Optimization of SPGD Algorithm Based on Adaptive Random Perturbation Voltages in Coherent Beam Combining

Jiaqin Qi; Wenhui Zheng; Wenjun Jiang; Guiyuan Tan; Liyun Zhong; Jianglei Di; Xiaoyan Wu; Guodong Liu; Yuwen Qin

doi:10.3788/LOP231638

Laser & Optoelectronics Progress, Volume. 61, Issue 15, 1514004(2024)

Optimization of SPGD Algorithm Based on Adaptive Random Perturbation Voltages in Coherent Beam Combining

Jiaqin Qi^1,2,3, Wenhui Zheng^1,2,3, Wenjun Jiang^1,2,3, Guiyuan Tan^1,2,3, Liyun Zhong^1,2,3, Jianglei Di^1,2,3、*, Xiaoyan Wu^4、**, Guodong Liu⁴, and Yuwen Qin^1,2,3

Author Affiliations

¹Institute of Advanced Photon Technology, School of Information Engineering, Guangdong University of Technology, Guangzhou 510006, Guangdong, China

²Key Laboratory of Synsensory Fusion Photonics Technology, Ministry of Education, Guangzhou 510006, Guangdong, China

³Guangdong Provincial Key Laboratory of Information Photonics Technology, Guangzhou 510006, Guangdong, China

⁴Institute of Fluid Physics, China Academy of Engineering Physics, Mianyang 621900, Sichuan, China

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Figures & Tables(12)

Fig. 1. Flow chart for executing SPGD algorithm

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Fig. 2. Interaction diagram between variables in the J-Based SPGD algorithm

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Fig. 3. Flow chart of data acquisition and statistics

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Fig. 4. Values of p₁ and η₁ under different perturbation voltage amplitudes

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Fig. 5. Iteration curves of each variable after optimization. (a) γ; (b) $δ u$ ; (c) $δ J$ ; (d) $u$ ; (e) $Δ J$ ; (f) $J$

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Fig. 6. Iteration curves of the evaluation function of Piecewise SPGD, AdmSPGD, ExpSPGD, and SPGD

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Fig. 7. Iteration curves of the evaluation function of each algorithm. (a) 3 beams; (b) 19 beams

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Fig. 8. Distribution of the iteration number when each algorithm converges. (a) Piecewise SPGD; (b) AdmSPGD; (c) ExpSPGD; (d) SPGD

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Table 1. The process of Piecewise SPGD algorithm

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Table 1. The process of Piecewise SPGD algorithm

Piecewise SPGD algorithm
1）Set	initial control voltages $u^{(0)} = \{0, \dots, 0\}$ ，gain coefficient $γ_{0} = 4.5$ ，and measure the initial value of the evaluation function $J^{(0)}$
2）For	$n = 0,1, 2, \dots, N$ do
3）	generate a set of random perturbation voltages that obey the amplitude of $δ u^{(n)} = π \times (1 - 0.7 \times J^{(n)}) / 3$
4）	apply forward perturbation voltages： $u^{(n)} + δ u^{(n)}$
5）	obtain performance evaluation functions： ${J_{+}}^{(n)}$
6）	apply negative perturbation voltages： $u^{(n)} - δ u^{(n)}$
7）	obtain performance evaluation functions： ${J_{-}}^{(n)}$
8）	obtain the change of the evaluation function： $δ J^{(n)} = {J_{+}}^{(n)} - {J_{-}}^{(n)}$
9）	determine if $m a x ({J_{+}}^{(n)}, {J_{-}}^{(n)})$ is greater than $J^{(n)}$ ，if yes or $J^{(n)}$ is convergent then execute 9.1，if no then execute 9.2
	9.1：update the control voltages， $\{\begin{matrix} γ = \frac{1}{\|{J_{+}}^{(n)} - {J_{-}}^{(n)}\|} \\ u^{(n + 1)} = u^{(n)} + γ δ J^{(n)} δ u^{(n)} \end{matrix},$ 9.2：update the control voltages， $u^{(n + 1)} = u^{(n)} + γ_{0} δ u^{(n)} δ J^{(n)}$
10）	obtain the performance evaluation function $J^{(n + 1)}$ and determine whether $J^{(n + 1)}$ meets the end of algorithm condition
11）End For

Table 2. Simulation parameter setting
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Table 2. Simulation parameter setting
Parameter Value
Distance： $L$ /m 2
Wavelength： $λ$ /10^-9 m 1064
Beam waist： $ω$ /10^-3 m 4
Beam spacing： $d$ /10^-2 m 1
Working mode Single-mode

Table 3. Initial parameter setting of each algorithm
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Table 3. Initial parameter setting of each algorithm
Algorithm Parameter
SPGD $γ = 1$ ，amplitude of $δ u = π / 3$
ExpSPGD $γ_{0} = 1.6$ ， $α = 0$ ，amplitude of $δ u = π / 3$
AdmSPGD $γ = 0.8$ ， $p = 0.3$ ， $ρ = 1$ ，amplitude of $δ u = π / 3$
Piecewise SPGD $γ = 4.5$ ，amplitude of $δ u^{(0)} = π / 3$

Table 4. Iteration number for algorithm convergence
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Table 4. Iteration number for algorithm convergence
Algorithm Iteration number of $J = 0.9$ Iteration number of $J = 0.95$
Piecewise SPGD 17.5 23.5
AdmSPGD 20.5 26.0
ExpSPGD 23.1 29.0
SPGD 27.5 34.0

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Jiaqin Qi, Wenhui Zheng, Wenjun Jiang, Guiyuan Tan, Liyun Zhong, Jianglei Di, Xiaoyan Wu, Guodong Liu, Yuwen Qin. Optimization of SPGD Algorithm Based on Adaptive Random Perturbation Voltages in Coherent Beam Combining[J]. Laser & Optoelectronics Progress, 2024, 61(15): 1514004

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