基于梯度下降算法的初级球差校正

Correction of Primary Spherical Aberration by Gradient Descent Algorithm

摘要:

固体激光器在实际工作过程中会因腔镜热变形而产生球差效应, 使激光的光强分布发生变化、聚焦能力下降、光束质量变差, 因此需要校正。基于这一目的, 利用梯度下降算法进行了初级球差的校正仿真。首先, 建立了初级球差和变形镜模型, 变形镜模型针对初级球差选取分立式环形阵列, 镜面利用率高。然后, 设计出算法的具体实现过程, 算法以变形镜单元的位移量为控制对象, 以离散化的各部分球差的方差为性能指标。最后, 仿真并给出了性能指标与迭代次数的关系、校正后的球差等结果, 结果显示达到了预期的校正效果。

Abstract:

In practical applications, solid-state lasers may produce spherical aberration effect due to the thermal deformation of the cavity mirror. And the spherical aberration can change the distribution of light intensity, reduce the beam focusing capability and decrease the beam quality, so it needs to be corrected. In this paper, simulations of correcting spherical aberration were carried out with the gradient descent algorithm. First, the models of spherical aberration and deformable mirror were established. Aiming at the spherical aberration, the discrete circular array was chosen as the deformable mirror model because of its high-usage. Then, the specific implementation procedure of the algorithm was designed. In the algorithm, the controlled member was the displacement of each unit of the deformable mirror, and the performance index was the variance of each part of the discrete spherical aberration. Lastly, simulations were performed to obtain the results such as the relationship between the performance index under the number of iterations, and the spherical aberration after correction. It is shown that expected correction effects are reached.