高数值孔径（NA）矢量全息图优化
High-NA vectorial hologram optimization
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中文总结 AI 辅助
该研究提出基于梯度的纯矢量相位框架，采用可微理查兹-沃尔夫前向模型优化高NA计算机生成全息图，实现高均匀度强度轮廓，可优化偏振相关目标，残差显著降低。
中文摘要 AI 辅助
我们提出一种基于梯度的计算机生成全息图优化的纯矢量相位框架。该方法解决了高数值孔径（NA）光学系统中的关键局限，在这类系统中，标准标量近似常出现显著的保真度下降。我们针对典型目标强度类别（光镊阵列与扩展平顶轮廓），强调了高NA下标量衍射模型（夫琅禾费与德拜模型）的局限。采用可微的理查兹-沃尔夫（Richards-Wolf）前向模型，我们数值证明了算法的稳定收敛性，以及在深非近轴区生成高度均匀的强度轮廓。在NA=0.9时，理查兹-沃尔夫（RW）优化达到平顶均匀度99.97%、光镊均匀度99.98%，光镊平均椭率为ε=1.007；而标量前向模型则表现出目标依赖的平台保真度或焦点几何退化。此外，由于RW模型返回完整矢量场，同一框架可优化依赖局域偏振的目标。我们针对偏振敏感的光偶极势目标验证了这一点，当包含矢量与张量光移项时，直接RW势优化使平均归一化残差降低一个数量级以上。
英文摘要
We present a vectorial phase-only framework for the gradient-based optimization of computer-generated holograms. Our approach addresses a critical limitation in high numerical aperture (NA) optical systems, where standard scalar approximations often experience significant fidelity degradation. We highlight the limitations of scalar diffraction models (Fraunhofer and Debye) at high NA for representative classes of target intensities, namely tweezer arrays and extended flat-top profiles. Using a differentiable Richards-Wolf forward model, we numerically demonstrate stable algorithmic convergence and the generation of highly uniform intensity profiles in the deep non-paraxial regime. At NA=0.9, Richards-Wolf (RW) optimization reaches flat-top and tweezer uniformities of 99.97 % and 99.98 %, respectively, with a mean tweezer ellipticity of $\varepsilon=$1.007, while scalar forward models show target-dependent degradation in plateau fidelity or focal geometry. Furthermore, because the RW model returns the full vectorial field, the same framework can optimize objectives that depend on local polarization. We demonstrate this for a polarization-sensitive optical-dipole-potential target, where direct RW-potential optimization reduces the mean normalized residual by more than an order of magnitude when including vector and tensor light-shift terms.
