Alignment Requirement in Cooperative OWPT

#### 5.1. Geometrical Configuration and Optics

#### 5.2. Requirement for Focus Adjustment

#### 5.3. Requirement for Beam Alignment

_{prj}is calculated by the method summarized in Appendix A and Appendix B. Setting $\delta \psi =\delta \varphi =\delta \omega =0$ and replacing the area of the array ${S}_{prj}$ with ${S}_{prj}cos\delta \theta $, these result in Figure 17.

## 6. Summary of Requirement for Focus Adjustment and Beam Alignment

## 7. Conceptual Discussion of Beam Alignment in Cooperative OWPT

#### 7.1. Rough Alignment Phase

- The objective of this phase is to introduce the image of the solar cell array within the image sensor’s FOV, which is used in a precise alignment phase, and to conduct initial alignment for the mutual relative attitude.

#### 7.2. Precise Alignment Phase

- Using the image sensor, the transmitter aligns the beam direction so that the beam center matches the array’s. Additionally, the image sensor detects the relative tilt angle of the array to the optical axis. The transmitter requests the array to align the array’s normal vector with the optical axis. The last step of the alignment is that the transmitter rotates the beam around its optical axis to match the beam shape (square) with the array’s shape (square) and the transmitter determines the necessary (de)focus adjustment by means of range information to the array. This concludes the alignment and beam shaping process. In the case of a moving target, the transmitter tracks the array using the image sensor and repeats the above procedures.

_{SC}is the size of the array. To detect a decrease of the apparent angler size of the array from θ = 0, it should be larger than the image sensor’s accuracy of 0.1 mrad. This means that ${l}_{SC}\left(1-cos\theta \right)/L\ge 0.1mrad$. When l

_{SC}= 10 cm and L = 100 m, the detection limit is θ = 451 mrad, which is less than the requirement (645 mrad). Even though 451 mrad itself is marginal for the requirement, using a zoom lens improves detection for longer L values. The transmitter requests the array to adjust its attitude, which corresponds to other 2 DoF. Finally, the transmitter rotates the beam around its optical axis to match its square beam shape with the array, which corresponds to the remaining 1 DoF.

## 8. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Ray Transfer Matrices of the Optics Used in this Study

_{x}, θ

_{x}be the height of the ray and the angle that makes with the optical axis in the X direction at the exit of the optics. l

_{y}and θ

_{y}are defined similarly. The ray transfer matrices of this optics are written as follows:

_{1}= 30 mm, which is the default value and is optimized for the power generation ratio and perturbed by the focus error. The rest are fixed parameters such as d

_{2}= 120 mm, d

_{3}= 20 mm, f

_{cnv}= 150 mm, f

_{ccv}= 30 mm, l

_{sc}= 5 mm, and θ

_{beam}= 0.8 deg.

## Appendix B. Beam Propagation and Power Generation Ratio Calculation

_{1}, P

_{2}, P

_{3}, P

_{4}of the square beam are expressed by the following equations using a real parameter, k. The beam is projected onto the XY plane, whose center is deviated length L from the Z-axis. This projection is written in terms of a rotation matrix. Since the origin of the rotation is $\left(\begin{array}{ccc}0,& 0,& H\end{array}\right)$ and the angle of the rotation is $tan\varphi =L/H$, the rotation matrix $R\left(\varphi \right)$ is written as:

_{1}, C

_{2}, C

_{3}, C

_{4}) are determined by (A3). The area of the projected beam (S

_{prj}) is determined by the coordinates of C

_{1}, C

_{2}, C

_{3}, C

_{4}. Since the position coordinates of the solar cell array are known, the two factors of power generation ratio are calculated as described in Section 3.

_{x}, Δ

_{y}) are introduced in ray transfer matrices as follows:

_{x}, Δ

_{y}are used for calculation and optimization of the power generation ratio. Setting ${l}_{x}=\left(sizeofsolararray\right)/2$ gives the optimum value of ${\mathsf{\Delta}}_{x}$, which depends on L. Similarly, setting ${l}_{y}=\left(sizeofsolararray\right)/2$ gives the optimum value of ${\mathsf{\Delta}}_{y}$.

