-
首先,在37单元DM下仿真分析了所提ABSPGD算法对波前畸变的校正效果,并比较了ABSPGD、ASPGD和SPGD算法在不同湍流强度下的收敛速度和稳定性。然后在69单元DM下分析了DM单元数的增加对算法性能的影响。这里使用
$ D/{r_0} = 5,10,15 $ 表示不同强度的大气湍流,其中$ {r_0} $ 是大气相干长度,$ D $ 是接收端望远镜的直径。采用前65阶Zernike多项式拟合不同湍流强度的波前畸变,并将SR作为性能评价指标。37单元DM中的参数$ \alpha $ 、$ d $ 、$ \omega $ 分别设置为2、0.3、0.36、69单元DM中相应参数分别设置为2、0.22、0.36。 -
不同湍流强度下的波前畸变以及经过ABSPGD算法校正后的残余波前如图3所示。图3也给出了相应的峰谷值(Peak-to-Valley, PV)和均方根(Root Mean Square, RMS),PV和RMS的值越小,证明波前畸变程度越弱,光束质量越好。在不同湍流强度下,校正前后的SR值如表1所示。
Figure 3. The wavefront distortion and the residual wavefront corrected by ABSPGD algorithm under different turbulence intensities. (a)
$ {D \mathord{\left/ {\vphantom {D {{r_0}}}} \right. } {{r_0}}} = 5 $ ; (b)$ {D \mathord{\left/ {\vphantom {D {{r_0}}}} \right. } {{r_0}}} = 10 $ ; (c)$ {D \mathord{\left/ {\vphantom {D {{r_0}}}} \right. } {{r_0}}} = 15 $ Intensity of turbulence Before correction After correction 5 $ {\text{0}}{\text{.33}} $ $ 0.83 $ 10 ${\text{9} }{\text{.62} } \times {\text{1} }{ {\text{0} }^ {-4} }$ $ 0.47 $ 15 ${\text{7} }{\text{.48} } \times {\text{1} }{ {\text{0} }^{-5} }$ $ 0.31 $ Table 1. SR values of wavefront distortion before and after correction by ABSPGD algorithm
从图3可以清楚地看出,对波前畸变校正之前,图中存在严重的像差。随着湍流强度的增加,PV和RMS的值增大,波前畸变越严重。对波前畸变校正后,像差明显变小,PV和RMS的值也相应地减小,这说明所提ABSPGD算法可以有效地校正波前畸变。根据表1可知,随着波前畸变程度的增加,校正后的SR值变小。校正后的SR值分别为0.83、0.47和0.31,这说明相同条件下,湍流强度越强,算法的收敛精度越低。
-
在实际应用中,算法的收敛速度和稳定性尤为重要。为了验证所提算法在收敛速度和稳定性方面的有效性,仿真了ABSPGD、ASPGD和SPGD算法在三种湍流强度下的SR曲线。由于算法本身的随机性,在不同湍流强度下,针对每个算法分别进行了30次仿真,取数据的平均值进行对比分析,同时分别随机选取每种算法的10组数据来对比算法稳定性。仿真结果如图4所示,不同湍流强度下各算法的最优增益系数如表2所示。
Figure 4. SR variation curves of SPGD, ASPGD and ABSPGD algorithms under different turbulence intensities. (a)
$ {D \mathord{\left/ {\vphantom {D {{r_0}}}} \right. } {{r_0}}} = 5 $ ;(b)$ {D \mathord{\left/ {\vphantom {D {{r_0}}}} \right. } {{r_0}}} = 10 $ ;(c)$ {D \mathord{\left/ {\vphantom {D {{r_0}}}} \right. } {{r_0}}} = 15 $ Intensity of turbulence SPGD ASPGD ABSPGD 5 0.7 0.065 0.065 10 2.8 0.065 0.065 15 4 0.065 0.065 Table 2. Optimal gain coefficients of SPGD, ASPGD and ABSPGD algorithms under different turbulence intensities
为了方便比较各个算法的收敛性能,文中在不同湍流下分别选取0.8、0.45、0.3作为阈值,对各个算法收敛到阈值时的迭代次数进行比较,因为在这几个阈值处,各个算法的收敛精度已经几乎达到了稳定。从图4可以看出,在不同湍流强度下,SPGD算法的收敛速度均低于ABSPGD和ASPGD算法。当湍流强度增大时,SPGD算法在收敛速度方面的劣势更加明显。在这三个算法当中,ABSPGD算法的收敛速度最快。对各组数据的平均值进行分析后可以得出,当湍流强度为5时,ABSPGD、ASPGD和SPGD算法的SR分别经过149次,179次和217次迭代后达到阈值0.8。当湍流强度为10和15时,SPGD算法的SR曲线在迭代100次和800次后开始上升,在447次和1247次时分别达到阈值0.45和0.3。ABSPGD算法和ASPGD算法的SR曲线在迭代开始时快速上升,其中ASPGD算法分别在323次迭代和312次迭代后达到阈值,而ABSPGD算法只需要229次迭代和230次迭代就可以达到阈值。此外,从图4中也可明显看出,虽然ASPGD算法在不同湍流强度下的收敛速度比传统SPGD算法有优势,但在迭代后期会出现震荡,导致算法收敛精度降低。相比之下,文中提出的ABSPGD算法不仅在收敛速度上优于ASPGD和SPGD算法,而且在迭代过程中不会产生震荡。
