基于双光斑的深度学习波前复原及校正

Double Spots Based Deep Learning Wavefront Reconstruction and Correction

探索了深度学习算法求解光强反演波前的非线性映射,实现了基于深度学习的波前探测(DLWFS)在自适应光学波前校正中的应用。采用聚焦和离焦双光斑反演波前,既简化了探测器结构,又减小了探测器体积。由于光强反演波前的过程在物理上不存在显式解,因此可以利用深度学习模型cGAN,通过类似图像处理的方式,建立光强-相位的非线性映射,将光斑的强度分布反演为波前分布,最终使波前校正系统配备较为紧凑的波前探测器。训练数据集通过物理衍射仿真获得,模型在测试集上的波前复原的最小残差RMS<0.3μm。在实验中,DLWFS与参考哈特曼波前探测器波前的残差RMS在0.0965~0.1531μm之间。在自适应光学波前校正实验中,将DLWFS作为自适应光学闭环校正过程中的波前探测器,验证了DLWFS的实用效果,光束质量因子从10.83校正至3.61。此外,还讨论了DLWFS的参数敏感性。

Objective The thermal effects and mechanical deformation of high-power lasers impede the output performance of laser systems.Compact laser systems,such as solid lasers,increasingly rely on adaptive optics (AO) featuring simpler structured wavefront sensors to improve beam quality.Unlike the traditional methods that retrieve wavefront from intensity distribution,deep learning,which is well-suited for nonlinear mapping,holds significant potential in this regard.In this article,we present a deep learning wavefront sensor (DLWFS) and demonstrate its applications in AO wavefront corrections.We use conditional generative adversarial networks(c GAN) to extract high-level features from the entire input intensity and retrieve wavefront from the intensity distribution.In other words,we view this intensity-to-wavefront nonlinear mapping as an image-translating problem.To overcome the compression of the wavefront information due to the diversity of coordinates during focusing propagation with a converged beam,the DLWFS relies on acquiring intensity from both the focal spot and the spot just before the focus,also called“double spots”,as input intensity distribution.By comparing the wavefront reconstruction results of DLWFS with those of commercial Shack-Hartmann wavefront sensor (SHWFS),and applying DLWFS in AO closed-loop of wavefront correction,the practicability of DLWFS can be proved.Methods We simulated the propagation of random initial wavefront through physical diffraction to obtain the intensity of spots on focus and defocus (0.98 times focal length) as training data and testing data of DLWFS.Network model c GAN was constructed by a generator (G) and discriminator (D).G had a U-Net structure comprising encoder-decoder convolutional neural networks (CNNs).It was trained to generate wavefront G (x) from input intensity distribution x (x_1,x_(2)),considering both on focus (x_1) and defocus (x_(2))intensity data.The discriminator with a U-Net structure of encoder-decoder was trained to distinguish between tuple (G (x),x) of generated results G (x) with condition x as fake,and tuple (y,x) of real wavefront y with condition x as real.The training of the generator was considered completed when G was able to successfully fool D.The concept is shown in Fig.2 and is expressed mathematically in Eqs.(2)?(5).We built an experimental platform of deformable mirrors (DM) for disturbing and correcting,and referencing SHWFS for comparison,as shown in Fig.7.DLWFS exhibits superior resolution compared to SHWFS,and SHWFS,in turn,offers higher resolution than DM for the purpose of wavefront correction.The laser beam was split 50/50 into SHWFS and DLWFS separately,to compare the wavefront results.Furthermore,by computing the wavefront response function of the DM,the closed-loop of AO used the wavefront generated from DLWFS for wavefront correction.Therefore,these experiments can serve to demonstrate the practicability of DLWFS as a wavefront sensor in AO systems.Results and Discussions DLWFS is capable of retrieving wavefront data with a root mean square (RMS) residual error of less than 0.3μm at best,as shown in Fig.4.When comparing the wavefront results of DLWFS with those from SHWFS experiments,as shown in Fig.6,it becomes clear that the DLWFS generated wavefront results are smoother than referencing SHWFS,but both results have similar magnitude and shape of distribution.The RMS residual error is approximately 0.0965?0.1531μm in this comparison.The most noticeable disparities are observed near edges,with a significant reduction in disparity toward central areas.We conduct multiple AO wavefront correction experiments through controlling parameters and utilizing different 3D-printed apertures inducing circle and square shapes of beams.The correction results obtained by utilizing DLWFS as the wavefront sensor closely resemble the results obtained from SHWFS,as shown in Fig.9.The results of utilizing DLWFS in the correction of wavefront distortion induced by DM1 are shown in Fig.10.The first two rows depict the results with and without AO correction of the 50 mm diameter circular beam,while the last two rows depict the results of the 50 mm×50 mm square beam.We improve the circle beam quality from β=8.18 without AO to β=2.40 with AO,while we improve the square beam quality from β=10.83 without AO toβ=3.61 with AO.These results demonstrate the practicability of using DLWFS in AO.Based on the experimental results mentioned earlier,we find that in retrieving wavefronts,the DLWFS shows a certain degree of deviation when compared to SHWFS.The primary causes of this deviation can be attributed to the sensitivity of DLWFS in these aspects:the parametric sensitivity of focal point position when acquiring spots,SNR of the wavefront with high frequency or small stroke aberrations,nonuniform distributed nearfield intensity,and irregularly shaped beams.Hence,the performance of DLWFS can be improved by using the real data acquired by experiments conducted using an improved model.Conclusions Compact wavefront sensor is highly suitable for improving the beam quality of compact solid lasers in AO systems.In this article,we introduce DLWFS as a new method of nonlinear mapping from intensity distribution of focus and defocus spots into wavefront.The model is trained using simulated data.By using c GAN-based generator to retrieve wavefront from input focus and defocus spots,we compare wavefront results of DLWFS with those of SHWFS.The residual error falls in the range of0.0965?0.1531μm.We also apply DLWFS for AO wavefront correction and correct square and circle beams with beam qualityβ=3.61 and β=2.40 separately.Although there is a noticeable deviation in wavefront results compared with the reference wavefront,the wavefront correction results demonstrate the practicability of DLWFS.We believe that future improvements in the model structure and the utilization of experimentally acquired training data will enhance the performance of DLWFS in future studies.