## Appendix C. Power Generation Ratio Calculation Including Perturbations

#### Appendix C.1. Focus Perturbation

_{x opt}and Δ

_{y opt}give the optimum of the power generation ratio in the X and Y directions’ focus. Additional focus perturbations Δ′

_{x}, Δ′

_{y}are introduced to estimate the requirement for focus adjustment with replacements ${\mathsf{\Delta}}_{x}\to {\mathsf{\Delta}}_{xopt}+{{\mathsf{\Delta}}^{\prime}}_{x}$ and ${\mathsf{\Delta}}_{y}\to +{\mathsf{\Delta}}_{yopt}+{{\mathsf{\Delta}}^{\prime}}_{y}$.

_{x}, Δ′

_{y}are used in calculation of the power generation ratio.

#### Appendix C.2. Rotational Perturbations

- The X direction deviation error is caused by an alignment error around the Y-axis. To calculate the power generation ratio, $\delta \omega $ and $\delta \psi $ are set to be zero.
- The Y direction deviation error is caused by an alignment error around the X-axis. To calculate the power generation ratio, $\delta \omega $ and $\delta \varphi $ are set to be zero.
- To calculate the power generation ratio with the Z-axis rotational alignment error, $\delta \psi $ and $\delta \varphi $ are set to be zero.

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**Figure 1.**Geometrical configuration of non-cooperative OWPT studied: (

**a**) general configuration of L ≠ 0; (

**b**) configuration of L = 0.

**Figure 12.**Range dependence of power generation ratio (Cooperative OWPT). (

**a**) When the focus is adjusted for each R, the power generation ratio is stably maintained at 100%; (

**b**) There is a large variation in the power generation ratio for the range from 0 m to 100 m in case where the focus is optimized and fixed at specific range.

Direction | Accuracy Requirement | |
---|---|---|

Non-Cooperative | Cooperative | |

(De)Focus (X direction) | 2.3 mm (L = 1 m) | 3.5 mm (R = 1 m) 350 μm (R = 10 m) 39 μm (R = 100 m) |

76 μm (L = 10 m) | ||

1.2 μm (L = 100 m) | ||

(De)Focus (Y direction) | 1.32 mm (L = 1 m) | |

132 μm (L = 10 m) | ||

1.2 μm (L = 100 m) | ||

Beam Deviation (X direction) | 2.21 mrad (L = 1 m) | 6.9 mrad (R = 1 m) 0.8 mrad (R = 10 m) 69 μrad (R = 100 m) X, Y directions are identical |

149 μrad (L = 10 m) | ||

11.7 μrad (L = 100 m) | ||

Beam Deviation (Y direction) | 2.51 mrad (L = 1 m) | |

631 μrad (L = 10 m) | ||

57.5 μrad (L = 100 m) | ||

Beam Rotation (Around Optical Axis) | 182 mrad (L = 1 m) | 180 mrad (R < 100 m) |

74.1 mrad (L = 10 m) | ||

6.7 mrad (L = 100 m) | ||

Solar Cell Array Tilt (X(Y) direction) | 645 mrad (R < 100 m) X, Y directions are identical |

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**MDPI and ACS Style**

Asaba, K.; Miyamoto, T.
System Level Requirement Analysis of Beam Alignment and Shaping for Optical Wireless Power Transmission System by Semi–Empirical Simulation. *Photonics* **2022**, *9*, 452.
https://doi.org/10.3390/photonics9070452

**AMA Style**

Asaba K, Miyamoto T.
System Level Requirement Analysis of Beam Alignment and Shaping for Optical Wireless Power Transmission System by Semi–Empirical Simulation. *Photonics*. 2022; 9(7):452.
https://doi.org/10.3390/photonics9070452

**Chicago/Turabian Style**

Asaba, Kaoru, and Tomoyuki Miyamoto.
2022. "System Level Requirement Analysis of Beam Alignment and Shaping for Optical Wireless Power Transmission System by Semi–Empirical Simulation" *Photonics* 9, no. 7: 452.
https://doi.org/10.3390/photonics9070452