由表2可知,随着湍流强度的增加,传统SPGD算法的增益系数需要不断调整,以保证算法的校正能力。但在实际应用中,这种调整一般是根据经验进行的,难以保证系统的及时性和准确性。相比之下,所提出的ABSPGD算法可以在不同湍流强度下自适应调整增益系数,大大提高了系统的实时性。
-
从图4中可以明显看出,算法的收敛精度随着湍流强度的增加而下降。为了研究DM单元数对算法性能的影响,本节采用69单元DM校正湍流强度为15的波前畸变,并对ABSPGD、ASPGD、SPGD算法在69单元DM和37单元DM下的SR曲线进行了对比分析。
如图5所示,在69单元DM下,SPGD算法的收敛速度相对于37单元DM有了明显的下降,且收敛精度也从0.31降为0.29。而ABSPGD算法的收敛精度从0.31提高到0.38,并且不会像ASPGD算法那样因为震荡而有所下降。除此之外,ABSPGD算法的收敛速度也要优于ASPGD算法。因此,当湍流强度增大时,可以通过增加DM单元数提高ABSPGD算法的收敛精度,进一步提升算法校正波前畸变的性能。
Adaptive optimization of SPGD method in wavefront distortion correction of space light
doi: 10.3788/IRLA20210697
- Received Date: 2021-12-08
- Rev Recd Date: 2022-02-10
- Publish Date: 2022-08-31
-
Key words:
- adaptive optics /
- atmospheric turbulence /
- wavefront distortion /
- stochastic parallel gradient descent algorithm
Abstract: In order to improve the performance of traditional stochastic parallel gradient descent (SPGD) algorithm for wavefront distortion correction, a novel SPGD optimization algorithm based on AdaBelief optimizer was proposed. The algorithm integrated the first-order momentum and second-order momentum of the AdaBelief optimizer in deep learning into the SPGD algorithm to improve the convergence speed of the algorithm and enable the algorithm to adaptively adjust the gain coefficient adaptively. In addition, adaptive dynamic clipping of the actual gain coefficient was carried out to avoid the oscillation caused by the extreme value of the actual gain coefficient. Simulation results show that under the 37-element deformable mirror (DM), the novel SPGD optimization algorithm can effectively correct wavefront distortion under different turbulence intensities, and the Strehl ratio (SR) of different wavefront distortions after correction is improved to 0.83, 0.47 and 0.31, respectively. In addition, the SR of the proposed algorithm only needs 149, 229 and 230 iterations to reach the threshold under different turbulence intensities. Compared with the traditional SPGD algorithm and other optimization algorithms, the proposed algorithm has a faster convergence speed, and has certain advantages in stability and parameter adjustment.