SPGD算法高精度静态像差校正方法

High-Precision Static Aberration Correction Method of SPGD Algorithm

随机并行梯度下降(SPGD)算法广泛应用于光学系统静态像差校正,其性能指标对校正效果影响较大。由于传统的环围能量(EE)校正精度低、平均半径(MR)稳定性差,提出性能指标组合法,以实现静态像差的高精度、稳定校正。所提方法将EE与MR性能指标相结合进行像差校正,首先以EE作为性能指标对畸变图像进行校正,待能量集中于环围区域后,利用MR性能指标继续进行校正,直至能量分布均匀,校正终止。首先进行了校正仿真,结果显示:相比于EE和MR方法,性能指标组合法对静态像差的校正精度高、稳定性好。搭建实验光路,验证了所提方法的有效性。模拟和实验结果均表明,采用性能指标组合法可以获得高的校正精度且校正稳定。该方法可以应用于光学系统静态像差的校正和消除,实现其接近衍射极限的光学性能。

Objective Due to the influence of the processing error of optical elements,system assembly error,and ambient temperature,the optical system usually has static aberrations,which reduce the imaging quality and significantly affects the optical performance.The stochastic parallel gradient descent(SPGD)algorithm is widely used to correct static aberrations.For the SPGD algorithm,the performance metrics,usually including the Strehl ratio(SR),encircled energy(EE),and mean radius(MR),have a great influence on the correction accuracy.In practical applications,SR is seldom chosen as it is difficult to achieve.In terms of EE,the convergence speed and correction accuracy depend closely on the selected encircled area,and hence,EE can only represent the total energy distribution of the surrounding area but cannot effectively reflect the entire intensity distribution.In contrast,the performance metric MR takes the whole intensity distribution into consideration,and higher correction accuracy is thus obtained.However,it is sensitive to small disturbance voltage,which makes the correction unstable.Therefore,to achieve high-precision and stable correction of static aberrations,we propose a combination method of performance metrics,which can not only concentrate the spot energy but also make the energy distribution uniform.Methods The proposed method combines the performance metrics EE and MR to correct the static aberrations.EE is first chosen as the performance metric and is computed with the acquired image.The control voltage is calculated and applied on the deformable mirror to correct the distorted wavefront.When most of the energy is concentrated in the encircled area,the performance metric is switched from EE to MR.Afterward,the energy distribution is further unified,which can also reduce the MR of the light spot.Thus,with the combination method,the energy can be better concentrated,and the intensity distribution can be more uniform.Meanwhile,the static aberrations can be corrected with higher accuracy.Results and Discussions First,to concentrate the energy at the center of the image plane,we use EE for correction.After the energy is concentrated,it is then corrected with MR so that the energy distribution can be more uniform(Fig.3).EE,MR,and the combination method of performance metrics are simulated and compared to verify the effectiveness of the proposed method(Fig.12),and the root-mean-square values of residual aberrations are 0.22λ,0.43λ,and 0.01λ,respectively.Compared with the EE and MR methods,the combination method can achieve better spot image quality and dramatically increased peak intensity.In addition,the corresponding SRs are computed to be 0.53,0.78,and 1.00,respectively.Moreover,the simulations of the correction results based on the three methods under different noises(Fig.14),different encircled diameters(Fig.15),and multiple random static aberrations(Fig.16)are compared and analyzed.For the combination method,SR remains stable at 1.00 after correction.Finally,an experiment is performed to further validate the proposed method.As a result,the corrected resolutions are improved to be 2.15,1.40,and 1.05 times the diffraction limit for the three methods,respectively,and in particular,the diffraction limit of the optical system is almost achieved with the combination method(Fig.18).The research reveals that the proposed method can realize higher correction accuracy and stability.Conclusions The combination method of performance metrics proposed in this paper can effectively improve the correction accuracy and stability of static aberrations.Simulations show that the SR corrected by the combination method can keep stable at 1.00 under different encircled diameters,different noises,and multiple static aberrations.As further demonstrated by experiments,with the combination method,the light spot is the most focused,and the resolution is improved to be 1.05 times the diffraction limit.Both the experimental results and simulations confirm the effectiveness of the proposed method in static aberration correction.The method provides a facile and effective way for the correction and elimination of static aberrations in optical systems with optical performance close to the diffraction limit.